Extension of topsis method for decision making problem with linguistic information based on axiomatic fuzzy set

In classical TOPSIS method, the criteria values and criteria weights are known precisely, whereas in the real world, in an imprecise and uncertain environment, it is an unrealistic assumption that the knowledge and representation of a decision maker or expert are so precise. A suitable approach for dealing with such a problem is to use linguistic assessments instead of numerical ones to represent the subjective judgment of decision makers by means of linguistic variables. In this paper, the linguistic values are represented by membership degrees applying the axiomatic fuzzy set (AFS) theory, then the application of TOPSIS method is extended. In addition, the semantic interpretations are provided for the decision results by AFS theory. A numerical example is used to illustrate the application of the proposed approach. © 2015 ICIC International.