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The selection of new energy vehicle power battery (NEVPB) recycling service outlet will promote the rapid development of new energy vehicle industry. In order to cope the green and low-carbon development path of NEVPB recycling under information uncertainty and interaction. This paper intends to construct a multidimensional consensus fusion framework of self-confidence Fermatean fuzzy trust network. Firstly, individuals express their opinions based on Fermatean fuzzy sets with self-confidence (FFS-SC). Subsequently, a novel trust propagation and aggregation is built to obtain complete trust relations, and weights of individuals are determined by trust network, self-confidence, and relative deviation. Meanwhile, the trust network- driven consensus feedback mechanism is developed to collect evaluation information. Furthermore, the correlation coefficient to eliminate the homogeneity influence of indicators. In addition, the decision results are derived by Multi-Attributive Border Approximation area Comparison (MABAC) method. Finally, an applied case with five NEVPB recycling service outlets selection is presented to verify the feasibility of the established framework, and the effectiveness is further demonstrated through sensitivity analysis and comparative analysis. The case results show that the indicator with demonstration of recycling service outlet and market supervision departments strengthen supervision indicators have great impact on NEVPB recycling service outlets selection. Furthermore, this paper has reference significance for standardizing the management policy and technology of power battery recycling and realizing the green and low-carbon environmental protection of the whole life cycle of new energy vehicles. [ABSTRACT FROM AUTHOR]

The concept of similarity measure is fundamental for evaluating the consistency between intuitionistic fuzzy sets (IFSs). Several researchers have developed various intuitionistic fuzzy similarity measures (IFSimMs) utilizing intuitionistic fuzzy distance measures (IFDisMs) or combinations of membership and non-membership degrees of IFSs. Nevertheless, there is still ample room for the improvement, as some of these measures do not satisfy the axiomatic properties of IFSimMs and produce unreasonable results. In this paper, we first establish a dual relationship between IFDisMs and IFSimMs based on fuzzy negations, enabling the construction of an infinite number of IFSimMs from a given IFDisM. We then propose two novel IFSimMs by directly manipulating the membership and non-membership degrees of IFSs and prove that they satisfy the axiomatic properties of strict IFSimMs (SIFSimMs). Furthermore, a comparative analysis reveals that the proposed SIFSimMs do not yield any unreasonable results in various scenarios. Finally, we apply these SIFSimMs to pattern recognition, medical diagnosis, and clustering analysis problems, demonstrating their superior performance compared to some existing measures. • Show the duality between intuitionistic fuzzy distance and similarity measures. • Identify the limitations of some existing intuitionistic fuzzy similarity measures. • The properties of strict intuitionistic fuzzy similarity measure are investigated. • Pattern recognition, medical diagnosis, and clustering analysis are discussed. • Superiority of the proposed approaches is explained. [ABSTRACT FROM AUTHOR]

The notion of linguistic interval-valued intuitionistic fuzzy set (LIVIFS) is one of the best tools in order to deal with the qualitative decision making problems. Therefore, in this paper a linguistic interval-valued intuitionistic fuzzy (LIVIF) QUALIFLEX method with a likelihood-based comparison approach is proposed. First, the notion of likelihood of fuzzy preference relation (FPRs) to compare the linguistic interval valued intuitionistic fuzzy numbers (LIVIFNs). By employing a criterion-wise preference assessment of alternatives through the comparison of likelihoods, we introduce a novel QUALIFLEX-based model. This model aims to quantify the degree of concordance in the complete preference order for effective management of decisions involving multiple criteria. We demonstrate the practicality and applicability of the proposed methods through an illustrative example, specifically focusing on the context of Supplier Selection Problems. To validate the efficacy of the proposed methodology, a comparative analysis is performed against other existing methods. [ABSTRACT FROM AUTHOR]

In addition to membership and non-membership degrees, linear Diophantine fuzzy set (LDFS) incorporates two reference parameters in fuzzy set definition to represent human judgment more comprehensively. It also provides flexibility in updating the decision setting by changing the meaning of the reference parameters when required by the decision-maker. Information measures in fuzzy sets have many application areas in the literature. Especially, distance and entropy measures are utilized in multiple attribute decision-making (MADM) field. Distance measures are needed by distance-based methods like TOPSIS and EDAS because their alternative ranking procedure is based on measuring the distances between alternatives and some artificial ideal or average solutions. Entropy measure is a very important tool being used in objective attribute weighting procedures of MADM applications. Thus, new distance and entropy measure propositions for LDFS are the first contribution of the study. Also, Additive Ratio Assessment (ARAS) method is extended into LDFS (LDF-ARAS) for the first time in the literature as a second contribution. In this extension, we selected ARAS as one of the most cited tools because it is found flexible and easily adaptable by researchers who do not have any background in MADM. The proposed entropy measure is integrated with the objective attribute weighting procedure of the novel LDF-ARAS approach. The third contribution is the newly developed decision model proposed for a real-life data storage system (DSS) selection problem. Three DSS options were evaluated with respect to thirteen attributes by five skilled and well-educated experts and LDF-ARAS was performed to rank alternatives. The entropy-based LDF-ARAS approach was validated by comparing the results of six different applications. In the first three, different entropy formulas are used and in the last three, these entropy measures are integrated with LDF-TOPSIS. All six comparisons gave similar alternative rankings. [ABSTRACT FROM AUTHOR]

Existing domain adaptation methods typically require access to raw data from both the source and target domains, increasing the risk of data leakage. In light of this, a fuzzy domain adaptation-based rotation machinery fault diagnosis method that does not require access to data is proposed in this paper. Specifically, during the source domain training phase, all source models are simultaneously trained by contributing model parameters. The developed joint training strategy significantly enhances the multi-domain performance of each private source model. Simultaneously, a model incorporating a fusion fuzzy strategy is constructed to acquire fuzzy rules for the source domain samples and anchor points corresponding to each fault mode. During the target domain adaptation phase, firstly, under the setting of frozen fuzzy rules, the source feature extractor is retrained using target data. Subsequently, an anchor point alignment strategy is introduced to transfer diagnostic knowledge between domains. Finally, a filtering strategy is devised to obtain high-confidence pseudo-labels for the target domain, coupled with a self-supervised learning strategy for the final optimization of the target model. Experimental results demonstrate significant achievements of the proposed method across twelve multi-source cross-domain fault diagnosis cases, with an average diagnostic accuracy of 98.88%. Encouragingly, the proposed method maintains outstanding performance even without accessing source data, outperforming several other methods. [ABSTRACT FROM AUTHOR]

Knowledge graph embedding has found widespread application across various fields due to its inherent structured data. However, some non-graph-based models necessitate improvement in accurately describing complex hierarchical structures and connecting intricate relational paths. Graph neural networks embedding methods provide a promising direction for exploring complex hierarchical modeling, facilitating the flow of information from nodes along relational paths. Nevertheless, the deficient interpretable characterization by the saliency estimation in entities, which contributes to the efficient performance of the model, is difficult to comprehend. This paper proposes a novel model to mitigate the described phenomenon by intensifying the original structure of knowledge graphs. Specifically, it integrates the Axiomatic Fuzzy Set entity semantic extraction framework with a heterogeneous relationship self-attention mechanism to bolster node representation. Next, this framework incorporates a convolutional neural network model to increase the interaction capabilities of entities and relations. This interpretable entity-level attention mechanism complements the structural information of the knowledge graphs, enabling more comprehensive neighbor information capture and improving the ability to identify the correct entity location. Experimental validation on two relationally complex datasets demonstrates superior performance compared to current methods, obtaining a new Hit@1 value of 45.6% on WN18RR. • Propose a hierarchical graph neural network knowledge representation framework. • Employ the Axiomatic Fuzzy Set to capture underlying semantics between entities. • The model has interpretable entity-level and heterogeneous relational attention. • Estimates of proximity values between nodes are yielded by semantic descriptions. • Produce promising performance compared to other knowledge graph embedding models. [ABSTRACT FROM AUTHOR]

Due to advancement of internet and lab based technologies, large volume of high dimensional data are generated every day. These data usually consisted of several issues such as class imbalance, noise, later uncertainty, irrelevant and/or redundant features, and redundancy in size. These issues degrade the overall performance measures of the various machine learning algorithms. An efficient method to cope with such issues for a large sized datasets is to apply efficient data reduction techniques. In the recent years, numerous data reduction techniques have been presented based on fuzzy rough set theory to tackle these obstacles. However, building such a method that can handle all the above mentioned issues simultaneously is still a challenging task. In this study, we handle all these obstacles simultaneously by introducing a novel approach to obtain the reduced dataset by combining kernelized intuitionistic fuzzy C-means with intuitionistic fuzzy rough set model. Intuitionistic fuzzy rough set handles the vagueness and uncertainty in a better way than fuzzy set aided models as it takes use of membership, non-membership as well as hesitancy to capture the uncertainty of real-valued datasets. To generate the membership and non-membership grades, kernelized intuitionistic fuzzy C- means based notion is introduced. Further, an intuitionistic fuzzy rough set model is established by addressing lower and upper approximations based on a novel similarity relation. Moreover, all the necessary conditions are justified with the relevant mathematical theorems. Next, this model is employed for dimensionality reduction based on the concept of discernibility matrix by using the idea of different classes' ratios to avoid the noise. Thereafter, positive region is defined with the help of lower approximation. The positive region information is applied to tackle problematic instances available in both minority and majority class for the imbalanced dataset after generation of artificial samples by synthetic minority oversampling technique (SMOTE). A comprehensive experimental study is added to show the effectiveness of the proposed technique. Finally, a framework is established to improve the prediction of animal toxin peptides. • Bireduct method is proposed by combining kernelized IF C-means with IFRS model. • Here, A novel IFRS model is presented using a similarity relation. • IFRS assisted feature selection using discernibility matrix concept is introduced. • An instance selection method is established to discard the problematic instances. • A framework is developed to improve the prediction of animal toxin peptides. [ABSTRACT FROM AUTHOR]

Three-way incomplete multi-attribute decision-making model (TWIMADM) for multiple decision makers is an important topic in data science, which is an effective tool for decision making. However, calculation results of neighborhood blocks are still affected by neighborhood radius. In addition, most of the existing models without considering the information from the evaluations of multiple decision makers separately is difficult to obtain a comprehensive assessment. To address these problems, this paper builds a novel multi-source TWD model based on multi-granularity ball. First, the well-established granular ball is extended to multi-granularity, by which a weighted conditional probability is generated to divide the concerned region into three parts: positive, negative and boundary region. The calculation of the multi-granularity ball is independence of the neighborhood radius parameter. Subsequently, the joint entropy is developed by using the defined multi-granularity to obtain the optimal decision. Furthermore, the relative utility function is utilized to capture the preferences of decision makers, the classification and ranking of each object are determined by calculating the threshold value and expected utility value. Evaluation information from all decision makers are combined and fused. Finally, a novel TWD model is developed to address the challenges of incomplete multi-attribute decision-making problems involving multiple decision makers. The comparative case analyses and experimental evaluations have demonstrated the stability, validity, and feasibility of our model. • We first extend the well-established granular ball to multi-granularity. • We utilize multi-granularity to compute neighborhood blocks. • We design the corresponding algorithm for multi-granularity ball generation. • Consider the multiple decision makers scenario. • We establish joint entropy to fully consider the information of each decision maker. [ABSTRACT FROM AUTHOR]

Each decision-making tool should be tested and validated in real case studies to be practical and fit to global problems. The application of multi-criteria decision-making methods (MCDM) is currently a trend to rank alternatives. In the literature, there are several multi-criteria decision-making methods according to their classification. During our experimentation on the Combined Compromise Solution (CoCoSo) method, we encountered its limits for real cases. The authors examined the applicability of the CoCoFISo method (improved version of combined compromise solution), by a real case study in a university campus and compared the obtained results to other MCDMs such as Preference Ranking Organisation Method for Enrichment Evaluations (PROMETHEE), Weighted Sum Method (WSM) and Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). Our research finding indicates that CoCoSo is an applied method that has been developed to solve complex multi variable assessment problems, while CoCoFISo can improve the shortages observed in CoCoSo and deliver stable outcomes compared to other developed tools. The findings imply that application of CoCoFISo is suggested to decision makers, experts and researchers while they are facing practical challenges and sensitive questions regarding the utilization of a reliable decision-making method. Unlike many prior studies, the current version of CoCoSo is unique, original and is presented for the first time. Its performance was approved using several strategies and examinations. [ABSTRACT FROM AUTHOR]

In the era of uncertainty and indeterminacy, probabilistic hesitant fuzzy sets (PHFS) an extension of hesitant fuzzy sets (HPS) have received much attention due to their ability to increase the reliability of information by considering the occurrence probabilities of each opinion. Considering the studies of PHFS following points can be identified, (i) preferences are aggregated without considering the inter-relationship among arguments, (ii) occurrence probabilities are not always prior known, (iii) approaches for attribute weights do not consider interactions among attributes (iv) decision-makers are not completely rational. Thus, we present a decision-making approach in which incomplete probabilities are estimated using the Shannon entropy optimization model. A projection entropy-based Shapley value method is used to attain attribute weights. Heronian operator (HM) is extended under the PHFS environment to capture the inter-relationship among arguments. Considering the psychological behavior of decision-makers, final ranking is provided combining the merits of prospect and regret theory. Finally, the proposed framework is applied to a real case study from the medical field. Comparative analysis verifies the effectiveness, and the sensitivity analysis determines the stability of the proposed approach. [ABSTRACT FROM AUTHOR]

Similarity measure is a useful tool to determine the similarity of two intuitionistic fuzzy sets (IFSs). Theoretically, there are two free variables of membership and non-membership on IFSs, and the most fuzzy set is not solely. Therefore, it is impossible to establish a similarity measure satisfying the classical axiom on it by using only the distance between any given IFSs and the assumed most fuzzy set. The motivation and innovation of this study lies in the exploration and use of the two most fuzzy sets, and the weighted average distance between IFSs and the two most fuzzy sets is used to define the similarity measure. Based on this analysis, a knowledge-based similarity measure on IFSs is proposed and some applications of this proposed measure in pattern recognition are introduced. The advantage of the introduced similarity measure is that it calculates the dissimilarity between the complementary sets well. Furthermore, it proves that the novel similarity measure satisfies axioms of the similarity measure on IFSs, and overcomes the drawbacks of the existing measures. Finally, a series of examples in pattern recognition fields are introduced to demonstrate the effectiveness of the proposed similarity measure. • This study proves that the fuzziest number in IFS is not solely. • Weighted average distances between IFSs and the two most fuzzy sets are proposed. • A novel knowledge-based similarity measure on IFSs is proposed. • The proposed novel similarity measure overcomes the drawbacks of the classical ones. [ABSTRACT FROM AUTHOR]

Feature selection facilitates uncertainty disposal and information mining, and it has received widespread research interests. Divergence-based fuzzy rough sets (Div-FRSs), a new kind of fuzzy rough sets, have been applied to feature selection and induced two efficient algorithms, FS-AFS and FS-RFS. Nevertheless, FS-AFS and FS-RFS still have advancement space, because the dependency functions only focus on lower approximation and ignore the uncertainty in upper approximation, which will certainly undermine the algorithmic evaluation effects. To this end, this paper introduces the upper approximation and fuses it with lower approximation via class-specific pattern and Spearman coefficient to construct a new information measurement for metric perfection, called Spearman-based self-information. Relying on this new measurement, a novel feature selection algorithm SPESI is established to improve FS-AFS and FS-RFS. At first, Spearman coefficient is introduced and upper approximation is defined. Second, class-driven precision and roughness are built by incorporating Spearman coefficient-based class-specific weight vectors with class-driven lower and upper approximations. Meanwhile, the granulation monotonicity of newly-defined measurements is also explored. Then, the core measurement Spearman-based self-information is firstly given and its feature significance motivates a feature selection algorithm SPESI with heuristic search. Finally, data experiments are implemented to validate the effectiveness of SPESI, and a conclusion can be drawn that SPESI outperforms FS-AFS and FS-RFS to acquire better classification performances with fewer feature numbers and less running time. • Upper approximation is first defined in Div-FRSs to induce measurement. • Class-specific information of D s enriches decision analysis. • Spearman correlation coefficient reveals the relevance between classes. • Algorithm SPESI outperforms FS-AFS and FS-RFS to offer better classification performances. [ABSTRACT FROM AUTHOR]

Due to energy's global reliance on fossil fuels and population growth, Greenhouse gas (GHG) emissions and their repercussions have attracted attention. Due to their cheaper cost and cleaner environment, renewable energy modes of transportation like electric vehicles are highly sought after. Electric vehicles are beneficial, but they also emit emissions indirectly in power plants that generate their electricity, which could affect small and medium communities. Thus, it is crucial to assess such modes of transportation's performance while considering key aspects and criteria. However, scholarly works in this field have not fully addressed the deployment of a comprehensive electric vehicle decision-making support system. This study addresses electric bus selection by introducing a novel approach to Multi Criteria Decision Making (MCDM) utilizing a developed integrated fuzzy set. We introduce an integrated approach that combines an Entropy weighting approach with a 2-tuple Linguistic T-Spherical Fuzzy Decision by Opinion Score Method (2TLTS-FDOSM). This approach is designed to tackle the challenges associated with evaluating the feasibility of electric bus models (EBMs) and addressing the theoretical challenge of MCDM in the context of the presented case study. These challenges include dealing with ambiguities and inconsistencies among decision-makers. The former method is utilized to ascertain the significance of assessment criteria, whereas the latter approach is applied to select the most favorable EBM by utilizing the weights obtained. As for the 2TLTS-FDOSM results, out of all the (n = 6) EBMs considered, A 3 (11-E) EBM obtained the highest score value, while the A 3 (9-E) EBM had the lowest score. The robustness of the results is confirmed through sensitivity analysis. [ABSTRACT FROM AUTHOR]

Game theory is a powerful tool in modeling actual decision-making problems. In many cases, it is difficult for players to give a crisp value of payoff. To conquer this issue, various extensions of fuzzy sets have been introduced to represent the payoffs. Although type-2 intuitionistic fuzzy (T2IF) set (T2IFS) can solve the game problem effectively, sometimes players prefer to give the primary (secondary) membership and non-membership degrees with some approximate ranges rather than crisp values. T2IFS cannot express such uncertain payoffs. Thus, this paper initiates a new concept called type-2 interval-valued intuitionistic fuzzy (T2IVIF) set (T2IVIFS) which has stronger ability than T2IFS and interval-valued intuitionistic fuzzy set (IVIFS) in representing uncertain information. Hamacher operations of T2IVIFSs are given. Hamming and Euclidean distances between T2IVIFSs are defined respectively. Some Hamacher aggregation operators for T2IVIFSs are developed and some desirable properties are analyzed. Afterwards, an effective method is proposed for solving T2IVIF matrix game, which can make game results more accurate and reliable. An example of new energy vehicle industry development is provided to validate the proposed T2IVIF matrix game. Comparative analyses reveal that the matrix game in T2IVIF environment has better flexibility and reliability than that in T2IF and IVIF environments. [ABSTRACT FROM AUTHOR]

Despite the significance of health and the threats natural disasters pose to public health and the well-being of the affected communities, comprehensive research that explores critical factors and indicators that measure health implications brought about by disasters is underdeveloped in the literature. The primary objective of this study is twofold: (1) to develop a list of indicators that assess health-related impacts during disasters through a literature survey, and (2) to create a "public health resilience index" that measures the resilience of affected communities with a case study in Southern Cebu, Philippines. A hybrid model based on the fuzzy stepwise weight assessment ratio analysis and the extended cumulative prospect theory was deployed to advance these objectives. The proposed model considers subjective judgment and cognitive biases while exhibiting high scalability and flexibility and accommodating diverse data input formats. Results revealed that the promptness of response, the allocated budget for humanitarian aid and services, the availability of drinking water per household, the number of personnel assigned for humanitarian aid, and the location of water distribution points are highly prioritized during natural disasters. On the other hand, among the 21 municipalities under consideration, 10 demonstrated strong performance, while the other 10 exhibited poor performance, leaving one municipality in the middle of both extremes. Sensitivity and comparative analyses show that the proposed hybrid model is not sensitive to model parameter changes. The findings of this study would aid decision-makers in developing initiatives aimed at optimizing resources and efforts, mitigating risks, and enhancing the overall health resilience of local communities in the onslaught of natural disasters. [ABSTRACT FROM AUTHOR]

In collaborative filtering recommendations, part of studies mainly focus on quantitatively learning user preferences based on explicit rating information. However, due to the uncertainty and complexity of decision-making scenarios, user preferences usually express ambiguity and diversity. Therefore, to fully capture user preferences from both qualitative and quantitative perspectives and improve the accuracy and reliability of recommendations, we propose a novel fuzzy neural collaborative filtering for recommender systems. Firstly, we qualitatively divide user preferences into fine-grained categories based on picture fuzzy set and transform the rating matrix into four preference degree matrices. Then, we employ Bernoulli matrix factorization to independently learn preference features of each submatrix to obtain picture fuzzy numbers. To enhance the adaptability of picture fuzzy set in recommender systems, we design an improved scoring function based on picture fuzzy number to effectively distinguish differences in user preference levels. In addition, we use a simple deep neural framework to quantitatively extract global preferences of users and fuse it with fine-grained preferences of users to thoroughly predict user preferences. Experiments on four benchmark datasets show that the proposed model outperforms other comparison methods in terms of recommendation accuracy. Compared with the closest competitor method, our model has the highest improvements of 5.08% and 4.04% in the metrics HR@10 and NDCG@10, respectively. • PFS is used to divide fine-grained user preferences during BeMF training. • Improved scoring function is designed to the adaptability of PFS in RSs. • A simple neural network MLP is employed to capture global user preferences. • Two preference modules are fused to thoroughly predict user preferences. • Results reveal that our model effectively improves the performance of RSs. [ABSTRACT FROM AUTHOR]

Driving risk evaluation is a critical task for traffic safety and vehicle insurance. Unfortunately, many existing methods disregard the unknown and uncertain nature of driving behavior in real-world scenarios. In this paper, we formula this task as a multi-criteria group decision-making problem and propose a dual perspective information volume method for evaluating the driving risk score based on linguistic Z-number. Our proposed method accurately captures the uncertainties and reliability of driving behavior by utilizing two fuzzy numbers A and B. The main contributions of our paper are as follows: firstly, we introduce the α -truncation set and the information volume-based utility function and credibility probability model, which form the basis of the vehicle evaluation method. Secondly, we consider cross-information to model the divergence of information between dual perspectives, based on different experts and features. We calculate the credibility value for each perspective using the Z + -based information volume. Thirdly, we present the dual perspective calculation method used to assess driving risk. This method assigns risk scores to individual vehicles based on a utility function. Finally, we conduct a case study using the historical trajectories of vehicles obtained from an insurance company. The results are compared against the damages coefficient. Furthermore, we perform dependability and parameter analysis to demonstrate the effectiveness and superiority of our approach. Our approach provides valuable insights and suggestions for the insurance industry and traffic safety departments in relevant fields. • Linguistic Z-number for driving behavior risk evaluation. • Dual perspective information volume calculation method. • Determines the credibility probability based on the information divergence value. • Utility function value based on Z-number for ranking of driving behavior risk. [ABSTRACT FROM AUTHOR]

The blockchain platforms (BPs) have emerged as important tools for improving enterprise data security. However, the selection of a suitable BP for is a challenging issue for enterprises. In this paper, a novel heterogenous multi-criteria decision-making (MCDM) model is proposed to facilitate the BP selection and evaluation process. First, the evaluation criteria for BPs are defined through an analysis of popular BPs. Second, based on the defined evaluation criteria, multiple types of fuzzy numbers are adopted to accurately represent the evaluation criteria. Then, to deal with multiple types of fuzzy numbers, a hybrid distance measure is proposed to determine the negative and positive ideal separation matrices of the evaluation criteria. In addition, using the axiomatic design's information content metric the as basis, an improved method is proposed to unify the evaluation of multiple types into a single number. An improved weight method is then proposed based on the combination of objective and subjective weighting to obtain the comprehensive weights of the criteria. Finally, a closeness degree metric is introduced to obtain the ranking order of all BP alternatives. An example case is analyzed to illustrate how to evaluate and select a suitable BP. The superiority of the proposed heterogeneous model is verified by comparisons with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Telescopic forklifts stand apart from other forklift types, boasting numerous benefits. They offer notable advantages, such as enhanced manoeuvrability, accessibility to elevated areas, versatility, and the capacity to operate at high speeds. Choosing appropriate telescopic forklifts can substantially enhance operational efficiency and efficacy within the industry. Concurrently, it can bolster business competitiveness by expediting logistical processes, yielding notable cost reductions. Nonetheless, the intricacy and specificity inherent in these machines complicate the decision-making process for stakeholders. Furthermore, conflicting criteria, the continuous evolution of manufacturers' models, and the industry's intricate nature compound the selection challenges. Hence, there is a pressing need for a resilient, dependable, and practical decision-making framework capable of adeptly navigating uncertainties to yield reliable and coherent outcomes. This study aimed to develop an integrated decision-making model based on interval-valued Fermatean fuzzy (IVFF) sets to respond to these requirements and address this critical decision-making problem in the relevant industry, which is also significantly affected by complex uncertainties. This work, therefore, introduces an integrated methodology for decision-making, IVFF–PIPRECIA and IVFF–WISP techniques. IVFF–PIPRECIA determines criteria importance weights, whereas IVFF–WISP identifies optimal alternatives. A case study in the textile industry validates the framework's practicality. Purchase price emerges as the primary criterion, exceeding 500 thousand euros for telescopic forklifts, followed closely by load-carrying capacity. The second alternative proves to be the best option. Comparative and sensitivity analyses confirm the model's credibility. The approach effectively handles decision-making uncertainties, yielding competitive outcomes. It can be applied to diverse engineering problems. Insights from this study assist users in selecting optimal equipment and may inform forklift manufacturers in improving machinery. Future research could focus on establishing real-time operational data collection frameworks for these vehicles. [ABSTRACT FROM AUTHOR]

In multi-attribute group decision-making (MAGDM), the social relationships among group members, professional backgrounds and psychological behaviors of decision makers are important factors for achieving high-quality group decisions. However, realizing the consideration of these factors in fuzzy and complex group decision-making scenarios is an important and urgent issue. In MAGDM problems, interval-valued hesitant fuzzy sets (IVHFSs) can better show the hesitant and fuzzy uncertainty information because they are an extension of fuzzy sets. This paper focuses on the score function of IVHFSs and develops a generalized TODIM evaluation method utilizing the novel score functions of IVHFEs and trust networks. The developed method effectively realizes the application of these factors in fuzzy and complex group decision making scenarios. In this contribution, a new deviation function for IVHFSs is created in this paper. It takes into account two types of deviation that are common in IVHFSs: the ambiguity of interval width and the hesitation and uncertainty of multiple intervals. In the sequel, a novel score function for IVHFSs is developed with help of the novel deviation function and the traditional score function. Concerning the perspective of group consistency, a model for determining expert weights is constructed using quality parameters, which combine the novel score function with the trust network. A subjective and objective comprehensive weighting model is made to get attribute weights based on how certain decision information is and the experts' subjective experience. This is done because the more uncertain something is, the higher the risk. Eventually, we develop a generalized TODIM technique for MAGDM based on the novel score function and trust network in IVHFS environment. The developed approach is demonstrated with a preventive engineering decision-making problem. Sensitivity and comparative analyses are implemented to demonstrate the superiority, stability, and validity of the proposed method in this paper. According to the findings of this study, we conclude that the proposed methodology offers a comprehensive and systematic approach to evaluate MAGDM in the context of IVHFS with trust networks. [ABSTRACT FROM AUTHOR]

Decision-making is an indispensable tool in many real-life situations. The classical set theory is insufficient to solve problems involving uncertainty and qualitative data. In order to tackle scenarios with qualitative information and imprecise boundaries, fuzzy set theory generalizes crisp sets. Thus, ranking is an essential methodology in decision-making in a fuzzy environment. In literature, generalized trapezoidal fuzzy numbers (GTrFNs) are used to model many real-life situations with imprecise, uncertain, and incomplete information. There are various techniques available to discriminate arbitrary GTrFNs. Several researchers are seeking a standard consensus technique to distinguish between arbitrary GTrFNs. The diagonal distance right position, diagonal distance left chord, diagonal distance center position, diagonal distance, and diagonal distance right chord scores are the five score functions that are used in this work to develop a complete ranking (total ordering) principle on the class of GTrFNs to distinguish arbitrary GTrFNs. To show the potentiality of the proposed method, we compare the proposed approach with the few existing approaches suggesting to rank GTrFNs. Further, we proposed a new GTrF-CoCoSo approach by incorporating the proposed complete ordering principle. Then the efficacy of the proposed ranking principle is examined in solving multi-criteria decision-making (MCDM) using the GTrF-CoCoSo approach to select the best banana supplier for food production company. Furthermore, a sensitivity analysis is presented to evaluate the performance of the suggested ranking principle with the GTrF-CoCoSo approach. [Display omitted] • We introduce a few score functions on the set of GTrFNs. • We develop a complete ranking principle on GTrFNs, using proposed scores. • We compare the proposed ranking principle with the familiar ranking methods. • We propose a GTrF-CoCoSo approach to solve an MCDM problem. • Sensitivity analysis is performed on this GTrF-CoCoSo approach. [ABSTRACT FROM AUTHOR]

• A model to determine the probability information of PIVHFS is proposed. • A model to realize the conversion from PIVHFS to cloud model is developed. • Cloud model is introduced to optimize the calculation of PIVHFSs. • Approaches to derive the stage weights and attribute weights are presented. • Regret theory is applied to a multi-stage multi-attribute decision-making problem. Due to the complexity of multi-stage multi-attribute decision-making (M A D M) problems, decision-makers (D M s) frequently provide incomplete and hesitant evaluation information. A crucial difficulty in multi-stage MADM problems is how to make a valid decision under uncertain environment. Firstly, we employ probabilistic interval-valued hesitant fuzzy set (P I V H F S) to characterize the hesitancy of DMs , and then build an optimization model to obtain the probability information based on the score function, deviation function of probabilistic interval-valued hesitant fuzzy element (P I V H F E) and information entropy. Secondly, cloud model is introduced to optimize the calculation process and an optimization model is developed to realize the transformation from PIVHFS to cloud model. Thirdly, a method to solve the stage weights is proposed by synthesizing the within-stage and between-stage decision information. Similarly, the attribute weights are obtained by constructing a mathematical model based on the within-attribute and between-attribute decision information. The noted method can utilize decision information to its fullest. Then, the regret theory is applied to a multi-stage MADM problem. Finally, the applicability and effectiveness of the method are illustrated through case analysis and methods comparison. [ABSTRACT FROM AUTHOR]

Recently, the transformer has exhibited remarkable performance across various applications, primarily owing to its exceptional capability in capturing global information through the attention mechanism. Nevertheless, the dot-product within attention results in inaccurate and confusing guidance in the presence of uncertain features, subsequently affecting robustness. Hence, introducing an approximate guided method to handle uncertain features is essential for achieving enhanced objectivity. In this study, we employed fuzzy preference relations to construct a matroids structure, introducing it into rough sets to form the fuzzy preference matroids rough sets. Detailed mathematical properties and axiomatic proofs are presented. The closed sets within the matroids form a subspace of the lower approximation proving that the proposed satisfy the approximation ability of rough sets. Further, an approximate guided representation method with a lower approximation of the matroids has been developed. It is integrated into a plug-and-play transformer block that can be flexibly deployed across various tasks. Experimental validation has demonstrated the outstanding performance of this method across 3D point cloud classification, named entity recognition, multimodal emotion recognition, and image classification. Specifically, on the Weibo NER and the IEMOCAP datasets, attain state-of-the-art (SOTA) F1-scores. The resource code is validated at https://github.com/WinnieSunning/FPMRST. • The concept of fuzzy preference matroids rough set is introduced. • A novel approximate guided representation method is developed. • Constructed a plug-and-play transformer block based on the proposed method. • The effectiveness and generality of the method have been validated. [ABSTRACT FROM AUTHOR]

The (p,q,r)-Spherical fuzzy set is a useful generalization of other fuzzy structures such as fuzzy, intuitionistic fuzzy, Pythagorean fuzzy, picture fuzzy, q-rung orthopair fuzzy, spherical fuzzy, and T-spherical fuzzy sets. In this paper, we define concept of interval-valued (p,q,r)-spherical fuzzy set (IVpqr-SFS) and Set-theoretical and arithmetic operations of them. Two aggregation operators named interval-valued (p,q,r)-spherical fuzzy weighted arithmetic (IVpqr-SFWAA) and interval-valued (p,q,r)-spherical fuzzy weighted geometric (IVpqr-SFWGA) aggregation operators are introduced for IVpqr-SF numbers (IVpqr-SFN) and their properties were examined. The proposed operators are explained with examples. Furthermore, the score and accuracy functions of an IVpqr-SFN are introduced. We also define distance measures between two same types IVpqr-SFSs based on Hamming, Euclidean, and Hausdorff distance measures. Moreover, a multi-criteria group decision-making (MCGDM) method is developed based on the TOPSIS method by using the proposed distance measures and score function, and a numerical example is given to show the process of the proposed MCGDM method. In addition, a multi-criteria decision-making (MCDM) method is developed using the proposed IVpqr-SFWAA, IVpqr-SFWGA operators, and an illustrative example is given to show the process of the proposed MCDM method. Finally, a comparative analysis is presented between the proposed methods and the existing methods. • The concept of IVpqr-SF sets is defined. • Distance measures between two IVpqr-SF sets are defined. • Some arithmetic and geometric aggregation operators for IVpqr-SF numbers are defined. • The TOPSIS method is developed under IVpqr-SF environment. • A MCDM method is developed and applied to an illustrative example. [ABSTRACT FROM AUTHOR]

Firms are adopting low-carbon strategies to stay competitive and manage operations sustainably. We studied how to reduce carbon emissions and design tailored solutions for different firms using the TOE framework. Our research used a three-pronged approach, including a supply chain model, panel regression analysis, and fuzzy sets of qualitative comparative analysis (fsQCA). We discovered that 80% is a significant threshold for determining the number of TOE factors. Our study also confirms the Matthew effect in carbon reduction. These results provide valuable insights and practical recommendations for managers to reduce emissions and promote sustainable development. • Firms adopt low-carbon strategies for competitiveness. • TOE framework tailors emission reduction plans. • Research combines supply chain, regression, fsQCA. • 80% threshold crucial in TOE factor determination. • Study confirms Matthew effect in carbon reduction. [ABSTRACT FROM AUTHOR]

Decision-making problem is a fundamental activity in human life every day. Regarding group decision-making, individuals have insufficient comprehension of the decision objects owing to the limited experience and knowledge and drawback the evaluation process. Therefore, the evaluation information is missing and the group cannot get the precise information for decision objects resulting in the generation of incomplete information systems. It is meaningful for individuals finding an approach to Leverage and tap into existing information. On the basis, the work presented in this paper focuses on group decision-making problems (GDM) with incomplete information. Under the framework of group decision-making, a GDM approach with an incomplete information system is presented combining the formal concept analysis and rough set theory. Firstly, we propose a concept called formal decision context and discuss the properties of the formal decision context, which could divide the incomplete information system into many cognitive units, and the definitions of cognitive units will be given. Then, the property and the relations of various cognitive units will be discussed. Additionally, the upper and lower approximation space under the formal decision context is founded considering the risk attitudes integrating fuzzy rough set and formal concept context. Considering the order relation of various cognitive units and decision objects, we introduce the dominance relation and the importance degree of each cognitive unit under the framework of formal decision context. Furthermore, a theoretical framework of the multi-criteria decision-making problem is presented and two models for the multi-criteria group decision-making problem are discussed combined with fuzzy rough set and formal decision context from two perspectives, including qualitative analysis and quantitative analysis. Finally, an illustrated example is applied to verify the validity and effectiveness of the proposed models. The contributions of this paper include two aspects. On the one hand, this paper provides a new perspective and paradigm considering MCGDM problems with the incomplete information system from the perspective of group consensus. On the other hand, this paper gives two approaches for group decision-making problems from sorting and set theory by the perspective of multi-granular rough set and group consensus. • A model of formal decision context with incomplete information to describe the cognitive situation. • An approach to MCDM problem combined rough set with formal decision context with incomplete information. • Two approaches to MCGDM problem from qualitative analysis and quantitative analysis. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a finite collection of fuzzy sets that are used to represent a given linguistic variable in real-world problems. These fuzzy sets are usually represented as fuzzy singletons, fuzzy numbers, or fuzzy G-numbers. In many cases, there are significant interactions between elements of a given set, so it is useful to evaluate and rank elements while taking the degree of interactions into consideration. To find the degree of interaction, we develop a fuzzy equivalence relation based on a similarity function and a triangular norm operator. The compositions of the (max -(T -norm)) and (min -(S -norm)) cause the membership function to change from the minimum values (certainty version) to the maximum values (possibility version). These concepts are also useful for improving fuzzy data mining, rough fuzzy set theory, etc. Furthermore, two indices, α and β , are introduced to determine the degree of certainty (α -certainty) and degree of possibility (β -possibility). Examples are provided to compare the proposed method with the existing method. After comparing the experimental results, it can be concluded that the proposed approach is satisfactory for many situations. Finally, we apply the proposed methodology to evaluate the results of a hospital efficiency study conducted for the Office of Inspector General(OIG)-Eastern Virginia Department of Health and Human Services. • The degree of interaction of fuzzy sets are found by fuzzy equivalence relations. • Two indices α and β determine the degree of certainty and possibility. • Certainty and possibility versions are used to analyze fuzzy information systems. • The proposed method is used to evaluate and rank 38 hospitals selected by the OIG. [ABSTRACT FROM AUTHOR]

Axiomatic fuzzy sets (AFS) theory has seen extensive application in classification tasks in recent years. Yet, efficiently generating precise fuzzy descriptions for each target class from a multitude of complex concepts is challenging. This study aims to bridge this gap by transforming the challenge into a combinatorial optimization problem. We adopt an advanced model-based evolutionary optimization method, Randomized Coordinate Shrinking Classification (RACOS), to create an interpretable classifier within the AFS framework. By refining the definition of the complex concept set in AFS theory, we define a feasible search space for the optimization method. Innovative fitness functions have been developed focusing on semantic discrimination and prediction accuracy. Concurrently, we establish an encoding–decoding mechanism to link the solution vector with the complex concept for each fitness function. Ultimately, the complex concepts, guided by various fitness functions, are integrated into the class's fuzzy description using AFS logical operations. Our method demonstrates competitive classification performance and superior interpretability compared to other evolutionary fuzzy rule-based classifiers. • Develop encoding–decoding mechanism to bridge complex concept and solution vector. • Design various fitness function to balance prediction accuracy and interpretability. • Covert training AFS-based classifier to solving combinatorial optimization problem. • Generate semantic description for prediction result in form of natural language. [ABSTRACT FROM AUTHOR]

This paper discusses the use of portfolio approaches based on bandit algorithms to optimize multicriteria decision-making in recommender systems (accuracy and diversity). While previous research has primarily focused on single-item recommendations, this study extends the research to consider the recommendation of several items per iteration. Two methods, Multiple-play Gorthaur and Budgeted-Gorthaur, are proposed to solve the algorithm selection problem and their performances on real-world datasets are compared. Both methods provide a generalization of the Gorthaur method, which enables it to operate with any Multi-Armed Bandit (MAB) and Contextual Multi-Armed Bandit (CMAB) algorithm as meta-algorithm in a multi-item recommendation scenario. For Multiple-play Gorthaur, an empirical evaluation shows that the use of Thompson Sampling for algorithm selection (Gorthaur-TS) yields better results than the original EXP3 method (Gorthaur-EXP3) and the exclusive use of the optimal algorithm in the portfolio in contextual recommendation problems. Additionally, the paper includes a theoretical regret analysis based on the TS sketch proof applied for this variant of the method. Concerning Budgeted-Gorthaur, experiments show that it allows more flexibility to achieve a suitable trade-off between criteria and a broader coverage of the Pareto set of solutions, overcoming a natural limit of "a-priori" methods. Finally, this paper provides a detailed review, including pseudocodes and theoretical bounds, for all the fundamental MAB and CMAB algorithms used in this study. • Bandit literature lacks formal algorithm review, hindering clarity and comparability. • There is no silver bullet: no algorithm can be the best performer in every instance. • Recommender systems need to balance accuracy, diversity, multi-item recommendations. • Optimal algorithm balances criteria, matching decision maker's preferred trade-off. • Dynamic selection ensures safe performance when optimal algorithm is unknown. [ABSTRACT FROM AUTHOR]

• Selection of an appropriate supplier pertaining to the hydrogen fuel cell industry. • A novel TODIM decision-making framework has been proposed. • Linear Diophantine linguistic uncertain fuzzy sets: information modeling. • Linear Diophantine uncertain power Einstein weighted averaging operator: aggregation. • 7 main criteria, 37 sub-criteria have been utilized for appraising the suppliers. • A comprehensive evaluation of the proposed approach. The burgeoning automotive sector is an energy-intensive industrial sector, amounting to 94 M tons of oil equivalents (MTOE). Owing to more significant environmental concerns, there is a dire need to transition the energy-intensive mobility space to sustainable mobility. In this direction, hydrogen is being researched as a potential alternative clean fuel for the automotive sector; however, in the context of developing countries, hydrogen fuel cell technology is at a very nascent stage. Various policies and research projects are underway to realize the shift, but they must be underpinned through a robust supply chain network. The selection of an optimal supplier is key to the development of a robust hydrogen supply chain network. To this end, this work proposes the selection of an appropriate supplier for supplying critical components for different research and development projects of hydrogen fuel cells. This is still a lacuna in the context of developing nations. To aid in addressing this issue, a novel TODIM (TOmada de Decisao Interativa Multicriterio) decision-making framework has been proposed to select the optimal supplier to supply critical hydrogen fuel cell components. Within the proposed approach, the linguistic evaluations provided by experts are modeled using a more generalized linear Diophantine linguistic uncertain fuzzy set that circumvents the algorithmic restrictions on the falsity and truth grades. The linguistic assessments from the experts were aggregated using the linear Diophantine uncertain linguistic power Einstein weighted averaging (LDULPEWA) operator. The power Einstein operations take care of the interaction between falsity and truth grades, which is important for the accuracy of the results. Finally, the TODIM approach was used to deduce the final ranking results. The proposed method considers the specialists' willingness to take risks during the decision-making process. Such a decision-making framework is still a lacuna in the domain of decision science. The supposed results were tested for their stability through sensitivity analysis. A past case study was solved using the proposed approach to validate the rankings. A comparison of the suggested strategy with the existing prominent decision-making frameworks was also carried out to clearly highlight the strengths and weaknesses of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper proposes a new information set of multiple interacting fuzzy linguistic set(MIFLS) to describe the interaction of uncertain linguistic information. The property of the MIFLS and its characteristic of processing consensus information are also discussed, the introduction of MIFLS provides a new perspective to improve the consistency of decision makers' evaluation information, and the application of MIFLS can improve the accuracy of decision making. Furthermore, we propose an optimization consistency information model based on the MIFLS and TOPSIS method, an example of emergency decision plan is used to illustrate the applicability and efficiency of the proposed model. The optimal consistency adjustment is not only the highly consistent evaluation information, but also the minimal difference between the original information and the adjusted information. The proposed MIFLS is fit for dealing with the interaction of decision information, which means MIFLS is one of the effective tools to processing the interaction of uncertain fuzzy set and dealing with the emergency decision making problem. More important, the MIFLS not only provides a way to quantify the correlation of multi-attribute information, but also provides a method how to improve the consistency of decision-maker information. [ABSTRACT FROM AUTHOR]

Three-way decision (TWD) and prospect theory (PT) are efficacious theories for investigating uncertain problems. TWD can mitigate the risks associated with rapid decision-making in traditional decision-making. PT can describe the psychological behavior of decision-makers. Furthermore, q-rung orthopair fuzzy sets (q-ROFSs) exhibit wider-ranging applications since they generalize intuitive fuzzy sets and Pythagorean fuzzy sets and unify them under one framework. However, the acquisition of q-ROFSs is an important issue in practical problems. In light of these considerations, this paper develops two TWD models under q-rung orthopair fuzzy environments, employing the principles of PT. To begin, we introduce two novel fuzzy β -covering rough sets that meet the inclusion property. Subsequently, utilizing the proposed fuzzy rough set, we provide an objective methodology to acquire q-ROFSs. Following this, the relative utility function is given through a combination of the value function and EDAS method. Additionally, the weighting function is constructed using two distinct approaches: one that continues to incorporate the ideas of EDAS method, and the other that utilizes the probabilistic dominance α -neighborhood classes to calculate conditional probabilities. After that, classification rules and sorting rules are derived. Ultimately, we substantiate the validity and excellence of the proposed TWD models through comparative and experimental analysis. • Two fuzzy β -covering rough sets satisfying the inclusion property are introduced. • A natural method to acquire q-rung orthopair fuzzy sets is presented. • An objective method to compute the state set is proposed. • Combining EDAS method and prospect theory, two three-way decision models are given. • Two models effectively solve uncertainty under q-rung orthopair fuzzy environments. [ABSTRACT FROM AUTHOR]

• A CODAS-based group decision model is designed for the T-spherical fuzzy context. • A T-spherical fuzzy Minkowski distance operator based on Heronian mean is proposed. • A novel ordered weighted Heronian Minkowski distance (TSFOWHMD) operator is advanced. • The TSFOWHMD operator is utilized to improve the CODAS method. • The applicability of the developed methodology is verified through a case study. T-spherical fuzzy sets (TSFSs) are more flexible and efficient tools to deal with ambiguous, uncertain and vague information in complex real-world decision-making problems than various extended intuitionistic fuzzy sets. This paper aims to develop a novel T-spherical fuzzy (TSF) Combinative Distance-Based ASsessment (CODAS) based on the Heronian Minkowski distance aggregation operator, this new method can capture interrelationship between input arguments. Some TSF weighted Heronian Minkowski distance (TSFWHMD) aggregation operators with generalization are developed based on Heronian mean and Minkowski-type distance, their properties are discussed as well as their families are analyzed. Furthermore, the TSF MAGDM methodology based on the improved CODAS is designed, where the Minkowski-type distance is used to define the TSF similarity for computing the expert weights and to construct the maximizing deviation method (MDM) for determining the attribute weights, respectively. The TSF ordered weighted Heronian Hamming distance (TSFOWHHD) and TSF ordered weighted Heronian Euclidean distance (TSFOWHED) operators derived from the TSFOWHMD operator are integrated into the CODAS method, which is an improved method for both measuring the deviation of the negative ideal solution from each alternative and capturing the correlation between attributes. Finally, the feasibility and practicality of developed methodology are illustrated with an example of CAE (Computer Aided Engineering) software selection for lithium-ion power battery (LiPB) design, sensitivity analysis and method comparisons are performed to elucidate the reliability and validity of the developed methodology. [ABSTRACT FROM AUTHOR]

• MCDM methods: AHP and TOPSIS. • AHP the decision-maker. • TOPSIS is stock to an ideal solution. Building an ideal stock portfolio is a difficult and important undertaking in the world of financial decision-making. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) technique and the Randomised Weighted Fuzzy Analytic Hierarchy Process (AHP) are combined in this research to create a powerful model for selecting the best stocks for a portfolio. To improve the portfolio's robustness under various market scenarios, our model also incorporates sensitivity analysis. Given the inherent uncertainty in financial markets, the suggested approach starts by using modified fuzzy AHP based on introducing the randomized weights and the novel normalization to get expert views and assign suitable weights to the underlying selection criteria. Based on the established criteria and associated fuzzy scores, the TOPSIS approach is then used to rank and choose the best stocks. Our model also includes sensitivity analysis to evaluate the performance of the portfolio under various market conditions. Extensive empirical tests are performed utilizing historical stock market data to assess the effectiveness of our strategy. The outcomes show the suggested model's superiority in building stock portfolios that beat conventional approaches in terms of risk-adjusted returns. [ABSTRACT FROM AUTHOR]

In fuzzy rough sets, fuzzy neighborhood operators and fuzzy rough approximate operators are mainly used by traditional methods to deal with the problem of attribute reduction (i.e., feature selection). However, they are parametric linear, while the corresponding weights are additive measures. For complex data, parametric linear operators and additive measures do not reflect correlations among data (or attributes). Therefore, it is important to develop non-additive measures and nonlinear operators for attribute reduction, which can effectively find those attributes that are not needed to reach a decision from the viewpoint of correlations. Along these lines, in this work, OI-fuzzy β -neighborhood measures (i.e., non-additive measures) and generalized Choquet integrals (i.e., nonlinear integrals) are presented by using overlap functions to deal with the problem of attribute reduction under the fuzzy β -covering approximation space. First, four pairs of OI-fuzzy β -neighborhood operators are constructed based on the implementation of overlap functions and their residual implications in a fuzzy β -covering approximation space. Furthermore, four pairs of OI-fuzzy β -neighborhood measures, as non-additive measures, are introduced to instead of rough approximate operators in data mining. Then, a novel method with respect to OI-fuzzy β -neighborhood measures is presented to deal with the attribute reduction in a fuzzy β -covering information decision table. Third, four pairs of generalized Choquet integrals based on the employment of OI-fuzzy β -neighborhood measures are constructed. On top of that, another method with respect to these generalized Choquet integrals is proposed to deal with the attribute reduction in a fuzzy β -covering information decision table. Finally, the presented methods are used to deal with the problem of classification. Several public data sets are applied to illustrate the feasibility and effectiveness of the above-mentioned proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes a rectified complex spherical fuzzy set (rCTSFS) model that enables the phase term of a complex number to function truthfully to its inherent meaning of representing directions, phases, or color hues. In addition, this paper proposes the score and accuracy functions for rectified complex spherical fuzzy numbers (rCTSFn), which allows the three types of membership degrees of an rCTSFn to fulfill human judgment/intuition. The proposed rCTSFS model proves to be a productive extension of the complex spherical fuzzy set (CSFS), complex fuzzy set (CFS), and spherical fuzzy set (SFS) models. On the other hand, Dombi t -norms prove more flexible and comprehensive than some of the other families of triangular norms, such as the algebraic t -norms and the Einstein t -norms, due to the presence of a parameter γ. The parameter γ determines the amount of aggressiveness at estimating the maximum and the minimum of a population based on a sample obtained. Therefore, this paper proposes two Dombi-Choquet integral operators, namely, the rectified complex t -spherical fuzzy arithmetic Dombi-Choquet integral (r C T S F A γ , w λ ) operator and the rectified complex t -spherical fuzzy geometric Dombi-Choquet integral (r C T S F G γ , w λ ) operator. A multi-criteria decision making (abbr. MCDM) algorithm utilizing the two Dombi-Choquet integral operators is innovated. The proposed Dombi-Choquet MCDM algorithm for the rCTSFS model is applied to an MCDM problem related to diabetic retinopathy detection on five real-life fundus images of different severity levels taken from the Messidor2 dataset. Our newly proposed algorithm proves to be the only algorithm that yields the correct diagnostic results that match the hard truth. On the other hand, none of the 50 algorithms observed among recent works in literature can produce the correct diagnostic results, even after lending the fuzzification procedure innovated in this work to them. [ABSTRACT FROM AUTHOR]

• A multi-attribute group decision method based on the interval-valued intuitionistic fuzzy set is proposed. • A sustainability evaluation of an agricultural water-land-energy-carbon nexus is provided. • Multidimensional indicators are combined through stability, coordinativity and connectivity. • The water, land, energy and carbon subsystems of the agricultural system are quantified based on dual uncertainty. • The model is shown to solve real-world relationship management problems. The interactions between agricultural subsystems, resource scarcity and ecological degradation increase the need for agricultural sustainability assessments in relation to water, land, energy and carbon emissions. In addition, uncertainties caused by natural factors and human activities complicate sustainability assessments. Therefore, this study proposes a regional agricultural sustainability assessment method based on the water-land-energy-carbon (WLEC) nexus system under high uncertainty. This method couples the interval-valued intuitionistic fuzzy set (IVIFS) and multi-attribute group decision making (MAGDM) methods to quantitatively characterise and assess element management and corresponding relationships within the agricultural WLEC nexus system in a multidimensional manner. The paper is able to (1) clarify the role of the coupled agricultural "water-land-energy-carbon" nexus and (2) address the double ambiguity and uncertainty in the indicators and more objectively reflect the interval fluctuations of natural resources and social activities in both positive and negative scenarios. (3) Sustainability management of agricultural resources is carried out according to different regional conditions. The method was applied to Heilongjiang Province in northeast China, and the coupling of agricultural WLEC nexus system in 13 administrative regions of the study area was quantitatively analysed. The degree of agroecological sustainability from a multidimensional perspective is higher in Daxinganling and lower in the provincial capital, Harbin. The recommended range of groundwater use in the study area is [16%,28%] to ensure ecological sustainability when total agricultural output fluctuates between 285,395.18 and 404,495.33 billion yuan. This methodology helps policy makers understand the overall dynamics of agricultural sustainability in an environment of multiple uncertainties and gives suggestions for better assessing management. [ABSTRACT FROM AUTHOR]

Given that the majority of existing approaches for multi-criteria group decision making (MCGDM) rely solely on the preferences of decision makers (DMs) and fail to consider the various relationships between alternatives, this paper attempts to model the relevant relational structures using graphs and introduce the concept of graph neural networks (GNNs) in the context of group decision-making. By leveraging the powerful expressive capabilities of GNNs, the aim is to mine additional information pertinent to the decision-making process and screen out alternatives for the final decision. To begin, we provide a mapping of MCGDM to the graph domain and construct a corresponding relation graph among alternatives. Additionally, to deal with uncertain or vague information, we transform the group decision-making problem into a Pythagorean fuzzy environment and define a novel measure of entropy specifically designed for Pythagorean fuzzy sets (PFSs) in the entropy weight model to determine the weights of criteria. Simultaneously, we propose a new distance measure for PFSs, which is then applied to the extended Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method to rank alternatives. Furthermore, we develop a GNNs-based Pythagorean fuzzy MCGDM approach that incorporates the aforementioned techniques for group decision-making. Finally, to validate the effectiveness and superiority of this approach, we employ it to address a supplier selection issue. Compared with baseline group decision-making approaches, our approach can indeed capture the relationships among alternatives in complex group decision-making scenarios and outperforms the best-performing baseline by nearly 2.8% in terms of ranking accuracy. • A mapping from multi-criteria group decision making to the graph domain is provided. • A normalized entropy measure is defined in Pythagorean fuzzy sets. • A modified Pythagorean fuzzy distance measure is proposed. • A Pythagorean fuzzy group decision-making approach based on graph neural networks is developed. [ABSTRACT FROM AUTHOR]

The demand for renewable energy sources is growing rapidly as a result of increasing energy consumption, fossil fuel depletion, climate change, and environmental degradation. The tide is one of the main sources of renewable energy in the ocean because of its huge potential to be harnessed. Wave-energy converters (WECs) are a potential alternative to present energy sources, with an emphasis on improving efficiency and increasing energy. With the goal of improving the uncertainty inherent in data representation, the literature gradually uses various fuzzy extensions that handle fuzzy information in subjective evaluations and decision-making processes. single-valued neutrosophic probabilistic hesitant fuzzy sets (SVNPHFS), a recent extension of neutrosophic fuzzy sets, address limitations associated with membership functions and the representation of hesitancy in multi-criteria decision-making (MCDM) approaches. In the decision-making process, uncertainty is successfully handled by SVNPHFS. The objective of this study is to investigate and select a potential converter for a WEC power plant using SVNPHFS. Seven criteria for WECs are selected as potential sites for establishing a wave-energy power plant. The paper proposes a novel hybrid MCDM methodology. Fuzzy SWARA (Stepwise Weighted Assessment Ratio Analysis) is utilized for assigning weights to the criteria for WEC selection, and fuzzy ELECTRE (Elimination and Choice Expressing Reality) is used to determine the most suitable alternative using these criteria weights. The proposed technique identifies the point absorber in the first rank for the best wave-to-energy converter power plant as it generates a high amount of electricity compared to other alternatives. The result shows that the proposed model is more robust compared to other approaches. [ABSTRACT FROM AUTHOR]

Interval-valued Fermatean fuzzy sets (IVFFSs) as an extension of Fermatean fuzzy sets (FFSs) are a new powerful mathematical tool that apply interval value to describe uncertainty. Compared to interval-valued intuitionistic fuzzy sets (IVIFSs) and interval-valued Pythagorean fuzzy sets (IVPFSs), IVFFSs can handle more uncertain information. This paper presents a novel fuzzy three-way multi-attribute decision-making approach with the probabilistic dominance relation, based on the model of IVFSSs. The proposed method firstly uses the probabilistic dominance relation to calculate the conditional probability of each alternative. Subsequently, it builds loss functions from the perspective of the ideal solution. Our suggested method is able to rank and classify the alternatives into the positive region, the boundary region, and the negative region while the existing MADM approaches under IVFSSs only sort them without classification. Additionally, the suggested solution involves a much lower error rate than the existing methods. And our method's conditional probability may be determined objectively and takes the relation between attributes and interactions among alternatives into account, which reduce the risk associated with subjectivity in the decision-making process of existing approaches. The effectiveness and suitability of the suggested approach are illustrated by two real-world applications such as the photovoltaic poverty alleviation project selection and the hotel location evaluation and experimental findings. [ABSTRACT FROM AUTHOR]

Intelligent computing is an independent algorithm system that imitates the laws and principles of nature's biological chain to design and solve practical problems in modern society, it can help people better handle some big data problems through artificial intelligence technology and different cognitive characteristics. Especially, when dealing with group decision problems, it is often considered as human behavior based on cognitive computing. The q-rung orthopair fuzzy set (q-ROFS) is not only a generalization of Pythagorean fuzzy set (PFS), but also can deal with the decision problem of multi-source information in a wider area. In this paper, we first give the detailed explanations of the relationship between the q-ROFS and q-rung orthopair fuzzy number (q-ROFN)by an example, and itis pointed out that there are some defects in the existing two ranking methods for the Pythagorean fuzzy numbers (PFNs) and intuitionistic fuzzy numbers (IFNs) through counterexamples, and then all q-ROFNs are mapped into the unit triangle of the first quadrant through q-compression mapping, and the concept of distance factor for q-ROFNs is proposed by Euclidean distance between each q-ROFN and the maximum element (1,0).Secondly, a novel inverse score function for q-ROFNs are put forward by the distance factor and hesitancy degree, and the monotonicity of the inverse score function are discussed. Finally, a new ranking criterion of q-ROFNs is given by the new score formula, and then the rationality of the ranking criterion is proved, and through the method of solving the conditional extreme value of multivariate function (Lagrange multiplier method), there is indeed an extreme value point (corresponding to the maximum q-ROFN) on υ = μ. Besides, a q-rung orthopair fuzzy decision-making method for multi-source information is given by the new ranking criterion and aggregation operations, and the comparison of examples shows that the inverse score function and decision-making method do have many advantages in the q-ROFN environment. [ABSTRACT FROM AUTHOR]

This paper abstracts the complex heterogeneous multi-attribute group decision-making (CHMAGDM) characterized by two-layer decision-makers (DMs), individual attribute sets, complex relationships among attributes and heterogeneous evaluation information. DMs are composed by internal decision-makers (IDMs) and external decision-makers (EDMs). The evaluation information is represented by linguistic variables (LVs), intervals and real numbers. To handle such CHMAGDM, this paper puts forward an integrated method of prospect theory, DEMATEL (decision-making trial and evaluation laboratory) and QUALIFLEX (qualitative flexible). Firstly, a novel reference point determining approach is proposed based on three special indicators. A linguistic variable inverse prospect value function is designed and introduced to the transformation process from LVs to clouds to reduce the impacts of DMs' psychological behaviors on decision-making. Secondly, a cloud-based DEMATEL approach is proposed to determine the attribute weights, where LVs are employed to judge the relationships among attributes. A new linguistic scale function is initiated and introduced to another transformation process from clouds to LVs. A representative indicator of cloud is designed for facilitating the normalization of direct relation matrix. Moreover, a linear programming model is built to calculate the attribute weights. Thirdly, an extended QUALIFLEX approach is developed to obtain the optimal ranking and EDM weights, where adoption coefficient is provided by IDMs. Another linear programming model is constructed to calculate the optimal collective concordance/discordance index of each permutation. The optimal ranking is generated by the maximum collective concordance/discordance index. Finally, a photovoltaic power station site selection example validates the proposed method. The advantages are demonstrated with sensitivity and comparison analyses. [ABSTRACT FROM AUTHOR]

• Proposing a physical asset criticality analysis decision model based on BIA. • Risk Appetite and physical asset continuity measures are related. • Defining sub-criteria for impact and likelihood estimation in criticality analysis. The paper tackles the issue of managing physical assets in asset-intensive industries, where continuity plans are crucial for business operations during disruptions. However, resource constraints often hinder companies from implementing these plans for all their assets. Moreover, efforts to maximize resource utilization efficiency and minimize environmental impacts are limited to isolated disciplines, necessitating an integrated approach across natural, social, and technological systems. To address these challenges, this study proposes a framework based on a hybrid fuzzy BWM-TOPSIS methodology for identifying critical physical assets. The framework incorporates Business Impact Analysis (BIA) to determine essential products, a physical asset risk assessment matrix (PARAM) to assess critical assets based on likelihood and impact, and a mathematical model to estimate asset continuity parameters. The framework is applied to a petrochemical company in a case study, offering a guide for estimating the probability and impact of physical asset failure while accounting for inherent uncertainties. By adopting this framework, companies can efficiently manage their physical assets, prioritize continuity plans, and address resource constraints and uncertainties. This research contributes to practical tools and approaches that assist industries in sustaining operations and ensuring business continuity during disruptions. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision-making (MAGDM) is an analytical decision-making framework which gathers the views of multiple experts, and they often assess alternatives by degree adverbs in realistic scenarios. In order to treat expert opinions well, q-rung orthopair fuzzy sets (q-ROF) emerged as a data disposal tool, however, how to aggregate the information rationally remains a challenge. In this paper, q-ROF evidential reasoning methodology (q-ROF ERM) is proposed to guarantee the functionality in the case of conflicting, extreme information evaluations from experts and attributes. Second, the q-ROF attribute reduction (AR) framework is invented for attribute importance measurement. The flexibility and elegance of the model are boosted by the variation of the λ parameter and its lead to the elimination of redundant attributes. In addition to this, the q-ROF output three-way decision (TWD) framework is created to give the classification and ranking of alternatives. The relative output function derived from fuzzy distance measure and the adjustable utility pursuit coefficient τ afford both objectivity and subjectivity to the program selection, allowing the evaluation outcomes to be relevant to human cognition. Finally, the comparative experiments and sensitivity analyses of the two cases illustrate the scientificity and reliability of the presented framework in the MAGDM scenario. • A q-ROF contradictory information fusion method is proposed. • A similarity attribute reduction with λ method is established for q-ROF weights. • Q-ROF output three-way decision considers the utility pursuit τ is designed. • A q-ROF classification and ranking that fits human psychology is conducted. [ABSTRACT FROM AUTHOR]

The move to predictive and prescriptive maintenance underlines the need for cost-effective methods to monitoring degradation and predicting failures. It is in hydroelectric power plants (HPPs) where the most powerful and unique techniques of this evolution were observed. The final premise of this transition is the need to improve the decision-making process for planning activities in the Prescriptive Maintenance Planning (MP). This encourages the use of fuzzy set theory in process management. Although there are many studies on MP in the literature, these studies do not fully reflect the real life as they ignore potential schedule delays and the indirect impact of sustainable strategy on revenues. Therefore, in the first stage of this study, it is aimed to weight the maintenance types (MTs) on a plant basis for the generator, which is the most critical system of the pumped storage HPP, and in the second stage, it is aimed to create MPs that minimize delays due to system shutdowns with weighted MTs. For this purpose, in the first stage, the MTs for the HPP were weighted by AHP-TOPSIS combination augmented with Pythagorean fuzzy numbers, and in the second stage, a Genetic Algorithm model was designed for the problem of coordinating maintenance durations and deadlines in addition to these weights. Averaged over 50 iterations, the average number of delayed MPs is 142.55, indicating that the algorithm is successful in reducing delayed MPs, while the average weighted delay value is 172.85, indicating that more work is needed in terms of weighted delay. [ABSTRACT FROM AUTHOR]

This article mainly addresses the hidden-Markovian model-based asynchronous sampled-data control (SDC) synthesis problem for interval type-2 (IT2) fuzzy semi-Markovian jump systems (S-MJSs) with stochastic actuator failures (SAFs). Herein, the asynchronous factor resulted from twofold: (1) hidden Markovian model (HMM) and (2) imperfectly matched membership functions (IMMFs) between the original plant and the controller. Aiming at approximating the nonlinearity along with randomness with high accuracy and broadening practical application background, the IT2 fuzzy S-MJSs associated with IMMFs is established. At the beginning, a HMM is borrowed to portray the discrepancy between the corresponding plant and the desired controller. Additionally, in comparison with majority of some previous sampled-data control mechanisms, a intrinsic lag signal and gain fluctuations are purposefully introduced in the double asynchronous control strategy, which exploited initially to settle the control synthesis issue. By considering the information of sampling intervals x (t k) → x (t) → x (t k + 1) along with x (t k − τ) → x (t − τ) → x (t k + 1 − τ) adequately, a fresh looped Lyapunov functional called bilateral looped Lyapunov functional is innovatively constructed. Whereafter, by suitably incorporating with the skills of stochastic analysis and relaxed integral inequality (including generalized free matrix-based integral inequality and canonical Bessel–Legendre integral inequality) together with symmetric slack matrices, numerically testable sufficient conditions are established in the form of a group of feasible multi-parameterized linear matrix inequalities (M-PLMIs). The theoretical developments are implies the hierarchy character, and the conservatism decreases with the increase of the degree of hierarchy. Conclusively, the design methodology brought forward herein is demonstrated by two practical examples, which show the potency and practicability. [ABSTRACT FROM AUTHOR]

Atanassov's intuitionistic fuzzy sets play a vital role in handling vagueness and uncertainty successfully as they associate an additional non-membership degree to each element of the universal set. Interval-valued intuitionistic fuzzy (IVIF) sets are more generalized quantities in this direction as they use intervals (⊂ [ 0 , 1 ]) to define the membership and non-membership grades of each element of the set. However, without defining basic arithmetic operations on the IVIF values/sets, the study is incomplete. This paper broadly examines the division and subtraction operations over any arbitrary IVIF values/sets using the concept of Hamming distance between them. A deterministic linear optimization model is proposed and solved in order to obtain the complete expressions for these operations. Next, various fundamental properties and relationships are examined and proved for the proposed arithmetic operations over IVIF values/sets. Furthermore, an example of a multi-criteria decision-making problem under uncertain conditions is studied and analyzed using the developed arithmetic operations on IVIF numbers. • Derived the generalized subtraction and division operations for IVIF values/sets. • The notion of Hamming distance and dual-simplex algorithm are used. • A deterministic LPP is proposed to obtain the expressions for the operations. • The fundamental properties and relationships for the basic operations are explored. • A case study of multi-criteria decision-making problems has been discussed. [ABSTRACT FROM AUTHOR]

In high-end equipment project selection, which involves high technical complexity, significant capital investment, and cross-industry applications, it is essential to involve experts from diverse fields in the decision-making process. To address the challenge of large-scale group decision-making, this paper proposes a three-way large-scale group decision-making model for triple-path consensus reaching process based on a rewards-and-punishments mechanism. The model consists of three stages. Firstly, the group consensus degree is calculated based on the initial input. If the specified threshold is not met, the consensus adjustment iteration stage is entered and decision makers are divided into three regions based on the Pareto principle. Secondly, separate calculations are conducted for the moving benefits and costs of decision makers in different regions, with the total benefits and costs used as targets for the NSGA-II algorithm. The Pareto solution set is obtained, and the solution with the least number of moving objects is selected as the three-way decision-making movement strategy. This process is repeated until the consensus threshold is reached or one of the regions is empty. Finally, based on the final adjustment results, scores are calculated for each project and a ranking is established as a selection suggestion. To demonstrate the feasibility and effectiveness of the model, ten high-end equipment projects are taken as examples, and the sensitivity of the model is tested by adjusting the number of decision makers. In conclusion, the proposed three-way large-scale group decision-making model based on a rewards-and-punishments mechanism for triple-path consensus reaching process is an effective and feasible approach for high-end equipment project selection. [ABSTRACT FROM AUTHOR]

Now-a-days, due to the increasing demand of the energy resources across the world, choosing the best sustainable biomass crop for the production of biofuels is a strategic decision-making problem. This is generally accepted that intuitionistic fuzzy sets (IFSs) are much more efficient in comparison with fuzzy sets at representing and processing the uncertainty in real-life problems. Proceeding on the same line, this paper attempts to introduce an extended combined compromise solution (CoCoSo) framework to analyze the sustainable biomass crop selection (SBCS) problem in an intuitionistic fuzzy environment. In this framework, we suggest a new integration function based on double normalization multiple aggregation approach to overcome the aggregation biases of the original CoCoSo approach and discuss its advantages with some numerical examples. We also develop a combined weighting strategy based on distance measure and decision experts' (DEs) opinions to evaluate the significance of criteria. For this, we propose a novel distance measure (DM) and establish its superiority through some numerical comparisons. Also, the rationality of the suggested measure over the extant measures is justified by the use of an algorithm based on the developed measure for pattern recognition issues. In this framework, the comparison issue of IFSs is resolved by proposing a new score function. Furthermore, a case study of the SBCS is presented for the implementation of the developed CoCoSo approach, which confirms the viability and effectiveness of the new methodology. The results of the sensitivity analysis demonstrate that option "Miscanthus" consistently achieves the highest rank and is independent of variations of trade-off parameter and balancing factor. Finally, a comprehensive comparison is carried out to ensure the steadiness and reliability of the introduced framework. • We propose a new distance measure and establish its validation. • We develop and visualize an improved score function for IFS with its basic properties. • A new integration function is used to overcome the biases of the original CoCoSo method. • We introduce an improved IFS-CoCoSo framework and apply it to multi-criteria decision-making. [ABSTRACT FROM AUTHOR]

Cutter-changing robot is a new product to automatically replace the cutter in shield machine, whose performance is affected by multiple criteria with diversity, multiplicity and correlation, which is a complex multiple criteria decision-making problem with limited and fuzzy available information. This paper proposes a comprehensive performance evaluation model including the performance indicator hierarchy, weight determination, measurement and assessment methods of indicators and sensitivity analysis. Fuzzy Analytical Hierarchy Process (FAHP) is applied to identify the construction requirements from external shield machine and environment and design characteristics in the whole cutter-changing process, weight for 3 first-level indicators and 14 s-level indicators are determined. The objective evaluation indexes measured by instrumentation and subjective evaluation indexes quantified by fuzzy logic are normalized within the range of 0–1. The scores and proportion of assessment grade for each indicator at each level are obtained through Fuzzy Comprehensive Evaluation (FCE). Furthermore, the sensitivity of weight and evaluation data on performance evaluation result are deeply analyzed. The applicability and validity of the proposed approach were demonstrated by a case study of a cutter-changing robot made by China Railway Construction Heavy Industry Co., Ltd. According to the result, operational capacity is the most important criteria in the first level, and cutter grasping ability is the most important indicator in the second level. Path planning ability is the weakest indicators. Cutter grasping ability and time of replacement are the most critical affecting factors. The proposed method not only helps the designers capture the weak indicators accurately and improve the design quality, but also provides engineers with a holistic perspective to the cutter-changing robot before actual application. [ABSTRACT FROM AUTHOR]