Abstract
In practical decision-making, the behavior factors of decision makers often affect the final decision-making results. Regret theory is an important behavioral decision theory. Based on the regret theory, a novel decision-making method is proposed for the multiattribute decision-making problem with incomplete attribute weight information, and the attribute values are expressed by Atanassov intuitionistic fuzzy numbers. At first, a new distance of intuitionistic fuzzy sets is put forward based on the traditional Canberra distance. Then, we utilize it for the definition of the regret value (rejoice) for the attribute value of each alternative with the corresponding values of the positive point (negative point). The objective of this method is to maximize the comprehensive perceived utility of the alternative set by the decision maker. The optimal attribute weight vector is solved, and the optimal comprehensive perceived utility value of each alternative is obtained. Finally, according to the optimal comprehensive perceived utility value, the rank order of all alternatives is concluded.
Highlights
Since Professor Zadeh introduced the concept of fuzzy set in 1965, it has been successfully applied in many fields such as intelligent control, military engineering, economic prediction, and decision-making [1,2,3,4,5]
Taking into account this distance measure, this paper develops a novel intuitionistic fuzzy distance based on the Canberra distance and further applies it to develop a new intuitionistic fuzzy decision-making method combined with the regret theory
For the multiattribute decision-making (MADM) problem in which attribute values are expressed by Atanassov intuitionistic fuzzy number (AIFN), this paper develops a new decisionmaking method based on the regret theory combined with an extension of the Canberra distance measure. e main contributions of this article are as follows: (1) Regret theory can describe humans’ psychological behavior under uncertain conditions more truthfully, and it can explain the phenomena that expected utility theory cannot
Summary
Since Professor Zadeh introduced the concept of fuzzy set in 1965, it has been successfully applied in many fields such as intelligent control, military engineering, economic prediction, and decision-making [1,2,3,4,5]. By introducing the parameter of nonmembership degree, IFS can express the information of affirmation and negation at the same time; it can describe the fuzzy concept of “not this or that,” and it can describe the hesitation and uncertainty of the decision maker’s judgment [9, 10] Because of this, it can depict the fuzzy essence of the objective world more delicately than Zadeh’s fuzzy set in the processing mode. As a classical distance measure, has been widely applied in image processing, pattern recognition, and other fields based on the exact number Taking into account this distance measure, this paper develops a novel intuitionistic fuzzy distance based on the Canberra distance and further applies it to develop a new intuitionistic fuzzy decision-making method combined with the regret theory.
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