A linguistic distribution behavioral multi-criteria group decision making model integrating extended generalized TODIM and quantum decision theory

The modern decision-making environment is complex and dynamic. Global supply chain networks are increasingly exposed to unsystematic risks. Therefore, decision-makers need greater flexibility and precision to better manage uncertain market changes and complex international environments. To construct an accurate multi-criteria group decision-making (MCGDM) model, it is necessary to select appropriate evaluation criteria and identify alternative ranking methods based on specific decision problems. To develop a suitable MCGDM model for dynamic environments, this paper develops a new MCGDM model based on probabilistic interval-valued intuitionistic hesitant fuzzy sets (PIVIHFSs), regret theory, and the extended ELimination Et Choice Translating Reality (ELECTRE) III method. Firstly, this paper proposes two new aggregation operators, including the generalized probabilistic interval-valued intuitionistic hesitant fuzzy weighted averaging (GPIVIHFWA) operator and the generalized probabilistic interval-valued intuitionistic hesitant fuzzy weighted geometric (GPIVIHFWG) operator. To incorporate the decision-maker (DM)'s regret aversion, a bidirectional projection measure is proposed to calculate the advantages and disadvantages between two probabilistic interval-valued intuitionistic hesitant fuzzy elements (PIVIHFEs). The regret values of PIVIHFEs are determined using the bidirectional projection measure instead of utility values in the regret-rejoice function. Then, this paper constructs an extended ELECTRE III method and establishes a decision-making model based on the Borda rule for ranking and selecting the best alternatives. Finally, the effectiveness and robustness of the proposed model are verified through a numerical example, and the results are discussed through sensitivity analysis and comparative analysis.

A trust-based quantum probabilistic linguistic multi-criteria group decision making model considering interference effect

A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers

Recently, the TODIM (an acronym in Portuguese for Interactive Multi-criteria Decision Making) method, which can characterize the decision makers’ psychological behaviors under risk, has been introduced to handle multiple attribute group decision making (MAGDM) problems. Moreover, the probabilistic linguistic term sets (PLTSs) are effective tool for depicting uncertainty of the MAGDM problems. In this paper, we extend the TODIM method to the MAGDM with PLTSs. Firstly, the definition, comparative method and distance of PLTSs are simply introduced, and the steps of the classical TODIM method for MAGDM problems are presented. Then, on the basis of the conventional TODIM method, the extended TODIM method is proposed to deal with MAGDM problems in which the attribute values are depicted in the PLTSs, and its significant characteristic is that it can fully consider the decision makers’ bounded rationality which is a real action in decision making. Finally, a numerical example for green supplier selection is proposed to verify the developed approach and its practicality and effectiveness.

Hesitant fuzzy linguistic term sets (HFLTSs) are very useful for dealing with the situations in which the decision makers hesitate among several linguistic terms to assess an alternative. Some multi-criteria decision-making (MCDM) methods have been developed to deal with HFLTSs. These methods are derived under the assumption that the decision maker is completely rational and do not consider the decision maker's psychological behavior. But some studies about behavioral experiments have shown that the decision maker is bounded rational in decision processes and the behavior of the decision maker plays an important role in decision analysis. In this paper, we extend the classical TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method to solve MCDM problems dealing with HFLTSs and considering the decision maker's psychological behavior. A novel score function to compare HFLTSs more effectively is defined. This function is also used in the proposed TODIM method. Final...

Multi-Criteria Group Decision Making (MCGDM) is a decision tool which is able to find a unique agreement from a group of decision makers (DMs) by evaluating various conflicting criteria. However, most multi-criteria decision making techniques utilizing a group of DMs (MCGDM) do not effectively deal with the large number of possibilities inherent in a domain with a variety of possibilities, different judgments, and ideas on opinions. In recent years, there has been a growing interest in developing MCGDM using type-2 fuzzy systems which provide a framework to handle the encountered uncertainties in decision making models. In addition, fuzzy logic is regarded as an appropriate methodology for decision making systems which are able to simultaneously handle numerical data and linguistic knowledge. In this paper, we will aim to modify the fuzzy logic theories based multi-criteria group decision making models to employ a suite of type-2 fuzzy logic systems in order to provide answers to the problems that are encountered in the real experts’ decision. In the proposed framework, we will present a MCGDM method based on interval type-2 fuzzy logic combined with intuitionistic fuzzy evaluation (from intuitionistic fuzzy sets). This combination handles the linguistic uncertainties by the interval type-2 membership function and simultaneously computes the non-membership degree from the intuitionistic evaluation. However, the interval values with hesitation index cannot fully represent the uncertainty distribution associated with the decision makers. Hence, we will present a final component of our framework employing general type-2 fuzzy logic based approach for MCGDM which is more suited for higher levels of uncertainties. In order to optimally find the type-2 fuzzy sets parameters (including interval type-2 and general type-2), we have employed the Big Bang Big Crunch (BB-BC) optimisation method. In order to validate the efficiency of the proposed systems in handling various DMs’ behaviour and opinion, we will present comparisons which were performed on two different real world decision making problems. As will be shown in the various experiment sections, we found that the proposed type-2 MCGDM based system better agrees with the users’ decision compared to type-1 fuzzy expert system and existing type-1 fuzzy MCDMs including the Fuzzy Logic based TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution). In addition, we will show how the different type-2 fuzzy logic based MCGDM systems compare to each other when increasing the level of uncertainties where the general type-2 MCGDM will outperform the MCGDM based interval type-2 fuzzy logic combined with intuitionistic fuzzy evaluation which will outperform the MCGDM based on interval type-2 fuzzy sets. Hence, this work can be regarded as a step towards producing higher ordered fuzzy logic approach for MCGDM (HFL-MCGDM) which could be applied to complex problems with high uncertainties to produce automated decisions much closer to the group of human experts.

With the increase of technological and societal demands, more and more decision makers are involved in the process of group decision making, which is called large-scale group decision making (LGDM). For an LGDM problem with linguistic information, it is common that different decision makers tend to provide linguistic assessments defined on multigranular linguistic term sets due to the difference in knowledge and culture background, and that hesitant fuzzy linguistic term sets (HFLTSs) are used by decision makers to model the hesitancy of their assessments. This article proposes first an algorithm to represent a linguistic distribution assessment (LDA) using a hesitant linguistic distribution (HLD). Two other algorithms are then proposed to transform an unbalanced HFLTS into a balanced LDA and to transform a balanced LDA into an unbalanced LDA, respectively. An approach is then proposed to deal with multiattribute LGDM problems with multigranular unbalanced hesitant fuzzy linguistic information based on these algorithms. In the proposed approach, all unbalanced hesitant fuzzy linguistic information is transformed into LDAs defined on a balanced linguistic term set, and then an LDA-based clustering algorithm is devised to cluster decision makers. Based on the clustering result, decision makers' linguistic distribution decision matrices are further fused to obtain collective assessments of alternatives. In order to provide easy-to-understand linguistic results for decision makers, all LDAs of alternatives are represented by HLDs defined on each decision maker's initial linguistic term set. Finally, an example for the selection of subway lines is used to demonstrate the proposed approach.

Extended TODIM for multi-criteria group decision making based on unbalanced hesitant fuzzy linguistic term sets

Nowadays TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method has been widely used to solve multi-criteria decision making (MCDM) problems for its validity in consideration of psychological behavior of the decision maker (DM). However, the classical TODIM method can only deal with crisp numbers, which fails to respond to the vagueness of the information and hesitancy of the DM in the real life. Thus, in this paper, we propose a concept of multi-granularity2-dimension fuzzy linguistic variable, which can describe the evaluation values provided by DM to the given alternatives and the subjective assessment about the dependability of the provided results simultaneously with fuzzy linguistic variables. Firstly, the background of fuzzy linguistic variable, 2-dimension linguistic variable and the classical TODIM method are introduced. Secondary, we give the definition to multi-granularity 2-dimension fuzzy linguistic variable, and so with some operational laws, the expectation and the distance of multi-granularity 2-dimension fuzzy linguistic variables. Furthermore, we extend the TODIM method to tackle the criterion values with 2-dimension fuzzy linguistic information, and the procedure is provided. Finally, a numerical example is used to illustrate the practicality and the effectiveness of the proposed method.

A semantic model for computing with flexible linguistic expressions and the application in MCGDM

Managing personalized individual semantics and consensus in linguistic distribution large-scale group decision making

The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment

Selection of energy performance contracting business models: A behavioral decision-making approach

Decision makers (DMs) are often viewed as autonomous in the majority of multicriteria group decision making (MCGDM) situations, and their psychological behaviors are seldom taken into account. Once more, we are unable to prevent both positive and negative flows of varying alternative preferences due to the nature of attributes or criteria in complicated decision-making problems. However, DMs’ perspectives are likely to affect one another in complicated MCGDM issues, and they frequently use subjective limited rationality while making decisions. The multicriteria quantum decision theory-based group decision making integrating the TODIM-PROMETHEE II strategy under linguistic Z-numbers (LZNs) is designed to overcome the aforementioned problems. In our established technique, the PROMETHEE II controls the positive and negative flows of distinct alternative preferences, the TODIM method manages the experts’ personal regrets over a criterion, and the quantum probability theory (QPT) addresses human cognition and behavior. Because LZNs can convey linguistic judgment and trustworthiness, we provide expert LZNs for their viewpoints in this work. We determine the criterion weights for each expert after first obtaining their respective expert weights. Second, to represent the limited rational behaviors of the DMs, the TODIM-PROMETHEE II approach is introduced. It is employed to determine each alternative’s dominance in both positive and negative flows. Third, a framework for quantum possibilistic aggregation is developed to investigate the effects of interference between the views of DMs. The views of DMs are seen in this procedure as synchronously occurring wave functions that affect the overall outcome by interfering with one another. The model’s efficacy is then assessed by a selection of renewable energy case studies, sensitive analysis, comparative analysis, and debate.

Recently, the TODIM (an acronym in Portuguese for Interactive Multi-criteria Decision Making) approach, which can characterize the decision makers’ psychological behaviors under risk, has been introduced to handle multiple attribute decision making (MADM) problems. Moreover, 2-tuple linguistic term set is an effective tool for depicting uncertainty of the MADM problems. In this paper, we will extend the TODIM method to the MADM with the 2-tuple linguistic information. Firstly, the definition and distance of 2-tuple linguistic information are briefly introduced, and the steps of the classical TODIM method for MADM problems are presented. Then, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MADM problems in which the attribute values are in the 2-tuple linguistic information, and its significant characteristic is that it can fully consider the decision makers’ bounded rationality which is a real action in decision making. Finally, a numerical example for evaluating the service quality of boutique tourist scenic spot is proposed to verify the developed approach and its practicality and effectiveness.