An interval type-2 fuzzy extension of the TOPSIS method using alpha cuts

摘要

A technique for order of preference by similarity to ideal solution (TOPSIS) currently is probably one of most popular method for Multiple Criteria Decision Making (MCDM). The method was primarily developed for dealing with real-valued data. Nevertheless, in practice often it is hard to present precisely exact ratings of alternatives with respect to local criteria and as a result these ratings are presented by as fuzzy values. Many recent papers have been devoted to the fuzzy extension of the TOPSIS method, but only a few works provided the type-2 fuzzy extensions, whereas such extensions seem to be very useful for the solution of many real-world problems, e.g., Multiple Criteria Group Decision Making problem. Since the proposed type-2 fuzzy extensions of the TOPSIS method have some limitations and drawbacks, in this paper we propose an interval type-2 fuzzy extension of the TOPSIS method realized with the use of α-cuts representation of the interval type-2 fuzzy values (IT2FV). This extension is free of the limitations of the known methods. The proposed method is realized for the cases of perfectly normal and normal IT2FVs. The illustrative examples are presented to show the features of the proposed method.