An intuitionistic fuzzy soft set method for stochastic decision-making applying prospect theory and grey relational analysis

2017 ◽  
Vol 33 (1) ◽  
pp. 15-25 ◽  
Author(s):  
Ningxin Xie ◽  
Zhaowen Li ◽  
Gangqiang Zhang
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Grey Relational Analysis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Relational Analysis ◽  
Intuitionistic Fuzzy ◽  
Grey Relational

scholarly journals An extension of grey relational analysis for intuitionistic and interval-valued intuitionistic fuzzy soft sets

2020 ◽  
Vol 13 (37) ◽  
pp. 3950-3959
Author(s):  
Muhammad Touqeer ◽  
Keyword(s):  
Decision Making ◽  
Grey Relational Analysis ◽  
Optimal Choice ◽  
Soft Set ◽  
Final Decision ◽  
Fuzzy Soft Set ◽  
Relational Analysis ◽  
Intuitionistic Fuzzy ◽  
Grey Relational ◽  
Interval Valued

Objectives: Neither any analytical (or numerical) nor any statistical approach is often helpful in these situations due to the reason that every person has his/her own choice. To cope with such situations usually we have to use fuzzy sets in combination with soft sets, which consist of predicates and approximate value sets as their images. Material: Choice values and comparison table techniques are two common decision-making techniques, which often don’t result in same preference order or optimal choice. To overcome this kind of situation in decision-making problems, grey relational analysis method is used to get on a final decision. Method: Here we have used grey relational analysis method involving “intuitionistic fuzzy soft set” and “interval-valued intuitionistic fuzzy soft set” and “AND operation” to deal with such kind of problems. Findings: The proposed method is effective in seeking on an optimal choice in the case when common decision-making techniques fail to get on a final decision. Novelty: By using grey relational analysis, a suitable method to choose one object from different choices has been proposed. It overcome the greyness in decisionmaking problems for getting on a final decision when one gets too many options and finds it difficult to choose an optimal choice. Keywords: Fuzzy soft set; intuitionistic fuzzy soft set; grey relational analysis; interval-valued intuitionistic fuzzy soft set

Grey relational analysis method based on cumulative prospect theory for intuitionistic fuzzy multi-attribute group decision making

2021 ◽  
Vol 41 (2) ◽  
pp. 3783-3795
Author(s):  
Shanshan Zhang ◽  
Hui Gao ◽  
Guiwu Wei ◽  
Xudong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Prospect Theory ◽  
Group Decision Making ◽  
Grey Relational Analysis ◽  
Group Decision ◽  
Cumulative Prospect Theory ◽  
Relational Analysis ◽  
Intuitionistic Fuzzy ◽  
Grey Relational

The Multi-attribute group decision making (MAGDM) problem is an interesting everyday problem full of complexity and ambiguity. As an extended form of fuzzy sets, intuitionistic fuzzy sets (IFSs) can provide decision-makers (DMs) with a wider range of preferences for MAGDM. The grey relational analysis (GRA) is an effective method for dealing with MAGDM problems. However, in view of the incomplete and asymmetric information and the influence of DMs’ psychological factors on the decision result, we develop a new model that GRA method based on cumulative prospect theory (CPT) under the intuitionistic fuzzy environment. Moreover, the weight of attribute is calculated by entropy weight, so as to distinguish the importance level of attributes, which greatly improves the credibility of the selected scheme. simultaneously, the proposed method is used to the selection of optimal green suppliers for testifying the availability of this new model and the final comparison between this new method and the existing methods further verify the reliability. In addition, the proposed method provides some references for other selection problems.

scholarly journals Evaluating Risks of Mergers & Acquisitions by Grey Relational Analysis Based on Interval-Valued Intuitionistic Fuzzy Information

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Liu Hongjiu ◽  
Liu Qingyang ◽  
Hu Yanrong
Keyword(s):  
Decision Making ◽  
Grey Relational Analysis ◽  
Programming Model ◽  
Analysis Method ◽  
Fuzzy Information ◽  
Relational Analysis ◽  
Intuitionistic Fuzzy ◽  
Ideal Solutions ◽  
Grey Relational ◽  
Interval Valued

Purpose. The purpose of our research is to explore a new grey relational analysis method when information of decision making is interval-valued, intuitionistic, fuzzy, and uncertain in risk analysis of Mergers & Acquisitions. Design/Methodology/Approach. We proposed a new method to evaluate risks of Mergers & Acquisitions. The process of our method is to determine the positive and negative ideal solutions of interval-valued intuitional fuzzy uncertain language firstly. Then, calculate grey relational grades of every evaluating value for positive or negative ideal solutions. Third, determine the weights of attributes by a linear programming model if part of attribute information is known. Fourth, calculate grey relational grades of each alternative for the positive or negative ideal solutions. Lastly, calculate relative grey relational grades and sort the alternatives. Findings. Our case analysis demonstrated that the new grey relational analysis is an effective tool to evaluate the risks of Mergers & Acquisition when information of decision making is interval-valued, intuitionistic, fuzzy, and uncertain. At the same time, we also bring forward the steps of evaluation. Originality/Value. Because risks of Mergers & Acquisitions decide its success or failure to some extent, it is very important to evaluate them by feasible and available method. However, the information of risks is fuzzy and uncertain usually. The new grey relational analysis based on Interval-Valued Intuitionistic Fuzzy Information does not only evaluate risks of Mergers & Acquisitions but also can be widely applied to similar problems of decision making in other fields.

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