A novel two-stage method for matching the technology suppliers and demanders based on prospect theory and evidence theory under intuitionistic fuzzy environment

Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.

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Trapezoidal Intuitionistic Fuzzy Multiattribute Decision Making Method Based on Cumulative Prospect Theory and Dempster-Shafer Theory

Journal of Applied Mathematics ◽

10.1155/2014/279138 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Xihua Li ◽

Fuqiang Wang ◽

Xiaohong Chen

Keyword(s):

Decision Making ◽

Prospect Theory ◽

Value Function ◽

Cumulative Prospect Theory ◽

Intuitionistic Fuzzy Numbers ◽

Attribute Weight ◽

Intuitionistic Fuzzy ◽

Dempster Shafer Theory ◽

Fuzzy Environment ◽

Shafer Theory

With respect to decision making problems under uncertainty, a trapezoidal intuitionistic fuzzy multiattribute decision making method based on cumulative prospect theory and Dempster-Shafer theory is developed. The proposed method reflects behavioral characteristics of decision makers, information fuzziness under uncertainty, and uncertain attribute weight information. Firstly, distance measurement and comparison rule of trapezoidal intuitionistic fuzzy numbers are used to derive value function under trapezoidal intuitionistic fuzzy environment. Secondly, the value function and decision weight function are used to calculate prospect values of attributes for each alternative. Then considering uncertain attribute weight information, Dempster-Shafer theory is used to aggregate prospect values for each alternative, and overall prospect values are obtained and thus the alternatives are sorted consequently. Finally, an illustrative example shows the feasibility of the proposed method.

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MADM method based on prospect theory and evidential reasoning approach with unknown attribute weights under intuitionistic fuzzy environment

Expert Systems with Applications ◽

10.1016/j.eswa.2017.07.012 ◽

2017 ◽

Vol 88 ◽

pp. 305-317 ◽

Cited By ~ 45

Author(s):

Tiantian Bao ◽

Xinlian Xie ◽

Peiyin Long ◽

Zhaokun Wei

Keyword(s):

Prospect Theory ◽

Evidential Reasoning ◽

Attribute Weights ◽

Intuitionistic Fuzzy ◽

Fuzzy Environment ◽

Evidential Reasoning Approach

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A DECISION-MAKING FRAMEWORK BASED ON THE PROSPECT THEORY UNDER AN INTUITIONISTIC FUZZY ENVIRONMENT

Technological and Economic Development of Economy ◽

10.3846/tede.2018.6981 ◽

2018 ◽

Vol 24 (6) ◽

pp. 2374-2396 ◽

Cited By ~ 1

Author(s):

Jing Gu ◽

Zijian Wang ◽

Zeshui Xu ◽

Xuezheng Chen

Keyword(s):

Decision Making ◽

Prospect Theory ◽

Value Function ◽

Behavior Pattern ◽

Weighting Function ◽

Intuitionistic Fuzzy ◽

Fuzzy Environment ◽

Decision Making Framework ◽

Decision Making Behavior ◽

The Value Function

Uncertainty and ambiguity are frequently involved in the decision-making process in our daily life. This paper develops a generalized decision-making framework based on the prospect theory under an intuitionistic fuzzy environment, by closely integrating the prospect theory and the intuitionistic fuzzy sets into our framework. We demonstrate how to compute the intuitionistic fuzzy prospect values as the reference values for decision-making and elaborate a four-step editing phase and a valuation phase with two key functions: the value function and the weighting function. We then conduct experiments to test our decision- making methodology and the key features of our framework. The experimental results show that the shapes of the value function and the weighting function in our framework are in line with those of prospect theory. The methodology proposed in this paper to elicit prospects that are not only under uncertainty but also under ambiguity. We reveal the decision-making behavior pattern through comparing the parameters. People are less risk averse when making decisions under an intuitionistic fuzzy environment than under uncertainty. People still underestimate the probability of the events in our experiment. Further, the choices of participants in the experiments are consistent with the addition and multiplication principles of our framework.

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A two-sided matching decision-making approach based on regret theory under intuitionistic fuzzy environment

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202720 ◽

2021 ◽

pp. 1-18

Author(s):

Xiang Jia ◽

Xinfan Wang ◽

Yuanfang Zhu ◽

Lang Zhou ◽

Huan Zhou

Keyword(s):

Decision Making ◽

Hamming Distance ◽

Optimal Solution ◽

Intuitionistic Fuzzy Sets ◽

Regret Theory ◽

Multi Objective ◽

Intuitionistic Fuzzy ◽

Fuzzy Environment ◽

Objective Model ◽

Single Objective

This study proposes a two-sided matching decision-making (TSMDM) approach by combining the regret theory under the intuitionistic fuzzy environment. At first, according to the Hamming distance of intuitionistic fuzzy sets and regret theory, superior and inferior flows are defined to describe the comparative preference of subjects. Hereafter, the satisfaction degrees are obtained by integrating the superior and inferior flows of the subjects. The comprehensive satisfaction degrees are calculated by aggregating the satisfaction degrees, based on which, a multi-objective TSMDM model is built. Furthermore, the multi-objective TSMDM model is converted to a single-objective model, the optimal solution of the latter is derived. Finally, an illustrative example and several analyses are provided to verify the feasibility and the effectiveness of the proposed approach.

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