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A Single-valued neutrosophic set (SVNS) has recently been explored as a comprehensive tool to assess uncertain information due to varied human cognition. This notion stretches the domain of application of the classical fuzzy set and its extended versions. Various comparison measures based on SVNSs like distance measure, similarity measure, and, divergence measure have practical significance in the study of clustering analysis, pattern recognition, machine learning, and computer vision-related problems. Existing measures have some drawbacks in terms of precision and exclusion of information and produce unreasonable results in categorization problems. In this paper, we propose a generic method to define new divergence measures based on common aggregation operators and discuss some algebraic properties of the proposed divergence measures. To further appreciate the proposed divergence measures, their application to pattern recognition has been investigated in conjunction with the prominent existing comparison measures based on SVNSs. The comparative assessment sensitivity analysis of the proposed measures establishes their edge over the existing ones because of appropriate classification results. [ABSTRACT FROM AUTHOR]

The normal wiggly hesitant fuzzy set (NWHFS) is one of the latest extensions of hesitant fuzzy set (HFS). It can depict experts' preference information consisting of several possible values and the potential information dug in the traditional hesitant fuzzy set (HFS) at the same time. However, traditional aggregation operators of NWHFSs always ignore the influence of psychological behaviors. Therefore, to make use of the potential information and manage the applications with incomplete rationality, this paper combines the advantages of TODIM (TOmada deDecisão Iterativa Multicritério) method and NWHFSs. Considering the structures and characteristics of NWHFSs, we also provide the definition of distance measure of NWHFSs. Based on this, we develop an improved TODIM method. The specific implementation process is also provided. Finally, we apply the improved TODIM method to the environmental quality evaluation. The comparison result with traditional aggregation operators indicates that the proposed method can enlarge the competitive relationship better. It also demonstrates the rationality and accuracy of our method. [ABSTRACT FROM AUTHOR]

One of characteristics of large-scale linguistic decision making problems is that decision information with respect to decision making attributes is derived from multi-sources information. In addition, the number of decision makers, alternatives or criteria of decision making problems in the context of big data are increasingly large. Correlation analysis between decision making attributes has become an important issue of large-scale linguistic decision making problems. In the paper, we concentrate on correlation analysis between decision making attributes to deal with large-scale decision making problems with linguistic intuitionistic fuzzy values. Firstly, we proposed a new similarity measure between two linguistic intuitionistic fuzzy sets to formally define correlation between decision making attributes. Then we propose linguistic intuitionistic fuzzy reducible weighted Maclaurin symmetric mean (LIFRWMSM) operator and linguistic intuitionistic fuzzy reducible weighted dual Maclaurin symmetric mean (LIFRWDMSM) operator to aggregate linguistic intuitionistic fuzzy value decision information of correlational decision making attributes, and analyze several important properties of the two operator. Inspired by evaluation based on distance from average solution (EDAS) method, we design a solution scheme and decision steps to deal with large-scale linguistic intuitionistic fuzzy decision making problems. To show the effectiveness and usefulness of the proposed decision method, we employ the choice of buying a house and the selection of travel destination to demonstrate our method and make comparative analysis with others aggregation operators or methods. [ABSTRACT FROM AUTHOR]

Since the unit interval with a t-norm or a t-conorm is a special monoid, a natural question is to consider the fuzzification of monoid. In this paper, we mainly present the fuzzy monoid and vague monoid with the help of aggregation functions. Firstly, the fuzzy submonoid about aggregation function is proposed, which can further be fuzzified to the fuzzy t-subnorm and t-subconorm to deal with imprecision. In particular, the corresponding concepts and properties can be obtained directly when aggregation function takes uninorm and nullnorm, respectively. Further, the concept of fuzzy submonoid is extended to lattice structure. Finally, the notion of vague monoid about aggregation operator is constructed and further the special cases under uninorms and nullnorms are considered. [ABSTRACT FROM AUTHOR]

The selection of the building orientations is the key to the pretreatment stage of models for additive manufacturing (AM) technology, which plays a significant role in product accuracy, material consumption, printing layout, etc., affecting the economy and time efficiency of printing. In this paper, an automatic selection system of the building orientation based on the double-layer priority aggregation multi-attribute decision-making (DLPA-MADM) method is proposed to select the optimal building orientation (OBO). The priority compensation restricted average (PCRA) aggregation operator is designed to handle the priority relationships among attributes. The alternative building orientations (ABOs) are constructed according to the reference orientations of the surface features via the STEP AP242 file. The models of the surface precision with feature (P&F), printing time (PT), layout area (LA), and support volume (SV) attributes who participate in decision-making are established. According to the tolerances given from the STEP file, the sub-precision values of ABOs for surface features with distinct priorities are aggregated in the first layer to obtain the precision value. Four attributes are aggregated in the second layer with priority to acquire the comprehensive evaluation value (CEV), through the ranking of which, the OBO can be found. The effectiveness and rapidity of the developed system are proved by experiments on the model. [ABSTRACT FROM AUTHOR]

As a more massive feasible and prominent tool than the complex interval-valued Pythagorean fuzzy (CIVPF) set and complex interval-valued intuitionistic fuzzy (CIVIF) set, the complex interval-valued q-rung orthopair fuzzy (CIVQROF) set has been usually used to represent ambiguity and vagueness for real-life decision-making problems. In this paper, we firstly proposed some distance measures, Yager operational laws, and their comparison method. Further, we developed CIVQROF Yager weighted averaging (CIVQROFYWA), CIVQROF Yager ordered weighted averaging (CIVQROFYOWA), CIVQROF Yager weighted geometric (CIVQROFYWG), CIVQROF Yager ordered weighted geometric (CIVQROFYOWG) operators with CIVQROF information, and some certain well-known and feasible properties and outstanding results are explored in detail. Moreover, we proposed a new and valuable technique for handling multi-attribute decision-making problems with CIVQROF information. Lastly, a practical evaluation regarding the high blood pressure diseases of the patient is evaluated to illustrate the feasibility and worth of the proposed approaches. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, identifying face masks with artificial intelligence was a crucial challenge for decision support systems. To address this challenge, we propose a quadratic Diophantine fuzzy decision-making model to rank artificial intelligence techniques for detecting masks, aiming to prevent the global spread of the disease. Our paper introduces the innovative concept of quadratic Diophantine fuzzy sets (QDFSs), which are advanced tools for modeling the uncertainty inherent in a given phenomenon. We investigate the structural properties of QDFSs and demonstrate that they generalize various fuzzy sets. In addition, we introduce essential algebraic operations, set-theoretical operations, and aggregation operators. Finally, we present a numerical case study that applies our proposed algorithms to select a unique face mask detection method and evaluate the effectiveness of our techniques. Our findings demonstrate the viability of our mask identification methodology during the COVID-19 outbreak. [ABSTRACT FROM AUTHOR]

Picture fuzzy sets (PFSs), the generalization of intuitionistic fuzzy sets (IFSs), are more capable of dealing with vague data in real-life problems. Models based on PFSs may be suitable particularly in those circumstances where human perceptions become challenging as well as various kinds of reasoning, like yes, no, abstention, or denial. The aggregation operators (AOs) are essential components in information aggregation as they have the ability to aggregate a group of fuzzy numbers into a single fuzzy number of the same kind. A lot of aggregation operations for PFSs have been developed. Nevertheless, the existing aggregation operators for picture fuzzy information are inaccurate as they fail to aggregate a group of picture fuzzy numbers into a single picture fuzzy number (PFN). To cover the drawbacks of existing AOs, we developed some modified picture fuzzy aggregation operators (PFAOs) named as picture fuzzy modified weighted averaging (PFMWA), picture fuzzy modified ordered weighted averaging (PFMOWA) and picture fuzzy modified hybrid averaging (PFMHA) aggregation operator along with their distinctive features. These operators are essential in developing new multi-criteria decision-making (MCDM) techniques. This paper defines a number of stakeholder roles (or tactics), with an objective of overcoming the challenges to executing Education 4.0 (EDUC4) that have recently been highlighted in the literature. A MCDM problem provides the basis for the evaluation of the responsibilities of the stakeholders with respect to these constraints. Several management concerns are provided as stepping stones for the development of EDUC4 implementation. The purpose of this study is to identify the qualities that influence the degree of optimism for the adoption and implementation of the EDUC4 in Pakistan's education system while taking government policies into account. [ABSTRACT FROM AUTHOR]

Teaching quality is the foundation and lifeline of colleges and universities. To establish a distinctive university, we must adhere to the scientific concept of development, deepen teaching reform and improve teaching quality. The classroom teaching quality (CTQ) evaluation of college physical education (PE) is an essential part of the teaching process. Building a scientific, comprehensive, reasonable and effective evaluation system is crucial to improve the quality of college PE classroom teaching. This process is not easy and needs long-term efforts and persistence. The CTQ evaluation of college volleyball training is viewed as the multi-attribute decision-making (MADM). In this paper, we connect the geometric Heronian mean (GHM) operator and power geometric (PG) operator with 2-tuple linguistic neutrosophic sets (2TLNSs) to build the generalized 2-tuple linguistic neutrosophic numbers weighted power GHM (G2TLNWPGHM) operator. Then, the G2TLNWPGHM operator is used to tackle MADM with 2TLNSs. Finally, an example for CTQ evaluation of college volleyball training is used to show the proposed methods. [ABSTRACT FROM AUTHOR]

There are various uncertainties in the multi-criteria group decision making (MCGDM) process, including the definition of the importance of decision information and the assignment of criterion assessment values, etc., which cause decision makers to be unconfident in their decisions. In this paper, an MCGDM approach based on the reliability of decision information is proposed in Fermatean fuzzy (FF) environment, allowing a decision to be made with confidence that the alternative chosen is the best performing alternative under the range of probable circumstances. First, we prove that the FF Yager weighted averaging operator is monotone with respect to the total order and note the inconsistency between the monotonicity of some FF aggregation operators and their application in MCGDM. Second, we extend the divergence measure of FFS to order σ for calculating the variance of decision information and accordingly develop an exponential FF entropy measure to measure the uncertainty of decision information. Then, the reliability of decision information is defined, which accounts for the degree of variance of decision information across criteria from the criterion dimension and the uncertainty of the decision information from the alternative dimension. Following that, an integrated MCGDM framework is completed. Finally, the applications to a numerical example and comparisons with previous approaches are conducted to illustrate the validity of the established approach. [ABSTRACT FROM AUTHOR]

Accumulation of q ˜ -rung picture fuzzy information plays an essential part in decision-making situations. q ˜ -rung picture fuzzy sets can handle the uncertain information more precisely and flexibly because of the presence of parameter q ˜. Also the Frank t-norm and t-conorm operations perform suitably for the data accumulation with the operational parameter. In this paper, we introduce q ˜ -Rung picture fuzzy Frank weighted averaging operator and q ˜ -rung picture fuzzy Frank weighted geometric operator by extending q ˜ -rung orthopair fuzzy Frank arithmetic and geometric aggregation operators respectively. We establish an algorithm to address the tedious decision-making problems using these operators. Eventually, we discuss a multiple attribute decision-making problem to demonstrate the utility and efficacy of the proposed method. A comparison of existing methods is made to reveal the supremacy and benefits of our proposed method. [ABSTRACT FROM AUTHOR]

Evaluation and selection problems are becoming increasingly difficult due to human judgment and unknown evaluation risks. These circumstances mean that contractor selection is impacted by a number of factors, many of which have a hybrid uncertainty of fuzziness and probability. The objective of this paper is to propose a multi-attribute group decision-making (MAGDM) model for the selection of the most suitable construction company. A decision problem based on the decisions of many experts, with multiple conflicting criterion, should be taken into account to evaluate multiple companies. For this purpose, we propose the notion of a linguistic interval-valued T-spherical fuzzy set (LIVt-SFS) to allow decision-makers to provide their evaluations in a wider space and to better deal with vague information. In this study, we developed some basic operations and score and accuracy functions to compare LIVt-SF numbers (LIVt-SFNs). Based on these operations, two aggregation operators: LIVt-SF weighted averaging and LIVt-SF weighted geometric operators, are established. Moreover, the technique for order of preference by similarity to ideal solution (TOPSIS) method is extended to solve the MAGDM problem under LIVt-SFS information. Furthermore, an example of the selection of the best construction company is given to demonstrate the effectiveness and feasibility of the proposed model. The computational results demonstrate that the suggested MAGDM model is capable of dealing with imprecision and subjectivity in complex decision-making situations. In addition, a sensitivity analysis is conducted to observe the influence of the parameter 'q' on the decision results. Finally, a comparison with existing decision-making methods is presented for the authentication of our proposed approach. [ABSTRACT FROM AUTHOR]

Multi-criteria group decision-making (MCGDM) problems, where correlations commonly exist among input arguments, are becoming increasingly complex. However, most of the existing consensus-reaching methods for MCGDM problems fail to adequately consider the effects of these interactions among criteria and experts, which may bring about inaccurate results. Therefore, this paper establishes a novel MCGDM framework based on the generalized Shapley value to solve the consensus-reaching problem with interval-valued Pythagorean fuzzy sets (IVPFS). First, experts' evaluations are collected using IVPFS, which offers a more flexible way to express this vague information. Second, the interval-valued Pythagorean fuzzy Choquet integral operator and the interval-valued Pythagorean fuzzy Shapley aggregation operator are developed to fuse the decision information with complementary, redundant, or independent characteristics. Third, an integrated consensus-reaching algorithm is established to improve group consensus by iteratively updating the evaluations until the group consensus level reaches the preset threshold. Then, the classical PROMETHEE method is extended using the generalized Shapley value within an IVPFS context to derive a more scientific ranking result. Finally, a case study for a sustainable supplier evaluation problem is presented to validate the proposed method. The results and comparative analysis show that the proposed method can represent experts' evaluations more flexibly, integrate inputs with interrelationships more effectively, and improve group consensus more efficiently. [ABSTRACT FROM AUTHOR]

Complex intuitionistic fuzzy (CIF) information covers the degree of membership and the degree of non-membership in the form of polar coordinates with a valuable and dominant characteristic where the sum of the real parts (the same rule for the imaginary parts) of the pair must be contained in the unit interval. In this paper, we first derive the Frank operational laws for CIF information and then examine the prioritized aggregation operators based on Frank operational laws for managing the theory of CIF information. These are the CIF Frank prioritized averaging (CIFFPA) operator, the CIF Frank prioritized ordered averaging (CIFFPOA) operator, the CIF Frank prioritized geometric (CIFFPG) operator, and the CIF Frank prioritized ordered geometric (CIFFPOG) operator with properties of idempotency, monotonicity, and boundedness. Furthermore, we derive the WASPAS (weighted aggregates sum product assessment) under the consideration or presence of the CIF information and try to justify it with the help of a suitable example. Additionally, we illustrate some numerical examples in the presence of the MADM (multi-attribute decision-making) procedures for evaluating the comparison between the proposed operators with some well-known existing operators to show the validity and worth of the proposed approaches. [ABSTRACT FROM AUTHOR]

The Pythagorean Probabilistic Hesitant Fuzzy (PyPHF) Environment is an amalgamation of the Pythagorean fuzzy set and the probabilistic hesitant fuzzy set that is intended for some unsatisfactory, ambiguous, and conflicting situations where each element has a few different values created by the reality of the situation membership hesitant function and the falsity membership hesitant function with probability. The decision-maker can effciently gather and analyze the information with the use of a strategic decision-making technique. In contrast, ambiguity will be a major factor in our daily lives while gathering information. We describe a decision-making technique in the PyPHF environment to deal with such data uncertainty. The fundamental operating principles for PyPHF information under Choquet Integral were initially established in this study. Then, we put up a set of new aggregation operator names, including Pythagorean probabilistic hesitant fuzzy Choquet integral average and Pythagorean probabilistic hesitant fuzzy Choquet integral geometric aggregation operators. Finally, we explore a multi-attribute decision-making (MADM) algorithm based on the suggested operators to address the issues in the PyPHF environment. To demonstrate the work and contrast the findings with those of previous studies, a numerical example is provided. Additionally, the paper provides sensitivity analysis and the benefits of the stated method to support and reinforce the research. [ABSTRACT FROM AUTHOR]

This paper aims to amalgamate the notion of a T-spherical fuzzy set (T-SFS) and a linear Diophantine fuzzy set (LDFS) to elaborate on the notion of the T-spherical linear Diophantine fuzzy set (T-SLDFS). The new concept is very effective and is more dominant as compared to T-SFS and LDFS. Then, we advance the basic operations of T-SLDFS and examine their properties. To effectively aggregate the T-spherical linear Diophantine fuzzy data, a T-spherical linear Diophantine fuzzy weighted averaging (T-SLDFWA) operator and a T-spherical linear Diophantine fuzzy weighted geometric (T-SLDFWG) operator are proposed. Then, the properties of these operators are also provided. Furthermore, the notions of the T-spherical linear Diophantine fuzzy-ordered weighted averaging (T-SLDFOWA) operator; T-spherical linear Diophantine fuzzy hybrid weighted averaging (T-SLDFHWA) operator; T-spherical linear Diophantine fuzzy-ordered weighted geometric (TSLDFOWG) operator; and T-spherical linear Diophantine fuzzy hybrid weighted geometric (TSLDFHWG) operator are proposed. To compare T-spherical linear Diophantine fuzzy numbers (TSLDFNs), different types of score and accuracy functions are defined. On the basis of the TSLDFWA and T-SLDFWG operators, a multiple attribute decision-making (MADM) method within the framework of T-SLDFNs is designed, and the ranking results are examined by different types of score functions. A numerical example is provided to depict the practicality and ascendancy of the proposed method. Finally, to demonstrate the excellence and accessibility of the proposed method, a comparison analysis with other methods is conducted. [ABSTRACT FROM AUTHOR]

T-spherical fuzzy sets (T-SPFSs) have gained popularity because of their ability to account for uncertainty more effectively and spanning a larger domain. The sum of the t-th power of membership grades in T-SPFSs is close to a unit interval, allowing for greater uncertainty. As a result, this set outperforms traditional fuzzy structures. The "multi-criteria decision-making" (MCDM) approach is a widely used technique that requires the use of some aggregation tools, and various such aggregation operators (AOs) have been developed over the years to achieve this purpose. The purpose of this paper is to propose some new operational laws and AOs for use in a T-spherical fuzzy environment. In this regard, we presented some new neutral or fair operational rules that combine the concept of proportional distribution to provide a neutral or fair solution to the membership, abstinence, and non-membership of T-spherical fuzzy numbers (T-SPFNs). Based on the obtained operational rules, we presented the "T-spherical fuzzy fairly weighted average operator" and the "T-spherical fuzzy fairly ordered weighted averaging operator". Compared to earlier methodologies, the proposed AOs provide more generalised, reliable, and accurate information. In addition, under T-SPFSs, an MCDM approach is developed employing suggested AOs with several decision-makers (DMs) and partial weight details. Finally, to demonstrate the applicability of the innovative technique, we give an actual case study of "food waste treatment technology" (FWTT) selection under T-SPFSs scenarios. A comparison with an existing model has also been undertaken to confirm the validity and robustness of the acquired results. [ABSTRACT FROM AUTHOR]

Traditional knowledge graph completion mainly focuses on static knowledge graph. Although there are efforts studying temporal knowledge graph completion, they assume that each relation has enough entities to train, ignoring the influence of long tail relations. Moreover, many relations only have a few samples. In that case, how to handle few-shot temporal knowledge graph completion still merits further attention. This paper aims to propose a framework for completing few-shot temporal knowledge graph. We use self-attention mechanism to encode entities, use cyclic recursive aggregation network to aggregate reference sets, use fault-tolerant mechanism to deal with error information, and use similarity network to calculate similarity scores. Experimental results show that our proposed model outperforms the baseline models and has better stability. [ABSTRACT FROM AUTHOR]

Business English teaching quality evaluation Business English is a new type of composite specialty, which is a discipline innovation made by China's higher education to adapt to the new market demand and international standards since the reform and opening up. Over the past 20 years, it has cultivated a number of compound talents for the cause of China's reform and opening up. However, the backwardness of business English theoretical research has greatly restricted the development of business English. At present, Business English has been officially approved as a new major for undergraduate enrollment by the Ministry of Education of the People's Republic of China. Its subject nature, specialty structure, training objectives, and specialty compound characteristics need to be qualitatively studied theoretically. The business English teaching quality evaluation is viewed as the multiple attribute decision making (MADM) issue. In this paper, we connect the geometric Heronian mean (GHM) operator and power geometric (PG) with 2-tuple linguistic neutrosophic numbers (2TLNNs) to propose the generalized 2-tuple linguistic neutrosophic power geometric HM (G2TLNPGHM) operator. Then, the G2TLNGHM operator is applied to deal with the MADM problems under 2TLNNs. Finally, an example for business English teaching quality evaluation is used to show the proposed methods. Some comparative analysis and parameter influence analysis are fully given. The results show that the built algorithms method is useful for business English teaching quality evaluation. [ABSTRACT FROM AUTHOR]

This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and sub-attributes. For grasping that field of parallel information, events, and realities flowing from the micro to the macro level of universes, we have constructed hypersoft and hyper-super-soft matrices in a Plithogenic Fuzzy environment. These Matrices classify the non-physical attributes by accumulating the physical subjects and further sort the physical subjects by accumulating their non-physical attributes. We presented them as Plithogenic Attributive Subjectively Whole Hyper-Super-Soft-Matrix (PASWHSS-Matrix) and Plithogenic Subjective Attributively Whole-Hyper-Super-Soft-Matrix (PSAWHSS-Matrix). Several types of views and level-layers of these matrices are described. In addition, some local aggregation operators for Plithogenic Fuzzy Hypersoft Set (PPFHS-Set) are developed. Finally, few applications of these matrices and operators are used as numerical examples of COVID-19 data structures. [ABSTRACT FROM AUTHOR]

Federated learning is currently a popular distributed machine learning solution that often experiences cumbersome communication processes and challenging model convergence in practical edge deployments due to the training nature of its model information interactions. The paper proposes a hierarchical federated learning algorithm called FedDyn to address these challenges. FedDyn uses dynamic weighting to limit the negative effects of local model parameters with high dispersion and speed-up convergence. Additionally, an efficient aggregation-based hierarchical federated learning algorithm is proposed to improve training efficiency. The waiting time is set at the edge layer, enabling edge aggregation within a specified time, while the central server waits for the arrival of all edge aggregation models before integrating them. Dynamic grouping weighted aggregation is implemented during aggregation based on the average obsolescence of local models in various batches. The proposed algorithm is tested on the MNIST and CIFAR-10 datasets and compared with the FedAVG algorithm. The results show that FedDyn can reduce the negative effects of non-independent and identically distributed (IID) data on the model and shorten the total training time by 30% under the same accuracy rate compared to FedAVG. [ABSTRACT FROM AUTHOR]

Ecological risks are characterized by a high degree of uncertainty about the chances of unfavorable event outcomes and the losses associated with those outcomes. Subjective expert judgment is widely used when baseline data are insufficient. This introduces additional uncertainties in the results of risk analyses. In order to successfully model the existing uncertainties, this paper presents a methodology for ecological risk analysis that is based on input evaluations in the form of intuitionistic fuzzy values (IFVs). The advantage of this approach is the ability to model a wide range of uncertainties in ecological risk analysis tasks. [ABSTRACT FROM AUTHOR]

Attitudinal Choquet integral (ACI) is a recent aggregation operator that considers in the aggregation process the criteria interaction and the DM’s attitude, both of which are specific to the decision-maker. However, this capability comes at the cost of increased complexity that hinders its applicability in big data analytics. To address the same, in this paper, we explore some heuristics-based forms of the ACI operator, so as to somehow overcome its complexity. We devise new and efficient forms of ACI, and test their validity in the real world datasets, against the backdrop of preference learning. [ABSTRACT FROM AUTHOR]

Interval neutrosophic sets (INSs), characterized by truth, indeterminacy and falsity membership degrees, handle the uncertain and inconsistent information that commonly exists in real-life systems, and constitute an extension of the interval valued fuzzy set and interval valued intuitionistic fuzzy set. The existing works on similarity measures for INSs are mostly constructed by distance measures and entropies. Meanwhile, the degree of similarity is expressed as a single number, even if the interval-valued information is considered. This may lead to a loss of interval-valued information. In order to cope with these issues, in this paper, we introduce a new approach to constructing the similarity measures for INSs using fuzzy equivalencies. First, based on fuzzy equivalencies and aggregation operators, the definition of interval-valued fuzzy equivalence is generalized to interval neutrosophic values. Then, based on the framework of INSs, we propose the definition and construction method of the similarity measure using the interval neutrosophic fuzzy equivalence. The similarity degree is expressed as an interval and could retain more information than ever before. In addition, according to practical situations, one can obtain different similarities by selecting the parameters in fuzzy equivalence. Due to the increase in edge computing, it is necessary to reasonably offload the client's resource and assign them to the edge server to balance the resource usage. The Similarity measure is conductive to select and match the client and edge server. Finally, an illustrative example verifies that the proposed method can find a reasonable client and edge server, as well as effectiveness in the edge computing application. [ABSTRACT FROM AUTHOR]

The T-spherical uncertain linguistic (TSUL) sets (TSULSs) integrated by T-spherical fuzzy sets and uncertain linguistic variables are introduced in this article. This new concept is not only a generalized form but also can integrate decision-makers' quantitative evaluation ideas and qualitative evaluation information. The TSULSs serve as a reliable and comprehensive tool for describing complex and uncertain decision information. This paper focuses on an extended MARCOS (Measurement of Alternatives and Ranking according to the Compromise Solution) method to handle the TSUL multi-attribute group decision-making problems where the weight information is completely unknown. First, we define, respectively, the operation rules and generalized distance measure of T-spherical uncertain linguistic numbers (TSULNs). Then, we develop two kinds of aggregation operators of TSULNs, one kind of operator with independent attributes is T-spherical uncertain linguistic weighted averaging and geometric (TSULWA and TSULWG) operators, and the other is T-spherical uncertain linguistic Heronian mean aggregation operators (TSULHM and TSULWHM) considering attributes interrelationship. Their related properties are discussed and a series of reduced forms are presented. Subsequently, a new TSUL-MARCOS-based multi-attribute group decision-making model combining the proposed aggregation operators and generalized distance is constructed. Finally, a real case of investment decision for a community group-buying platform is presented for illustration. We further test the rationality and superiorities of the proposed method through sensitivity analysis and comparative study. [ABSTRACT FROM AUTHOR]

Probabilistic linguistic term sets (PLTSs) are suitable for enunciating evaluators' complex linguistic perceptions more accurately within the intricate qualitative setting. Usually, the PLTS is based on a balanced concept and does not serve as a good information representation for an unbalanced qualitative concept. Therefore, to reflect experts' distinct preferences and uncertainties, this paper proposes a new PLTS called the probabilistic multiplicative unbalanced linguistic term set (PM-ULTS), where both probabilities and non-uniform spacing of the linguistic labels are considered simultaneously. Afterwards, we put forward specific operational laws for the newly constructed PLTS to preserve the resultant linguistic labels and corresponding probability information. Some elementary aggregation operators beneficial in aggregating probabilistic linguistic information in decision-making problems are also constructed, and their excellent properties are addressed. Furthermore, based on the proposed concept, this study initiates the design of a unified two-person linguistic matrix game model with the new PLTS as a parameter. It addresses the imprecise information by the information measure function. Such a two-player probabilistic unbalanced linguistic matrix game is considered a convenient technique for multiple decision scenarios. Additionally, the proposed game model involves a re-translation process to convert the output back into the original probabilistic unbalanced linguistic domain without information loss, thereby escalating the interpretability of the game model compared with other existing uncertain matrix game methodologies. Finally, we discuss the significance of the proposed methodology and concept to question its validity and usefulness by presenting suitable examples. [ABSTRACT FROM AUTHOR]

The picture hesitant fuzzy sets (PHFSs), which consider neutral membership degree as well as positive and negative membership degrees, provide decision makers (DMs) a flexible attitude to evaluate criteria values in complex multi-criteria decision-making (MCDM) situations. However, existing MCDM approaches based on PHFSs still have some drawbacks in both evaluation information expression and criteria values fusion. In this paper, our aim is to overcome these shortcomings by proposing new decision-making methods. To achieve this purpose, a new fuzzy information representation tool, called probabilistic picture hesitant fuzzy sets (P-PHFSs), is first introduced by capturing the probability of each element in PHFSs. The characteristic of P-PHFSs is that they provide more freedom to DMs so that criterion values of each alternative can be adequately described. To facilitate the use of P-PHFSs, we define the basic operational rules and comparison method of P- PHFSs. Then we also propose some aggregation operators for P-PHFSs and provide information fusion process. Furthermore, some desirable properties of these operators is discussed, and the relationship between the developed operators and the existing ones is investigated. Based on the proposed operators, two MCDM methods are developed under probabilistic picture hesitant fuzzy environment. Finally, two numerical examples are given to show the application of the developed methods, and a comparison analysis is conducted to demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In today's fast-paced and dynamic business environment, investment decision making is becoming increasingly complex due to the inherent uncertainty and ambiguity of the financial data. Traditional decision-making models that rely on crisp and precise data are no longer sufficient to address these challenges. Fuzzy logic-based models that can handle uncertain and imprecise data have become popular in recent years. However, they still face limitations when dealing with complex, multi-criteria decision-making problems. To overcome these limitations, in this paper, we propose a novel three-way group decision model that incorporates decision-theoretic rough sets and intuitionistic hesitant fuzzy sets to provide a more robust and accurate decision-making approach for selecting an investment policy. The decision-theoretic rough set theory is used to reduce the information redundancy and inconsistency in the group decision-making process. The intuitionistic hesitant fuzzy sets allow the decision makers to express their degrees of hesitancy in making a decision, which is not possible in traditional fuzzy sets. To combine the group opinions, we introduce novel aggregation operators under intuitionistic hesitant fuzzy sets (IHFSs), including the IHF Aczel-Alsina average (I H F A A A) operator, the IHF Aczel-Alsina weighted average (I H F A A W A ϣ) operator, the IHF Aczel-Alsina ordered weighted average (I H F A A O W A ϣ) operator, and the IHF Aczel-Alsina hybrid average   (I H F A A H A ϣ) operator. These operators have desirable properties such as idempotency, boundedness, and monotonicity, which are essential for a reliable decision-making process. A mathematical model is presented as a case study to evaluate the effectiveness of the proposed model in selecting an investment policy. The results show that the proposed model is effective and provides more accurate investment policy recommendations compared to existing methods. This research can help investors and financial analysts in making better decisions and achieving their investment goals. [ABSTRACT FROM AUTHOR]

Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval-valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS. [ABSTRACT FROM AUTHOR]

In this paper, in order to apply the concept of IVI-octahedron sets to MCDGM problems, we define some aggregation operators via IVI-octahedron sets and obtain some their properties. We define some aggregation operators via IVIoctahedron sets and obtain some their properties. We present a MCGDM method with linguistic variables in IVIoctahedron set environment. Finally, we give a numerical examples for MCGDM problems. [ABSTRACT FROM AUTHOR]

Recently, Zhao et al. [55] characterized the distributivity equations of null-uninorms with continuous and Archimedean underlying operators over overlap or grouping functions. Moreover, Liu et al. [34] studied the distributive laws of continuous t-norms over overlap functions. In this paper, we proceed with the distributivity characterization of idempotent null-uninorms over overlap or grouping functions. In order to do that, we introduce a class of weak overlap and grouping functions with weak coefficients, and obtain the full characterizations of overlap and grouping functions by considering the different values of underlying uninorms’ associated functions of idempotent null-uninorms on the interval endpoints and comparing them with the weak coefficients. Obviously, idempotent null-uninorms generalize idempotent uninorms. Thus, the obtained results also generalize the distributivity of idempotent uninorms proposed as future work in [34]. [ABSTRACT FROM AUTHOR]

Cubical fuzzy sets, a novel structure, deal with the fuzziness of information more effectively than picture fuzzy sets and spherical fuzzy sets. Each member of a CFS is an ordered quadruple consisting of an element of the universe of discourse and three numbers in the unit interval called, respectively, membership grade, neutral membership grade, and non-membership grade, such that their cubic sum is bounded by one. CFSs, being an extension of PFSs and CFSs by enlarging the space of membership grades, give decision-makers more leeway in assigning values. In this paper, we first integrate the notion of Hamacher T-norm and T-conorm with the structure of CFSs to devise the novel cubical fuzzy Hamacher operations and discuss their essential properties. Then, by employing the idea of cubical fuzzy Hamacher operations, we introduce novel aggregation operators called cubical fuzzy Hamacher aggregation operators. The concepts of the cubical fuzzy Hamacher weighted average operator, the cubical fuzzy Hamacher ordered weighted average operator, and the cubical fuzzy Hamacher hybrid average weighted operator are presented and discussed thoroughly in the first section of this work. The cubical fuzzy Hamacher weighted geometric operator, the cubical fuzzy Hamacher ordered weighted geometric operator, and the cubical fuzzy Hamacher hybrid geometric operator are introduced in the second portion, and its essential features are explored. The proposed operators are then used to create some strategies for solving cubical fuzzy information-based multiple attribute decision-making issues. Finally, to demonstrate the applicability and efficiency of the proposed methodology, a real-world example of cyclone disaster appraisal is provided. [ABSTRACT FROM AUTHOR]

The development of tourism and society has made people's travel routes under complex and uncertain information an important issue. In this paper, we introduce a novel Pythagorean hesitant fuzzy linguistic term set (PHFLTS) to describe the information in more detail and unify the Pythagorean fuzzy linguistic term set (PFLTS) and hesitant fuzzy linguistic term set (HFLTS) to make the calculation more convenient. To help travelers consider time, distance, economic cost, and other factors, the Pythagorean hesitant fuzzy linguistic (PHFL) aggregation operators are proposed. Based on this, the PHFL route recommendation dynamic programming model is established to find the optimal route considering multiple factors, and the PHFL Dijkstra's algorithm is studied to find the shortest directed route. Different travelers value different factors when choosing a route, so the weights of each factor are uncertain. By combining the PHFL aggregation operator and the PHFL Dijkstra's algorithm, a route intelligent recommendation algorithm (RIRA) is proposed to help travelers choose the most suitable route according to their intentions. Finally, a numerical example is given to illustrate the effectiveness and practicality of the dynamic programming model and algorithm. [ABSTRACT FROM AUTHOR]

The Complex Pythagorean fuzzy set (CPyFS) is an efficient tool to handle two-dimensional periodic uncertain information, which has various applications in fuzzy modeling and decision making. It is known that the aggregation operators influence decision-making processes. Algebraic aggregation operators are the important and widely used operators in decision making techniques that deal with uncertain problems. This paper investigates some complex Pythagorean fuzzy geometric aggregation operators, such as complex Pythagorean fuzzy weighted geometric (CPyFWG), complex Pythagorean fuzzy ordered weighted geometric (CPyFOWG), complex Pythagorean fuzzy hybrid geometric (CPyFHG), induced complex Pythagorean fuzzy ordered weighted geometric (I-CPyFOWG), and induced complex Pythagorean fuzzy hybrid geometric (I-CPyFHG), and their structure properties, such as idempotency, boundedness, and monotonicity. In addition, we compare the proposed model with their existing models, such as complex fuzzy set and complex intuitionistic fuzzy set. We analyze an example involving the selection of an acceptable location for hospitals in order to demonstrate the effectiveness, appropriateness, and efficiency of the novel aggregation operators. [ABSTRACT FROM AUTHOR]

The recently proposed q-rung orthopair fuzzy set (q-ROFS) whose main feature is that the qth power of membership degree (MD) and the qth power of non-membership degree (NMD) is equal to or less than 1, is a powerful tool to describe uncertainty. The major contribution of this paper lies to investigate power point average (PPA) aggregation operators with q-rung orthopair fuzzy information based on Frank t-conorm and t-norm. Since the existing power average (PA) operators all rely on the traditional distance measures to measure support degree between the input values, it cannot reflect decision makers' attitude. In response, this paper introduces firstly a series of distance measures for q-rung orthopair fuzzy numbers (q-ROFNs) based on point operators, from which the corresponding support measures can be obtained. Secondly, based on the proposed point distance measures, new Frank power point average aggregation operators are proposed to aggregate q-rung orthopair fuzzy information. Finally, a novel multiple attribute decision making (MADM) technique is presented based on the proposed Frank power point average aggregation operators. The developed MADM method not only can get more objective information, but also avoid the influence of unduly high or low attribute values on the decision result, providing a new way for decision makers (DMs) under q-rung orthopair fuzzy environment. [ABSTRACT FROM AUTHOR]

The paper aims to introduce the novel concept of q-connection number (q-CN) for interval-valued q-rung orthopair fuzzy set (IVq-ROFSs) and thus to develop a method for solving the multiple-attribute group decision making (MAGDM) problem. The IVq-ROFS is a tool to represent the uncertain information with an integer parameter q ≥ 1 , while the connection number (CN) processes the uncertainties and certainties into a single system with three degrees, namely "identity", "contrary" and "discrepancy". Driven by these required properties, this paper introduces a q-CN for IVq-ROFSs to represent the information in a more concise way. To this end, we divide the paper into three aspects. First, we define q-CN and a scoring function to evaluate the numbers. Second, we give some new q-exponential operation laws (q-EOLs) and operators over q-CNs in which bases are real numbers and exponents are q-CNs. Moreover, we define an operator based on these laws and derive their properties. Third, a novel MAGDM method for solving decision problems with IVq-ROFS information is illustrated with several examples. The advantages and superiority analysis of the proposed framework are also given to assert the results. [ABSTRACT FROM AUTHOR]

The selection and evaluation of solid rocket multi-stage combined schemes with multiple attributes are main issues needed to be resolve. This paper innovatively applied the power generalised compensative weighted averaging (PGCWA) aggregation operator to help multi-stage combined solid rocket select optimal compositional scheme among multiple schemes under multi-attribute environment. The attribute values of each scheme of solid rocket are aggregated to evaluate the scheme, where the weight of attributes is incorporated into the aggregation procedures. Numerical example verifies the proposal method exhibits sound performances in decision support of the aerospace field, the effectiveness and feasibility are further illustrated. [ABSTRACT FROM AUTHOR]

With respect to multiple attribute group decision making (MAGDM) problems in which the attributes are dependent and the attribute values take the forms of intuitionistic linguistic numbers and intuitionistic uncertain linguistic numbers, this paper investigates two novel MAGDM methods based on Maclaurin symmetric mean (MSM) aggregation operators. First, the Maclaurin symmetric mean is extended to intuitionistic linguistic environment and two new aggregation operators are developed for aggregating the intuitionistic linguistic information, such as the intuitionistic linguistic Maclaurin symmetric mean (ILMSM) operator and the weighted intuitionistic linguistic Maclaurin symmetric mean (WILMSM) operator. Then, some desirable properties and special cases of these operators are discussed in detail. Furthermore, this paper also develops two new Maclaurin symmetric mean operators for aggregating the intuitionistic uncertain linguistic information, including the intuitionistic uncertain linguistic Maclaurin symmetric mean (IULMSM) operator and the weighted intuitionistic uncertain linguistic Maclaurin symmetric mean (WIULMSM) operator. Based on the WILMSM and WIULMSM operators, two approaches to MAGDM are proposed under intuitionistic linguistic environment and intuitionistic uncertain linguistic environment, respectively. Finally, two practical examples of investment alternative evaluation are given to illustrate the applications of the proposed methods. [ABSTRACT FROM AUTHOR]

A cubic bipolar fuzzy set (CBFS) is a new approach in computational intelligence and decision-making under uncertainty. This model is the generalization of bipolar fuzzy sets to deal with two-sided contrasting features which can describe the information with a bipolar fuzzy number and an interval-valued bipolar fuzzy number simultaneously. In this paper, the Dombi's operations are analyzed for information aggregation of cubic bipolar fuzzy numbers (CBFNs). The Dombi's operations carry the advantage of more pliability and reliability due to the existence of their operational parameters. Owing to the pliable nature of Dombi's operators, this research work introduces new aggregation operators named as cubic bipolar fuzzy Dombi weighted averaging (CBFDWA) operator and cubic bipolar fuzzy Dombi ordered weighted averaging (CBFDOWA) operator with ℙ -order and ℝ -order, respectively. Additionally, this paper presents some significant characteristics of suggested operators including, idempotency, boundedness and monotonicity. Moreover, a robust multi-criteria decision making (MCDM) technique is developed by using ℙ -CBFDWA and ℝ -CBFDWA operators. Based on the suggested operators a practical application is demonstrated towards MCDM under uncertainty. The comparison analysis of suggested Dombi's operators with existing operators is also given to discuss the rationality, efficiency and applicability of these operators. [ABSTRACT FROM AUTHOR]

The emergency response to the health care management in the hospital do not have enough systems for providing medical service to the COVID19 patients (e.g., scheduled or nonemergency). Therefore, in this paper, we developed an emergency decision support model for consideration of patients care and admission scheduling (PCAS). The complex decision support model assigns a set of patients into a number of restricted resources like rooms, time slots, and beds depending on satisfying a number of predefined constraints such as disease severity, waiting time, and disease types. This is a crucial issue with multi‐criteria decision making (MCDM). In this paper, we first begin an assessment into the admission and care to tackle this issue and collect four factors effecting the admission and care of COVID‐19 patients that form a system of criteria. While there is a lot of vague and uncertain data that can be effectively depicted for these indicators by the spherical hesitant fuzzy set, then, we implement a strong MCDM method based on list of aggregation operators to address the patients' hospital admission and care. Last of all, a numerical real‐life application about PCAS is provided to demonstrate the validity of the proposed approaches along with relevant discussions, the merits of proposed approaches are also analyzed by validity test. The proposed methodology has been shown to help hospitals manage the admissions and care of COVID‐19 patients in a flexible manner. [ABSTRACT FROM AUTHOR]

The paper aims are to impersonate some robust sine-trigonometric operations laws to determine the group decision-making process under the Pythagorean fuzzy set (PFS) situation. The PFS has a notable feature to trade with the dubious information with a broader membership representation space than the intuitionistic fuzzy set. Based on it, the present paper is classified into three phases. The first phase is to introduce new operational laws for PFS. The main idea behind these proposed operations is to incorporate the qualities of the sine function, namely periodicity and symmetric about the origin towards the decisions of the objects. Secondly, based on these laws, numerous operators to aggregate the information are acquired along with their requisite properties and relations. Finally, an algorithm to interpret the multiattribute group decision making problem is outlined based on the stated operators and manifest it with an illustrative example. A detailed comparative interpretation is achieved with some of the existing methods to reveal their influences. [ABSTRACT FROM AUTHOR]

In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and fuzziness information. This paper presents a multi-attribute group decision making method based on novel sine aggregation operators to help decision makers choose the optimal alternative. Moreover, the well-known sine trigonometry function preserves the periodic and symmetric nature about the origin, and hence, it satisfies the decision makers preferences over the multi-time phase parameters. Keeping these features and the importance of the spherical fuzzy (SF) sets, the objective of this paper is to present some robust sine trigonometric (ST) operation laws for SF sets. Associated with these laws, we define some series of new aggregation operators (AOs) named as ST-weighted averaging and geometric operators to aggregate the spherical fuzzy information. Afterward, we present group decision making techniques to solve the multi-attribute group decision making problems based on proposed AOs and illustrate with a numerical example of an internet finance soft power evaluation problem to validate it. Also, we conduct some comparison analysis to study the reasonability and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

The population growth and urbanization has caused an exponential increase in waste material. The proper disposal of waste is a challenging problem nowadays. The proper disposal site selection with typical sets and operators may not yield fruitful results. To handle such problems, the exponential aggregation operators based on neutrosophic cubic hesitant fuzzy sets are proposed. For appropriate decisions in a decision-making problem, it is important to have a handy environment and aggregation operators. Many multi attribute decision making methods often ignore the uncertainty and hence yields the results which are not reliable. The neutrosophic cubic hesitant fuzzy set can efficiently handle the complex information in a decision-making problem, as it combines the advantages of neutrosophic cubic set and hesitant fuzzy set. In this paper first we establish exponential operational laws in neutrosophic cubic hesitant fuzzy sets, in which the exponents are neutrosophic cubic hesitant fuzzy numbers and bases are positive real numbers. In order to use neutrosophic cubic hesitant fuzzy sets in decision making, we are developing exponential aggregation operators and investigate their properties in the current study. In many multi expert decision-making methods there are different decision matrices but same weighting vector for attributes. The results of a multi expert decision-making problem becomes more reliable if every decision expert has its own decision matrix along with his own weighting vector for attributes. In this study, we are developing multi expert decision-making method that uses different weights for an attribute corresponding to different experts. At the end we present two applications of exponential aggregation operators in environmental protection multi attribute decision making problems. [ABSTRACT FROM AUTHOR]