The TOPSIS Method in the Interval Type-2 Fuzzy Setting

The technique for establishing order preference by similarity to the ideal solution (TOPSIS) now 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 seen as fuzzy values. A number of papers have been devoted to fuzzy extension of the TOPSIS method in the literature, but only a few works provided the type-2 fuzzy extensions, whereas such extensions seem to be very useful for solution of many real-world problem, 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 realised with the use of a-cuts representation of the interval type-2 fuzzy values (IT2FV). This extension is free of the limitations and drawbacks of the known methods. The proposed method is realised for the cases of perfectly normal and normal IT2FVs.