An Evidential Aggregation Method of Intuitionistic Fuzzy Sets Based on Belief Entropy

Abstract

Intuitionistic fuzzy sets (IFSs) are essential in the multi-criteria decision making (MCDM) under uncertain environment. However, how to reasonably aggregate them with considering the uncertainty contained in the IFSs is still an open issue. In this paper, a new method is proposed to solve such a problem based on the Dempster-Shafer evidence theory, belief entropy, and the weighted ordered weighted averaging (WOWA) operator. One of the advantages of the presented model is that the uncertainty contained in the IFSs is effectively modeled based on belief entropy and the conversion from the IFS to Dempster-Shafer evidence theory. In the framework of evidence theory, the uncertain information contained in the IFSs can be embodied effectively. Then, the belief entropy is calculated to determine the certainty weights for each IFS. With the various definitions of the regular increasing monotone (RIM) quantifier Q function, the preference relationship of a decision maker is considered. A numerical example is shown to illustrate the feasibility and effectiveness of the proposed method.

Keywords

• Intuitionistic fuzzy sets
• multi-criteria decision making
• Dempster-Shafer evidence theory
• belief entropy
• weighted ordered weighted averaging operator
• preference