Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

Feng Feng · Zeshui Xu · Hamido Fujita · Meiqi Liang

148 citations0/0 files storedInternational Journal of Intelligent Systems

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Multi-Criteria Decision Making Rough Sets and Fuzzy Logic Fuzzy and Soft Set Theory

Abstract

The notion of intuitionistic fuzzy soft sets (IFSSs) provides an effective tool for solving multiple attribute decision making with intuitionistic fuzzy information. The most crucial issue in decision making based on IFSSs is how to derive the ranking of alternatives from the information quantified in terms of intuitionistic fuzzy values. In this study, we propose a new extension of the preference ranking organization method for enrichment evaluation (PROMETHEE), by taking advantage of IFSSs. In addition to presenting a myriad of new notions, such as intuitionistic fuzzy membership (or nonmembership) deviation matrices, intuitionistic fuzzy membership (or nonmembership) preference matrices, and aggregated intuitionistic fuzzy preference matrices, we put more emphasis on the construction of three distinct preference structures and related utility functions on the corresponding weakly ordered sets by considering the positive, negative, and net flows of the alternatives based on the aggregated intuitionistic fuzzy preference matrix. We present a new algorithm for solving multiple attribute decision-making problems with the extended PROMETHEE method based on IFSSs. Moreover, a benchmark problem concerning risk investment is investigated to give a comparative analysis and show the feasibility of our approach.

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References

1965Fuzzy sets 1986Intuitionistic fuzzy sets 1999Soft set theory—First results 2013Pythagorean Membership Grades in Multicriteria Decision Making 1985Note—A Preference Ranking Organisation Method 2007Intuitionistic Fuzzy Aggregation Operators 2006Some geometric aggregation operators based on intuitionistic fuzzy sets 2003Soft set theory

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