Dynamic Aggregation Operators Based on Intuitionistic Fuzzy Tools and Einstein Operations

Peer review under responsibility of Fuzzy Information and Engineering Branch of the Operations Research Society of China.

Abstract

The idea of combine aggregation and intuitionistic fuzzy information plays essential role in multi criteria decision making (MCDM) process. However, this new branch has attracted researchers that study in different fields recently. In this paper, we study MCDM problems with intuitionistic fuzzy environment. Firstly, we introduce some operations related with Einstein t-norm and t-conorm such as, Einstein sum, product and exponentiation. After that, we define dynamic intuitionistic fuzzy Einstein averaging (DIFWA${}^{ϵ}$) operator and dynamic intuitionistic fuzzy Einstein geometric averaging (DIFWG${}^{ϵ}$) operator. Their notable property is that collect and aggregate values in different period based on Einstein operations in intuitionistic fuzzy set (IFS)s. In addition, we compare the defined operators with the existing intuitionistic fuzzy dynamic operators and get the corresponding relations. We establish two methods using with DIFWA${}^{ϵ}$ and DIFWG${}^{ϵ}$ to solve MCDM problems with intuitionistic fuzzy tools. Finally, an illustrated example is presented to show the applicability of the introduced methods.

Keywords:

• Dynamic operator
• Weighted averaging operator
• Intuitionistic fuzzy set
• Einstein operations

Notes

Peer review under responsibility of Fuzzy Information and Engineering Branch of the Operations Research Society of China.