Applying Fuzzy Similarities Between Evaluation Alternatives and Extreme Solutions for Fuzzy Multi-Criteria Decision-Making

Abstract

Abstract Many researchers generalize classical multi-criteria decision-making (MCDM) methods under fuzzy environment into fuzzy multi-criteria decision-making (FMCDM) for solving decision-making problems, such as the approaches of Chen, Liang, Raj and Kumar, Wang, and Wang et al. However, some problems occurred in the approaches above. For instance, the intersection of fuzzy numbers is a null set, the calculation for pooled fuzzy numbers is complex work, or the criteria values of anti-ideal/ideal solutions or lower/upper boundaries may not exist in feasible alternatives. In addition, there are too many computation steps to be realized and utilized for decision-makers. Recently, Wang proposed a method-associating technique for order preference by similarity to ideal solution (TOPSIS) with a relative preference relation to solve the above drawbacks of FMCDM. Wang resolved most of the problems with the above approaches, but we still desired to develop a method that was simpler than Wang's on computation. Therefore, we proposed an FMCDM method applying fuzzy similarities between evaluation alternatives and extreme solutions in this paper. The fuzzy similarities between evaluation alternatives and extreme solutions are based on a similarity relation between two fuzzy numbers, and this similarity relation was converted from Lee's extended preference relation. With the fuzzy similarities between evaluation alternatives and extreme solutions, alternative performance indices are easily yielded and then FMCDM are easily and efficiently finished in practice. Furthermore, the computation steps of FMCDM were simplified and reduced through the fuzzy similarities. Furthermore, we compared the proposed method with other methods including Wang's to demonstrate the feasibility and rationality of the method.