The fuzzy-TOPSIS method based on credibility measure

This paper extended the TOPSIS method for multi-criteria decision-making by the credibility measure in fuzzy environment. Originated in the compromise programming method, TOPSIS is on the basis of an aggregating function representing "closeness to the ideal", the basic principles of it are that the chosen alternative should have the shortest distance from the positive ideal solution (PIS) and the farthest from the negative ideal solution (NIS). In reality, decision data are usually represented by vague concepts such that the precise value is inadequate to model real-life multi-criteria decision-making situations. To deal with linguistic or uncertain attributes in decision data, which should be allowed to assume fuzzy numbers, the paper provided a detailed discussion on one extension of TOPSIS method adopting the fuzzy uncertainty theory. In the presented fuzzy-TOPSIS method, the performance ratings and the weights of the criteria were given as triangular fuzzy numbers. In addition, the measure of distances between the fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) were replaced by credibility measure, where distance was a special measure. Finally, the proposed method was illustrated with a numerical example, showing its central procedure.