Ranking Alternatives Using a Fuzzy Preference Relation-Based Fuzzy VIKOR Method

Abstract

The process of evaluating and ranking alternatives, including the aggregation of various qualitative and quantitative criteria and weights of criteria, can be recognized as a fuzzy multiple criteria decision-making (MCDM) problem. In fuzzy MCDM problems, qualitative criteria and criteria weights are usually indicated in linguistic values expressed in terms of fuzzy numbers, and values under quantitative criteria are usually crisp numbers. How to properly aggregate them for evaluating and selecting alternatives has been an important research issue. To help decision-makers make the most suitable selection, this paper proposes a fuzzy preference relation-based fuzzy VIKOR method. VIKOR is a compromise ranking method to solve discrete MCDM problems in complex systems. In this study, the F-preference relation is applied to compare fuzzy numbers with their means to produce a single index of a dominance level while still maintaining fuzzy meaning of the original linguistic values. The inverse function is applied to obtain the defuzzification values of Beta 1–4 to assist in the completion of the proposed method, and formulas can be clearly derived to facilitate the ranking procedure. Introducing fuzzy preference relation into fuzzy VIKOR can simplify the calculation procedure for more efficient decision-making. The proposed method is new and has never been seen before. A numerical example and a comparison of the proposed method are conducted to show and verify its expedience and advantage.

Keywords

• fuzzy preference relation
• fuzzy VIKOR
• F-preference relation
• inverse function