Improved arithmetic operations on generalized fuzzy numbers

Abstract

Determining the arithmetic operations of fuzzy numbers is a very important issue in fuzzy sets theory, decision process, data analysis, and applications. In 1985, Chen formulated the arithmetic operations between generalized fuzzy numbers by proposing the function principle. Since then, researchers have shown an increased interest in generalized fuzzy numbers. Most of existing studies done using generalized fuzzy numbers were based on Chen's (1985) arithmetic operations. Despite its merits, there were some shortcomings associated with Chen's method. In order to overcome the drawbacks of Chen's method, this paper develops the extension principle to derive arithmetic operations between generalized trapezoidal (triangular) fuzzy numbers. Several examples demonstrating the usage and advantages of the proposed method are presented. It can be concluded that the proposed method can effectively resolve the issues with Chen's method. Finally, the proposed extension principle is applied to solve a multi-criteria decision making (MCDM) problem.