Improved extensions of the TOPSIS for group decisionmaking under fuzzy environment
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TL;DR
An improved fuzzy TOPSIS model is suggested, where membership functions for the weighted normalized fuzzy ratings are presented and a simple method is also proposed for ranking fuzzy numbers with mean of relative areas.
Abstract
Abstract Chen [2] extended the TOPSIS to a fuzzy environment. In his work, a vertex method was proposed to measure the distance between two given triangular fuzzy numbers. He further applied the vertex method to measure the distance between the weighted normalized fuzzy ratings and the fuzzy positive (negative}-ideal solutions to complete the fuzzy TOPSIS model. Despite the merits of his work, this application is not reasonable. Because the weighted normalized fuzzy ratings are truly not triangular fuzzy numbers. To overcome the above shortcomings, we suggest an improved fuzzy TOPSIS model, where membership functions for the weighted normalized fuzzy ratings are presented. A simple method is also proposed for ranking fuzzy numbers with mean of relative areas. This ranking method is further applied to establish the proposed model. Illustrative examples demonstrate the merits of the proposed ranking method and the feasibility of the improved fuzzy TOPSIS model, respectively. Keywords: TopsisFuzzy numbersRankingRelative areas