A New Multiple Criteria Decision Making Approach Based on Intuitionistic Fuzzy Sets, the Weighted Similarity Measure, and the Extended TOPSIS Method

Abstract

Many real-world multiple criteria decision making (MCDM) problems are rather complicated and uncertain to handle. In recent years, some MCDM methods have been proposed based on intuitionistic fuzzy sets (IFSs). In this paper, we propose a new MCDM method based on IFSs, the weighted similarity measure (WSM), and the extension of the technique for order preference by similarity to ideal solution (TOPSIS) method with completely unknown weights of criteria. Firstly, we calculate the weights of criteria using the normalized intuitionistic fuzzy entropy values (IFEVs) when the weights of criteria was not given by decision maker. Secondly, we propose a novel weighted similarity measure (WSM) between the IFSs that takes the hesitancy degree of elements of IFSs into account. Finally, we combine the WSM with the Extended TOPSIS Method to propose a new MCDM approach based on IFSs which can overcome the drawbacks and limitations of some existing methods that they cannot get the preference order of the alternatives in the context of the “division by zero” (“DBZ”) situations. The proposed method provides us an easier way to handle MCDM problems under intuitionistic fuzzy (IF) environments.