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The purpose of the development of the paper is to construct probabilistic interval-valued hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model and to improve some preliminary aggregation operators such as probabilistic interval-valued hesitant fuzzy averaging (PIVHFA) operator, probabilistic interval-valued hesitant fuzzy geometric (PIVHFG) operator, probabilistic interval-valued hesitant fuzzy weighted averaging (PIVHFWA) operator, probabilistic interval-valued hesitant fuzzy ordered weighted averaging (PIVHFOWA) operator, probabilistic interval-valued hesitant fuzzy weighted geometric (PIVHFWG) operator and probabilistic interval-valued hesitant fuzzy ordered weighted geometric (PIVHFOWG) operator to cope with multicriteria group decision-making (MCGDM) problems in an efficient manner.

(1) To design probabilistic interval-valued hesitant fuzzy TOPSIS model. (2) To improve some of the existing aggregation operators. (3) To propose the Hamming distance, Euclidean distance, Hausdorff distance and generalized distance between probabilistic interval-valued hesitant fuzzy sets (PIVHFSs).

The results of the proposed model are discussed in comparison with the aggregation-based method from the related literature and found the effectiveness of the proposed model and improved aggregation operators.

A case study concerning the healthcare facilities in public hospital is addressed.

The notion of the proposed distance measure is used as rational tool to extend TOPSIS model for probabilistic interval-valued hesitant fuzzy setting.

The purpose of this paper is to propose a multi-criteria decision-making model based on the case-based reasoning (CBR) method for interval-valued probabilistic linguistic term set (IVPLTS), which can cluster different categories of building suppliers for targeted management.

First, a new score function and distance measure for IVPLTS are proposed. Second, a green building supplier evaluation criterion system is constructed from five aspects: operation management, green management, cooperation potential, service level and product information. Finally, the IVPLTS-CBR model is used to evaluate the green building suppliers and groups them into three preset categories.

The feasibility and validity of the proposed method are verified by comparing with the advanced TOPSIS method and the IVPLTS-based VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. The compared results show that the proposed method is more consistent with the actual situation and has strong theoretical significance and practical value.

This paper presents a new method for clustering construction suppliers. Decision makers can use this method to classify construction suppliers into different categories, so that they can be targeted management. In this way, suppliers can be better guided and motivated to accelerate the green transformation and contribute their share to achieve the strategic goal of carbon neutral and carbon peak as soon as possible.

A new score function and distance measure for IVPLTS are proposed. Besides, a novel IVPLTS-CBR method is applied to rank and cluster building suppliers.

Constructing a fuzzy control chart with interval-valued fuzzy data is an important topic in the fields of medical, sociological, economics, service and management. In particular, when the data illustrates uncertainty, inconsistency and is incomplete which is often the. case of real data. Traditionally, we use variable control chart to detect the process shift with real value. However, when the real data is composed of interval-valued fuzzy, it is not feasible to use such an approach of traditional statistical process control (SPC) to monitor the fuzzy control chart. The purpose of this paper is to propose the designed standardized fuzzy control chart for interval-valued fuzzy data set.

The general statistical principles used on the standardized control chart are applied to fuzzy control chart for interval-valued fuzzy data.

When the real data is composed of interval-valued fuzzy, it is not feasible to use such an approach of traditional SPC to monitor the fuzzy control chart. This study proposes the designed standardized fuzzy control chart for interval-valued fuzzy data set of vegetable price from January 2009 to September 2010 in Taiwan obtained from Council of Agriculture, Executive Yuan. Empirical studies are used to illustrate the application for designing standardized fuzzy control chart. More related practical phenomena can be explained by this appropriate definition of fuzzy control chart.

This paper uses a simpler approach to construct the standardized interval-valued chart for fuzzy data based on traditional standardized control chart which is easy and straightforward. Moreover, the control limit of the designed standardized fuzzy control chart is an interval with (LCL, UCL), which consists of the conventional range of classical standardized control chart.

The purpose of this article is to conduct a main path analysis of 627 articles on the theme of Pythagorean fuzzy sets (PFSs) in the Web of Science (WoS) from 2013 to 2020, to provide a conclusive and comprehensive analysis for researchers in this field, and to provide a study on preliminary understanding of PFSs.

The research topic of Pythagorean fuzzy fields, through keyword extraction and describing the changes in characteristic themes over the past eight years, are firstly examined. Main path analysis, including local and global main paths and key route paths, is then used to reveal the most influential relationships between papers and to explore the trajectory and structure of knowledge transmission.

The application of Pythagorean fuzzy theory to the field of decision-making has been popular, and combinations of the traditional Pythagorean fuzzy decision-making method with other fuzzy sets have attracted widespread attention in recent years. In addition, over the past eight years, research interest has shifted to different types of PFSs, such as interval-valued PFSs.

This paper implicates to investigate the growth in certain trends in the literature and to explore the main paths of knowledge dissemination in the domain of PFSs in recent years.

This paper aims to identify the topics in which researchers are currently interested, to help scholars to keep abreast of the latest research on PFSs.

The purpose of this paper is to develop a methodology based on TODIM (an acronym in Portuguese for interactive and multicriteria decision-making) approach for the selection of the best alternative in the context of multi criteria group decision-making (MCGDM) problems under possibilistic uncertainty in interval-valued Pythagorean fuzzy (IVPF) environment.

In this paper, IVPF-TODIM method is proposed. Some new point operator-based similarity measures (POSMs) for IVPF sets (IVPFSs) are introduced which have the capability to reduce the degree of uncertainty of the elements in the universe of discourse corresponding to IVPFS. Then the newly defined POSMs are used to compute the measure of relative dominance of each alternative over other alternatives in the IVPF-TODIM context. Finally, generalized mean aggregation operator is used to find the best alternative.

As the TODIM method is used to solve the MCGDM problems under uncertainty, POSMs are developed by using three parameters which can control the effect of decision-makers’ psychological perception under risk.

The decision values are used in IVPF numbers (IVPFNs) format.

The proposed method is capable to solve real-life MCGDM problems with not only IVPFNs format but also with interval-valued intuitionistic fuzzy numbers.

As per authors’ concern, no approach using TODIM with IVPFNs is found in literature to solve MCGDM problems under uncertainty. The final judgment values of alternatives using the extended TODIM methodology are highly corroborate in compare to the results of existing methods, which proves its great potentiality in solving MCGDM problems under risk.

In the literature, many multi attributes decision making (MADM) models allow evaluation of the alternatives considering their current or last performance. However, in some MADM problems, not only current performance of alternatives but also their past performance should be taken into account in order to select the most appropriate alternative. For this reason, the purpose of this paper is to develop four procedures to evaluate the alternatives in MADM problems with multi terms.

This study uses dynamic operators to aggregate the evaluation in different terms and then, grey relational analysis (GRA) and technique for order preference by similarity to ideal solution (TOPSIS) methods are utilized to determine the most appropriate alternative. Thus, four procedures which consist of these operators and methods are developed to evaluate the alternatives in multi terms.

Some numerical examples are presented for the proposed procedures in multi-terms. Moreover, these four procedures are compared with other four procedures. The analyses of the results show that dynamic aggregation operators based on intuitionistic fuzzy set (IFS) and interval valued intuitionistic fuzzy sets (IVIFS) with GRA and TOPSIS can be used jointly for MADM problems in which alternatives are evaluated for different terms.

One of the significant mistakes faced in some MADM problems is to take into account the current performance of alternatives or is to ignore their past performance. The right selection depends on past and current performance of the alternatives. The novelty of this study is to propose four procedures for solving MADM problems in multi terms based on IFS and IVIFS using dynamic aggregation operators and GRA and TOPSIS methods.

The purpose of this paper is to present one modification of the fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and to develop a corresponding computer program which could be used for the multicriteria decision making for problems in practice.

This method is based on the uncertainties and probabilities of input data for ratings of alternatives with respect to criteria and weights of criteria that are presented by triangular fuzzy numbers as probabilistic fuzzy values. These input data are transformed in the procedure into output data that are relevant for the ranking of alternatives and decision making.

The proposed method is based on the generalized mean and spread of fuzzy numbers that are calculated according to probability of fuzzy events due to Zadeh. Ranking of alternatives for relevant criteria performs according to relative expected closeness, coefficient of variation and relative standard deviation of distance of alternatives to the ideal solutions. The most acceptable rule is related to the minimal value of the expected relative distance to positive ideal solution, especially when the coefficient of variation of distance to this solution is small. The attached example, related to a real project, confirms these findings.

This paper proposes three novel contributions in this area. Unlike the methods proposed by other authors, the weighted fuzzy decision matrix is expressed by the matrix of generalized expected values and matrix of generalized variances. To compute elements of these two matrices, exact formulae are derived and then the modified fuzzy TOPSIS procedure is carried out.

The purpose of this paper is to provide a new approach to solving the interval-valued intuitionistic fuzzy stochastic multi-criteria decision-making (MCDM) problems.

To transform the interval-valued intuitionistic fuzzy number (IVIFN) into a computational numerical value, a new precision score (P-score) function is developed based on the degrees of membership, non-membership and hesitation. The prospect decision-making matrix is derived by applying P-score function and Prospect theory. A new criteria weighting model is put forward based on the least square method, the maximizing deviation method and Prospect theory. Consequently, combined criteria weighting model with the prospect decision-making matrix, the integrated prospect value is derived which presents a measurement scale for ranking the order of alternatives.

As a result, the method of the interval-valued intuitionistic fuzzy stochastic MCDM is suggested. In this method, the new P-score function responses the comprehensive information of the criteria. The prospect decision-making matrix can reflect the risk attitude of the decision maker. The new criteria weighting model can express both the subjective considerations of the decision maker and the objective information meaning.

The research results may lack generalizability for other fuzzy decision making because of the chosen research approach for IVIFN decision making. Therefore, researchers are encouraged to test the proposed propositions further.

The developed approach can be applied in many decision-making fields such as selection of renewable energy alternatives, assessment of flexible manufacturing system alternatives and human resource alternatives performance evaluation, etc. where the evaluation values are IVIFNs.

This paper succeeds in studying the interval-valued intuitionistic fuzzy MCDM based on Prospect theory, which has not been reported in the existing academic literature.

The aim of this research is to establish a new type of aggregation operator based on Hamacher operational law of spherical uncertain linguistic numbers (SULNs).

First, the authors define spherical uncertain linguistic sets and develop some operational laws of SULNs. Furthermore, the authors extended these operational laws to the aggregation operator and developed spherical uncertain linguistic Hamacher averaging and geometric aggregation operators.

The authors were limited in achieving a consistent opinion on the fusion in group decision-making problem with the SULN information.

In order to give an application of the introduced operators, the authors first constrict a system of multi-attribute decision-making algorithm.

The purpose of this paper is to develop a multi-criterion group decision-making (MCGDM) method by combining the regret theory and the Choquet integral under 2-tuple linguistic environment and apply the proposed method to deal with the supplier selection problem.

When making a decision, the decision-maker is more willing to choose the alternative(s) which is preferred by the experts so as to avoid the regret. At the same time, the correlative relationships among the criterion set can be sufficiently described by the fuzzy measures, later the evaluations of a group of criteria can be aggregated by means of the Choquet integral. Hence, the authors cope with the MCGDM problems by combining the regret theory and the Choquet integral, where the fuzzy measures of criteria are partly known or completely unknown and the evaluations are expressed by 2-tuples. The vertical and the horizontal regret-rejoice functions are defined at first. Then, a model aiming to determine the missing fuzzy measures is constructed. Based on which, an MCGDM method is proposed. The proposed method is applied to tackle a practical decision-making problem to verify its feasibility and the effectiveness.

The vertical and the horizontal regret-rejoice functions are defined. The relationships of the fuzzy measures are expressed by the sets. A model is built for determining the fuzzy measures. Based on which, an MCGDM method is proposed. The results show that the proposed method can solve the MCGDM problems within the context of 2-tuple, where the decision-maker avoids the regret and the criteria are correlative.

The paper proposes an MCGDM method by combining the regret theory and the Choquet integral, which is suitable for dealing with a variety of decision-making problems.