An approach to generalization of the intuitionistic fuzzy topsis method in the framework of evidence theory

A generalization of technique for establishing order preference by similarity to the ideal solution (TOPSIS) in the intuitionistic fuzzy setting based on the redefinition of intuitionistic fuzzy sets theory (A−IFS) in the framework of Dempster-Shafer theory (DST) of evidence is proposed. The use of DST mathematical tools makes it possible to avoid a set of limitations and drawbacks revealed recently in the conventional Atanassov’s operational laws defined on intuitionistic fuzzy values, which may produce unacceptable results in the solution of multiple criteria decision-making problems. This boosts considerably the quality of aggregating operators used in the intuitionistic fuzzy TOPSIS method. It is pointed out that the conventional TOPSIS method may be naturally treated as a weighted sum of some modified local criteria. Because this aggregating approach does not always reflects well intentions of decision makers, two additional aggregating methods that cannot be defined in the framework of conventional A−IFS based on local criteria weights being intuitionistic fuzzy values, are introduced. Having in mind that different aggregating methods generally produce different alternative rankings to obtain the compromise ranking, the method for aggregating of aggregation modes has been applied. Some examples are used to illustrate the validity and features of the proposed approach.