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Multi-attribute decision-making (MADM) is a methodology for solving decision problems with a finite set of alternatives. The several methods of MADM require weights for the criteria and the alternatives to provide a solution. The Ordinal Priority Approach (OPA) is a recently proposed method for MADM that innovates; it does not require these inputs, just the rankings of criteria and alternatives. This article introduces a new hybrid method for MADM: the Intuitionistic Fuzzy Ordinal Priority Approach with Grey Relational Analysis (OPA-IF-GRA). OPA-IF-GRA combines GRA with OPA-IF, a newer extension of OPA that includes intuitionistic fuzzy sets to incorporate uncertainty into the decision-making process. The article presents an OPA-IF-GRA application for solving an electronics engineering problem, considering four criteria and six alternatives. The solution of OPA-IF-GRA is compared with the solutions obtained with three other MADM methods. [ABSTRACT FROM AUTHOR]

A novel score function based on the Poincaré metric is proposed and applied to a decision-making problem. Decision-making on Fuzzy Sets (FSs) has been considered due to the flexibility of the data, and it is applied to the decisionmaking. However, decisions with FSs are sometimes nondecisive even for different membership degrees. Hence, Intuitionistic Fuzzy Sets (IFSs) data is applied to design a score function for the decision-making with the Poincaré metric. This function is supported by the profound information of IFSs; IFSs include hesitation degree together with membership and non-membership degree. Hence, IFS membership and non-membership degree are expressed as two-dimensional vectors satisfying the Poincaré metric for simplification. At the same time, the proposed approach addresses the hesitation information in the IFS data. Next, a score function is proposed, constructed and provided. The proposed score function has a strict monotonic property and addresses the preference without resorting to the accuracy function. The strict monotonic property guarantees the preference of all attributes. Additionally, the existing problem of score function design in IFSs is addressed: they return zero scores even with different meanings for the same membership and non-membership degree. The advantages of the proposed score function over existing ones are demonstrated through illustrative examples. From the calculation results, the proposed decision score function discriminates between all candidates. Hence, the proposed research provides a solid foundation for the hesitation analysis on the decision-making problem. [ABSTRACT FROM AUTHOR]

Real-world multi-criteria problems can be solved using multi-criteria decision-making (MCDM) techniques that allow a variety of qualitative and quantitative aspects to be taken into account simultaneously. There have been an increasing number of theories and approaches created for solving distinct MCDM situations with proportionate and conflicting aspects. Judgments about alternatives considered in MCDM methods may change according to the circumstances and conditions that may occur in the future. Many existing decision-making approaches do not take this situation into account, which may cause wrong decisions. Therefore, it is necessary to create adaptable decision models that make use of both current and future information in order to handle a dynamic decision system. The novelty of this study is to develop a novel MCDM method and its intuitionistic fuzzy set extension, Multi-Period Dynamic ASsessment (MP-DAS) and Intuitionistic Fuzzy Multi-Period Dynamic ASsessment (IF MP-DAS), to provide a dynamic decision approach based on present and future information simultaneously. The objective is to present a dynamic-based MCDM method with as many future time points as experts prefer and a stronger multi-measurement system. By concentrating on medium- and long-term judgments that take into account potential variations of the addressed components, the established method enables more informed decisions to be made for complicated problems. In the study, a multi-measurement system is developed by using both Euclidean distance and distance from average solution. The proposed dynamic decision method can be applied by managers and decision-makers as a decision support system. To show the efficiency and applicability of the developed method, a renewable energy source selection problem is handled, where the assessments include possible variations for both developed methods. A comprehensive sensitivity analysis is conducted to confirm the effectiveness and stability of the method for the developed methods. The results of the comparison analysis with distance-based MCDM and intuitionistic fuzzy distance-based MCDM methods showed that the developed method is superior to other MCDM methods. [ABSTRACT FROM AUTHOR]

Divergence measure between intuitionistic fuzzy sets (IFSs) is important due to its wide range of applications in various fields including pattern recognition, image segmentation, decision-making and clustering. This paper introduces the characterization of belief and plausible intuitionistic fuzzy sets (BP-IFSs) to explore novel logarithmic and non-logarithmic divergence measures between two BP-IFSs. These measures are regarded as highly useful approaches to express ambiguous information within the framework of Dempster–Shafer Theory (DST). An axiomatic definition based on proposed divergence measures is also stated within a frame work of newly established theory. Furthermore, the proposed divergence measures are utilized in three different applications: (i) an example related to the recognition of BP-IFS patterns is provided to demonstrate the practicality of the proposed method in pattern recognition. (ii) An example of Hierarchical agglomerative clustering is also provided. (iii) Introduces an innovative Belief and Plausible Combinative Distance-based Assessment (BP-CODAS) method based on proposed measures for resolving Multicriteria Decision Making (MCDM) problems connected to child labor in under developed countries. The examples provided in these different directions are sufficient to demonstrate the effectiveness, applicability and viability of the suggested methods within the framework of generalized DST. [ABSTRACT FROM AUTHOR]

We provide an analytic examination for a new proposed relative weights to find the inherent property of this new relative weight. Our findings will help researchers in the future to apply this new relative weight and develop their own new relative weights to face the complex and changing real world. [ABSTRACT FROM AUTHOR]

We studied a paper to apply a method of maximizing deviations to multiple attribute decision-makings under intuitionistic fuzzy environment that have found several new methods and theorems for maximum problem under some specific conditions with insufficient information environment. We showed that the Lagrange multiplication method used by the paper can be replaced by our simplify approach with the Cauchy Schwarz inequality. The purpose of this paper is fourfold. First, the iteration method for the problem within the range of weights is well developed and with appropriate explanation if the weight vector of attributes is bounded. Second, if the weight vector of attributes is completely unknown, we could directly and swiftly derive the weight by the Cauchy-Schwarz inequality such that the complicated approach by the Lagrange multiplication method becomes redundant. Third, we prove the results of score function and rank for one-norm will not be preserved in the two-norm. Fourth, the same numerical examples are examined again and have different outcome to demonstrate our findings is superior to the previously published results. [ABSTRACT FROM AUTHOR]

Neutrosophy is the study of neutralities and extends the discussion of the truth of opinions. Neutrosophic logic may be employed in any domain, for providing the solution for the ambiguity problems. Several real-time data experience problems such as indeterminacy, incompleteness, and inconsistency. A fuzzy set provides an uncertain solution, and intuitionistic fuzzy set handles incomplete data, but both fail to manage uncertain data. Before bankruptcy, financial distress is the early stage. Bankruptcies caused by financial problems can be seen in the financial statement of the company. The capability to predict financial problems became a crucial area of research since it provides earlier warning for the company. Moreover, predicting financial problems is advantageous for creditors and investors. In this article, we develop a new Dimensionality Reduction with Neutrosophic Net-RBF Neural Networks (DR-NSRBFNN) technique for FCP process. The DR-NSRBFNN technique concentrates on the predictive modelling of financial distress. In the DR-NSRBFNN technique, two major stages are involved. In the preliminary phase, the high dimensionality features can be reduced by the use of arithmetic optimization algorithm (AOA). In the second phase, the DR-NSRBFNN technique applies the NSRBFNN model to predict financial distress. The performance evaluation of the DR-NSRBFNN technique can be examined using distinct aspects. The widespread study stated the improved performance of the DR-NSRBFNN technique compared to other systems. [ABSTRACT FROM AUTHOR]

Kernel matching pursuit (KMP) requires every step of the searching process to be global optimal searching in the redundant dictionary of functions in order to select the best matching signal structure. Namely, the dictionary learning time of KMP is too long. To solve the above drawbacks, a rough dataset was divided into some small-sized dictionaries to substitute local searching for global searching by using the property superiority of dynamic clustering performance, which is also superior in the intuitionistic fuzzy c-means (IFCM) algorithm. Then, we proposed a novel technique for KMP based on IFCM (IFCM-KMP). Subsequently, three tests including classification, effectiveness, and time complexity were carried out on four practical sample datasets, the conclusions of which fully demonstrate that the IFCM-KMP algorithm is superior to FCM and KMP. [ABSTRACT FROM AUTHOR]

This study introduces an innovative method to implement Failure Mode and Effect Analysis (FMEA) in an Intuitionistic Fuzzy (IF) environment and targets inherent limitations of traditional FMEA, particularly its reliance on precise numerical values that can lead to human subjectivity and compromise accuracy of analysis. The primary aim is to increase the objectivity in evaluating Failure Modes (FMs) in industrial settings, thus enhancing safety and quality assessments. The novel approach integrates the Measurement Alternatives and Ranking according to the Compromise Solution (MARCOS) method within an IF framework. An implementation at a defense industry company is performed for evaluation of the FMs by four Decision Makers (DMs), each possessing different levels of experience and system knowledge. A key innovation of this study is the unique weighting methodology applied to DMs, based on predefined rules, which acknowledges and quantifies their varied expertise and insights. Our methodology significantly contributes to the study's practicality and significance in ranking FMs, emphasizing its effectiveness, robustness, and accuracy. The findings reveal that this method greatly reduces the subjectivity found in traditional FMEA, also providing a more detailed and reliable assessment. This is achieved by adapting the analysis to the specific knowledge levels of the DMs, leading to more dependable and objective quality evaluations in industrial processes. The application of this method in the real‐world setting demonstrates its practical relevance and potential for wider adoption. [ABSTRACT FROM AUTHOR]

Convolutional Neural Networks (CNNs) are a kind of artificial neural network designed to extract features and find out patterns for tasks such as segmentation, recognizing objects, and drawing up classification. Within a CNNs architecture, pooling operations are used until the number of parameters and the computational complexity are reduced. Numerous papers have focused on investigating the impact of pooling on the performance of Convolutional Neural Networks (CNNs), leading to the development of various pooling models. Recently, a fuzzy pooling operation based on type-1 fuzzy sets was introduced to cope with the local imprecision of the feature maps. However, in fuzzy set theory, it is not always accurate to assume that the degree of non-membership of an element in a fuzzy set is simply the complement of the degree of membership. This is due to the potential existence of a hesitation degree, which implies a certain level of uncertainty. To overcome this limitation, intuitionistic fuzzy sets (IFS) were introduced to incorporate the concept of a degree of hesitation. In this paper, we introduce a novel pooling operation based on intuitionistic fuzzy sets to incorporate the degree of hesitation heretofore neglected by a fuzzy pooling operation based on classical fuzzy sets, and we investigate its performance in the context of image classification. Intuitionistic pooling is performed in four steps: bifuzzification (by the transformation of data through the use of membership and non-membership maps), first aggregation (through the transformation of the IFS into a standard fuzzy set, second aggregation (through the transformation and use of a sum operator), and the defuzzification of feature map neighborhoods by using a max operator. IFS pooling is used for the construction of an intuitionistic pooling layer that can be applied as a drop-in replacement for the current, fuzzy (type-1) and crisp, pooling layers of CNN architectures. Various experiments involving multiple datasets demonstrate that an IFS-based pooling can enhance the classification performance of a CNN. A benchmarking study reveals that this significantly outperforms even the most recent pooling models, especially in stochastic environments. [ABSTRACT FROM AUTHOR]

The innovation process typically follows a predefined sequence of phases: idea generation, screening, evaluation/selection, development, and launch/diffusion. This process exhibits a dynamic and cyclic structure. At each stage, potential ideas may undergo elimination or redefinition based on considerations such as their problem–solution fit or product–market fit. Consequently, the idea evaluation phase can be conducted continuously, involving varying numbers of potential ideas. To address the challenges associated with this process, a systematic approach for selecting the best new project ideas is essential. This study introduces the IF-ABAC method, which extends the alternative-by-alternative comparison-based (ABAC) method to the intuitionistic fuzzy (IF) environment. The proposed approach represents the first combination of fuzzy sets and ABAC within a group decision-making environment. The IF-ABAC method is employed during the evaluation phase, with the best–worst method determining the criteria weights. The study describes how the IF-ABAC approach adeptly manages changes in the set of alternatives after the decision process, addressing the dynamics inherent in decision-making environments. The study further includes an analysis of innovative business ideas in a real case study from Turkey, demonstrating the feasibility and efficiency of the proposed approach. A comprehensive sensitivity analysis is conducted to illustrate the stability and utility of the method. Finally, the results are compared with three other IF-based multi-criteria decision-making methods from the literature. The study concludes by asserting that the proposed IF-ABAC method provides a comprehensive and practical approach to select innovation project ideas in an environment of uncertainty and complexity. [ABSTRACT FROM AUTHOR]

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a novel methodology to the three-way decision idea. Initially, we revamp the three-way decision model using rough set theory and incorporate interval-valued classes to handle intuitionistic fuzzy data. Secondly, we explore the use of intuitionistic fuzzy power weighted and intuitionistic fuzzy power weighted geometric aggregation operators to consolidate attribute values within the data system. Furthermore, we present a case study in the medical field to exhibit the validity and efficiency of our offered technique. This innovative method enables us to classify participants into three distinct zones based on their symptoms. The manuscript concludes with a summary of key points provided by the authors. [ABSTRACT FROM AUTHOR]

The extensions of ordinary fuzzy sets are problematic because they require decimal numbers for membership, non-membership and indecision degrees of an element from the experts, which cannot be easily determined. This will be more difficult when three or more digits' membership degrees have to be assigned. Instead, proportional relations between the degrees of parameters of a fuzzy set extension will make it easier to determine the membership, non-membership, and indecision degrees. The objective of this paper is to present a simple but effective technique for determining these degrees with several decimal digits and to enable the expert to assign more stable values when asked at different time points. Some proportion-based models for the fuzzy sets extensions, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets are proposed, including their arithmetic operations and aggregation operators. Proportional fuzzy sets require only the proportional relations between the parameters of the extensions of fuzzy sets. Their contribution is that these models will ease the use of fuzzy set extensions with the data better representing expert judgments. The imprecise definition of proportions is also incorporated into the given models. The application and comparative analyses result in that proportional fuzzy sets are easily applied to any problem and produce valid outcomes. Furthermore, proportional fuzzy sets clearly showed the role of the degree of indecision in the ranking of alternatives in binomial and trinomial fuzzy sets. In the considered car selection problem, it has been observed that there are minor changes in the ordering of intuitionistic and spherical fuzzy sets. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy (IF) sets are valuable tools for describing uncertain information in Multi-Criteria Group Decision Making (MCGDM), where the elements have degrees of membership and non-membership. IF aggregation operator is a popular data processing method that can be used for data dimensionality reduction, feature extraction, data compression, and so on. Some existing MCGDM techniques based on IF aggregation operators have been criticized for reasons that include disregarding the comprehensive correlations of the criteria and ignoring the monotonicity of the decision information. This paper aims to construct some IF aggregation operators based on Yager's triangular norms and Heronian mean to shed light on decision-making issues. At first, some novel IF operations such as Yager sum, Yager product, and Yager scalar multiplication on IFSs are presented. Based on these new operations, the generalized IF Yager Heronian average (GIFYHA) operator and the generalized IF Yager weighted Heronian average (GIFYWHA) operator are proposed and their corresponding properties are also proved in detail. Then, an improved MCGDM algorithm is constructed that relies on suggested operators. Its effectiveness and applicability are verified by applying it to select the best location for a company. In addition, the sensitivity of the parameters in the proposed operator to decision findings is also discussed. Finally, the comparative analysis of the proposed operator with the existing operators shows that the proposed operator is suitable for aggregating IF information with correlations both on "non-empty lattice" and total orders on IF values. [ABSTRACT FROM AUTHOR]

To achieve better surface quality and close dimensional tolerance, finishing operations, like surface and cylindrical grinding are widely employed in many of the manufacturing industries. For determining the optimal values of various grinding parameters, like wheel speed, feed rate, depth of cut, width of cut, wheel material etc., multi-criteria decision making (MCDM) methods have already proven to be an effective way to simultaneously deal with multiple input parameters, affecting attainment of the required surface finish. In this paper, three MCDM tools, i.e. multi-attributive border approximation area comparison (MABAC), compromise ranking of alternatives from distance to ideal solution (CRADIS) and evaluation based on distance from average solution (EDAS) are adopted in intuitionistic fuzzy (IF) environment to demonstrate their effectiveness in solving parametric optimization problems of a surface grinding process and a cylindrical grinding process, while considering varying opinions of multiple stakeholders with respect to relative importance assigned to the responses. In the surface grinding process, all the three IF-MCDM tools identify grinding wheel speed = 90 m/s, infeed speed = 0.5 m/min and grinding depth = 0.1 mm as the optimal parametric combination. In the cylindrical grinding process, an intermix of different input parameters as work speed = 36 m/min, feed rate = 25 mm/min and depth of cut = 0.02 mm is singled out as the best by IF-MABAC and IF-CRADIS, and ranked second-best by IF-EDAS method. Thus, the derived results validate applicability of the considered IF-MCDM methods in effectively optimizing different grinding processes in an uncertain group decision making environment. [ABSTRACT FROM AUTHOR]

The fuzzy set theory was introduced to handle uncertainty due to imprecision, vagueness and partial information. Then, its extensions such as intuitionistic fuzzy set, intuitionistic interval-valued fuzzy set, Pythagorean fuzzy set were introduced and applied successfully in many fields. Then another extension of orthopair fuzzy set was introduced as Fermatean fuzzy set which is characterized by membership degree and non-membership degree which makes it to provide an excellent tool to present imprecise opinions of humans in decision-making processes. This study is devoted to construct a novel Fermatean fuzzy divergence measure along with its evidence of legitimacy and to deliberate its key properties. The proposed divergence measure for Fermatean fuzzy sets with weighted aggregation operators is applied to fix decision-making problems through numerical illustrations. A comparative study is given between the proposed Fermatean fuzzy divergence measure and the extant methods to test its effectiveness, viability and expediency. Their results were compared in order to check the superiority of the proposed measure. [ABSTRACT FROM AUTHOR]

Uncertainty in medical diagnosis is the main challenge in medical emergencies (MEs) experienced by triage nurses and physicians in the emergency department (ED). The intuitionistic fuzzy correlation coefficient (IFCC) approach is used to analyze and interpret the relationship between variables in an uncertain environment. Assorted methods that involve applying a correlation coefficient under intuitionistic fuzzy sets (IFSs) were constructed based on Pearson's correlation model with various drawbacks. In this work, we construct two new intuitionistic fuzzy correlation measures (IFCMs) based on Spearman's correlation model. It is demonstrated that the Spearman-based IFCMs are appropriate for measuring correlation coefficients without any drawbacks. In addition, we show that the Spearman-based IFCMs overcome all the shortcomings of the associated IFCC methods. Equally, the Spearman-based IFCMs satisfy the maxims of the correlation coefficient that have been delineated in the classical case of correlation coefficient. Due to the challenges that uncertainty in medical diagnosis pose to MEs and the proficiency of the IFCC approach, we discuss the application of the constructed IFCMs in a triage process for an effective medical diagnosis during an ME. The medical data for the triage process are obtained via a knowledge-based approach. Finally, comparative analyses are carried out to ascertain the validity and authenticity of the developed Spearman-based IFCMs relative to other IFCC approaches. [ABSTRACT FROM AUTHOR]

Purpose: Identifying and prioritizing supply chain risk is significant from any product's quality and reliability perspective. Under an input-process-output workflow, conventional risk prioritization uses a risk priority number (RPN) aligned to the risk analysis. Imprecise information coupled with a lack of dealing with hesitancy margins enlarges the scope, leading to improper assessment of risks. This significantly affects monitoring quality and performance. Against the backdrop, a methodology that identifies and prioritizes the operational supply chain risk factors signifies better risk assessment. Design/methodology/approach: The study proposes a multi-criteria model for risk prioritization involving multiple decision-makers (DMs). The methodology offers a robust, hybrid system based on the Intuitionistic Fuzzy (IF) Set merged with the "Technique for Order Performance by Similarity to Ideal Solution." The nature of the model is robust. The same is shown by applying fuzzy concepts under multi-criteria decision-making (MCDM) to prioritize the identified business risks for better assessment. Findings: The proposed IF Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) for risk prioritization model can improve the decisions within organizations that make up the chains, thus guaranteeing a "better quality in risk management." Establishing an efficient representation of uncertain information related to traditional failure mode and effects analysis (FMEA) treatment involving multiple DMs means identifying potential risks in advance and providing better supply chain control. Research limitations/implications: In a company's supply chain, blockchain allows data storage and transparent transmission of flows with traceability, privacy, security and transparency (Roy et al., 2022). They asserted that blockchain technology has great potential for traceability. Since risk assessment in supply chain operations can be treated as a traceability problem, further research is needed to use blockchain technologies. Lastly, issues like risk will be better assessed if predicted well; further research demands the suitability of applying predictive analysis on risk. Practical implications: The study proposes a hybrid framework based on the generic risk assessment and MCDM methodologies under a fuzzy environment system. By this, the authors try to address the supply chain risk assessment and mitigation framework better than the conventional one. To the best of their knowledge, no study is found in existing literature attempting to explore the efficacy of the proposed hybrid approach over the traditional RPN system in prime sectors like steel (with production planning data). The validation experiment indicates the effectiveness of the results obtained from the proposed IF TOPSIS Approach to Risk Prioritization methodology is more practical and resembles the actual scenario compared to those obtained using the traditional RPN system (Kim et al., 2018; Kumar et al., 2018). Originality/value: This study provides mathematical models to simulate the supply chain risk assessment, thus helping the manufacturer rank the risk level. In the end, the authors apply this model in a big-sized organization to validate its accuracy. The authors validate the proposed approach to an integrated steel plant impacting the production planning process. The model's outcome substantially adds value to the current risk assessment and prioritization, significantly affecting better risk management quality. [ABSTRACT FROM AUTHOR]

Uncertainty in medical diagnosis is the main challenge in medical emergencies (MEs) experienced by triage nurses and physicians in the emergency department (ED). The intuitionistic fuzzy correlation coefficient (IFCC) approach is used to analyze and interpret the relationship between variables in an uncertain environment. Assorted methods that involve applying a correlation coefficient under intuitionistic fuzzy sets (IFSs) were constructed based on Pearson's correlation model with various drawbacks. In this work, we construct two new intuitionistic fuzzy correlation measures (IFCMs) based on Spearman's correlation model. It is demonstrated that the Spearman-based IFCMs are appropriate for measuring correlation coefficients without any drawbacks. In addition, we show that the Spearman-based IFCMs overcome all the shortcomings of the associated IFCC methods. Equally, the Spearman-based IFCMs satisfy the maxims of the correlation coefficient that have been delineated in the classical case of correlation coefficient. Due to the challenges that uncertainty in medical diagnosis pose to MEs and the proficiency of the IFCC approach, we discuss the application of the constructed IFCMs in a triage process for an effective medical diagnosis during an ME. The medical data for the triage process are obtained via a knowledge-based approach. Finally, comparative analyses are carried out to ascertain the validity and authenticity of the developed Spearman-based IFCMs relative to other IFCC approaches.

Introduction: Retailers are powerful agents in product distribution due to their proximity to final consumers and their potential to create markets. Choosing the location of a retail store is a strategic decision and a long-term investment, impacting both customer satisfaction and company profitability amidst market changes and fierce competition. This study aims to develop a method for selecting the best retail store locations for Ofogh Kourosh by strategically ranking potential locations using criteria such as population, store location characteristics, economic considerations, and competition. Methods: Given the increasing complexity of retail store location selection and the uncertainty in evaluating criteria, a multi-criteria decision-making structure is used alongside a fuzzy intuitionistic approach. Intuitionistic fuzzy numbers extend traditional fuzzy numbers by incorporating a hesitation degree in addition to membership and non-membership degrees, better modeling the uncertainty faced by decision-makers. In this study, five main criteria are considered: cost, competition, traffic density, vehicle traffic volume, physical characteristics, and store location. These criteria were identified through expert interviews. Twelve sub-criteria, including rent cost, equipment cost, competitor strength, number of competitors, distance to competitors, vehicle traffic volume, pedestrian traffic volume, store size, parking space, proximity to main streets, proximity to commercial centers, and proximity to residential complexes, were selected to choose the best location among five potential sites. The proposed method integrates the Analytical Hierarchy Process (AHP) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) based on interval-valued intuitionistic fuzzy sets to evaluate criteria and rank the proposed options. The AHP method, based on interval-valued intuitionistic fuzzy sets, was used to consider uncertainty in decision-making and to calculate the weight of the criteria. The TOPSIS method was applied to prioritize the proposed options for locating a new retail store. Region 4 of Tehran city, the most populous area in the city, was considered for the case study. Ofogh Kourosh has 40 stores in this region, supplied by two large warehouses. Results and discussion: The numerical results indicate that the sub-criteria of rent cost (from the cost criterion) and proximity to commercial centers (from the store location criterion) were the most and least important criteria, respectively. Among the five candidate locations, locations four and one were ranked highest and lowest for establishing new stores. To validate the proposed method, the evaluation results were compared with those obtained using the AHP-WASPAS method based on interval-valued intuitionistic fuzzy sets. Both methods identified location four as the best site for a new retail store and location one as the least suitable due to its location and competitor conditions. Conclusion: The study demonstrates that using a combined AHP-TOPSIS method based on interval-valued intuitionistic fuzzy sets is effective for evaluating and ranking potential retail store locations. This approach accounts for the uncertainty in decision-making and provides a comprehensive evaluation of various criteria, ultimately aiding strategic planning and investment decisions in the retail sector.

Sustainable battery supplier (SBS) selection of battery-swapping station belongs to a complex multi-criteria decision-making (MCDM) problem due to the fact that included multiple and often conflicting criteria. To this end, this study presents a comparative analysis of selecting SBS using four fuzzy MCDM methods, and a case is executed to compare the ranking results obtained by the proposed four MCDM methods. From the weighting results of criteria, it is observed that economic criteria is the first priority in all evaluation criteria, followed by the technical, social, and environmental criteria in descending order. In terms of the priorities and recommendations of multiple SBSs for the battery swapping station, the comparative analysis demonstrates that the rankings of all alternatives obtained by all approaches are in high agreement, except that determined by fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) slightly varies from the other three approaches, and none of these MCDM methods are deemed to be absolutely "perfect". If possible, we recommend that more than one method should be applied to the same problem to provide a more comprehensive decision basis. If not possible, it is suggested to use the fuzzy VIKOR since it shows more superior potential in sustainable supplier decision analysis. [ABSTRACT FROM AUTHOR]

Spatial and temporal uncertainties are found in data for many critical applications. This paper describes the use of interval-based representations of some spatial and temporal information. Uncertainties in the information can arise from multiple sources in which degrees of support and non-support occur in evaluations. This motivates the use of intuitionistic fuzzy sets to permit the use of the positive and negative memberships to capture these uncertainties. The interval representations will include both simple and complex or nested intervals. The relationships between intervals such as overlapping, containing, etc. are then developed for both the simple and complex intervals. Such relationships are required to support the aggregation approaches of the interval information. Both averaging and merging approaches to interval aggregation are then developed. Furthermore, potential techniques for the associated aggregation of the interval intuitionistic fuzzy memberships are provided. A motivating example of maritime depth data required for safe navigation is used to illustrate the approach. Finally, some potential future developments are discussed. [ABSTRACT FROM AUTHOR]

In this paper we have introduced intuitionistic fuzzy semi γ* generalized irresolute mappings and investigated some of their properties. Also we have provided some characterization of intuitionistic fuzzy semi γ* generalized irresolute mappings. [ABSTRACT FROM AUTHOR]

The disaster caused by landslide is huge. To prevent the spread of the disaster to the maximum extent, it is particularly important to carry out landslide disaster treatment work. The selection of landslide disaster treatment alternative is a large scale group decision-making (LSGDM) problem. Because of the wide application of social media, a large number of experts and the public can participate in decision-making process, which is conducive to improving the efficiency and correctness of decision-making. A IF-TW-LSGDM method based on three-way decision (TWD) and intuitionistic fuzzy set (IFS) is proposed and applied to the selection of landslide treatment alternatives. First of all, considering that experts and the public participate in the evaluation of LSGDM events, respectively, the method of obtaining and handling the public evaluation information is given, and the information fusion approach of the public and experts evaluation information is given. Second, evaluation values represented by fuzzy numbers are converted into intuitionistic fuzzy numbers (IFNs), and the intuitionistic fuzzy evaluation decision matrix described by IFNs is obtained. Then, a new LSGDM method of alternatives classification and ranking based on IFS and TWD is proposed, the calculation steps and algorithm description are given. In this process, we first cluster the experts, then consider the identification and management of non-cooperative behavior of expert groups. This work provides an effective method based on LSGDM for the selection of landslide treatment alternatives. Finally, the sensitivity of parameters is analyzed, and the feasibility and effectiveness of this method are compared and verified. [ABSTRACT FROM AUTHOR]

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A highly relevant topic in the actuarial literature is so-called "claim reserving" or "loss reserving", which involves estimating reserves to be provisioned for pending claims, as they can be deferred over various periods. This explains the proliferation of methods that aim to estimate these reserves and their variability. Regression methods are widely used in this setting. If we model error terms as random variables, the variability of provisions can consequently be modelled stochastically. The use of fuzzy regression methods also allows modelling uncertainty for reserve values using tools from the theory of fuzzy subsets. This study follows this second approach and proposes projecting claim reserves using a generalization of fuzzy numbers (FNs), so-called intuitionistic fuzzy numbers (IFNs), through the use of intuitionistic fuzzy regression. While FNs allow epistemic uncertainty to be considered in variable estimation, IFNs add bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis is grounded in the ANOVA two-way framework, which is adapted to the use of intuitionistic regression. Similarly, we compare our results with those obtained using deterministic and stochastic chain-ladder methods and those obtained using two-way statistical ANOVA. [ABSTRACT FROM AUTHOR]

In the dynamic world of financial investment, crafting an optimal stock portfolio that judiciously balances risk, return, and efficiency emerges as a critical challenge. Despite the wealth of research on financial portfolio optimization, prevailing methodologies predominantly emphasize either risk minimization or return maximization, often overlooking the imperative for a holistic strategy that simultaneously boosts efficiency and effectiveness. Addressing this gap in the literature, this study introduces an innovative four-objective model that intricately blends risk, return, and efficiency considerations for the strategic selection of stock portfolios. This model ingeniously integrates the foundational principles of Markowitz’s mean-variance analysis with the sophisticated network data envelopment analysis (NDEA) techniques, significantly refining the portfolio selection methodology. It further distinguishes itself by incorporating returns represented as trapezoidal intuitionistic fuzzy numbers, adeptly capturing the inherent uncertainties in financial returns. Additionally, the model employs the network data envelopment analysis’s cross-efficiency principle, providing a nuanced measure of company performance. To effectively navigate the complexities of this model, we deploy the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a multi-objective genetic algorithm, demonstrating the model’s capability to unearth optimal solutions efficiently. The comparative analysis highlights that the proposed model significantly outperforms the efficiency and effectiveness of existing models, marking a substantial advancement in portfolio optimization strategies. [ABSTRACT FROM AUTHOR]

This paper introduces a semi-automated approach for the prioritization of software features in medium- to large-sized software projects, considering stakeholders' satisfaction and dissatisfaction as key criteria for the incorporation of candidate features. Our research acknowledges an inherent asymmetry in stakeholders' evaluations, between the satisfaction from offering certain features and the dissatisfaction from not offering the same features. Even with systematic, ordinal scale-based prioritization techniques, involved stakeholders may exhibit hesitation and uncertainty in their assessments. Our approach aims to address these challenges by employing the Binary Search Tree prioritization method and leveraging the mathematical framework of Intuitionistic Fuzzy Sets to quantify the uncertainty of stakeholders when expressing assessments on the value of software features. Stakeholders' rankings, considering satisfaction and dissatisfaction as features prioritization criteria, are mapped into Intuitionistic Fuzzy Numbers, and objective weights are automatically computed. Rankings associated with less hesitation are considered more valuable to determine the final features' priorities than those rankings with more hesitation, reflecting lower indeterminacy or lack of knowledge from stakeholders. We validate our proposed approach with a case study, illustrating its application, and conduct a comparative analysis with existing software requirements prioritization methods. [ABSTRACT FROM AUTHOR]

The literature frequently uses fuzzy inference methods for time series forecasting. In business and other situations, it is frequently necessary to forecast numerous time series. The q-Rung orthopair fuzzy set is a beneficial and competent tool to address ambiguity. In this research, a computational forecasting method based on q-Rung orthopair fuzzy time series has been created to deliver better prediction results to deal with situations containing higher uncertainty caused by large fluctuations in consecutive years' values in time series data and with no visualization of trend or periodicity. The main objective of this article is to handle time series forecasting with the usage of q-Rung orthopair fuzzy sets for things like floods, admission of students, number of patients, etc. After this, people can then manage issues that will arise in the future. Previously, there was a gap in determining the forecasting of data whose entire value of membership and non-membership exceeded 1. To fill this kind of gap, we used q-Rung orthopair fuzzy sets in time series forecasting. We also used numerous algebraic components for the q-Rung orthopair fuzzy time series, which has a union, max-min composition, cartesian product, and algorithm that are useful to calculate the method of data forecasting. Moreover, we also defined the algorithm and proposed MATLAB code that facilitates the execution of mathematical calculations, design, analysis, and optimization (structural and mathematical), and gives results with speed, correctness, and precision. At the end, we tested the model using historical student enrollment data and the annual peak discharge at Guddu Barrage. Furthermore, we calculated the error to get an idea of to what extent this method is suitable. [ABSTRACT FROM AUTHOR]

In response to the shortcomings of existing image noise detection algorithms that rely on the flawed intuitionistic fuzzy entropy (IFE) theory, a method of image noise detection and removal based on intuitionistic fuzzy amount of knowledge (IFAK) is proposed by introducing the latest knowledge measure (KM) theory and model. In the noise detection stage, the optimal average intensity of the noisy image foreground and background is determined based on the maximum IFAK, and the parametric model of noise detection is constructed accordingly to mark the probability of noise pixels and suspected noise pixels, showing excellent performance of noise detection. In the noise removal stage, a denoising model based on IFAK and probability of noise pixels is proposed by using the noise probability matrix, which can not only effectively denoise, but also better protect the characteristics of image edges and non-noise extreme pixels. Comparative experiments are carried out on standard datasets and classical test images, respectively. Experimental results show that the proposed method can accurately identify the image impulse noise and effectively realize image denoising. The overall performance outperforms other similar algorithms. The key metrics PSNR and SSIM are increased by 14.81% and 11.35%, respectively. In this paper, the latest KM theory is applied to image denoising, and excellent evaluation metrics and visual effects are obtained, while innovative applications of this theory in other related fields are also achieved.