An approach to generalization of fuzzy TOPSIS method

The TOPSIS method is a technique for establishing order preference by similarity to the ideal solution, and was primarily developed for dealing with real-valued data. This technique is currently one of most popular methods for Multiple Criteria Decision Making (MCDM). In many cases, 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 extensions of the TOPSIS method in the literature, but these extensions are not complete since the ideal solutions are usually presented as real values (not by fuzzy values) or as fuzzy values which are not attainable in the decision matrix. In most of these papers, a defuzzification of elements of the fuzzy decision matrix is used, which leads inevitably to a loss of important information and may even produce the wrong results. In this paper, we propose a new direct approach to the fuzzy extension of the TOPSIS method which is free of the limitations of other known approaches. We show that the distances of the alternatives from the ideal solutions may be treated (in some sense) as modified weighted sums of local criteria. It is known that using weighted sums is not the best approach to the aggregation of local criteria in many real-world situations. Therefore, here, we propose the use, in addition to weighted sums, some other types of local criteria aggregation in the TOPSIS method and we develop a method for the generalization of different aggregation modes, providing compromised final results. (C) 2013 Elsevier Inc. All rights reserved.