Intuitionistic fuzzy variational inequalities and their applications

Abstract

In this paper, a new class of generalized convex (concave) fuzzy mappings are introduced, which is called intuitionistic convex (concave) fuzzy mappings from the convex set $ {K\subseteq \mathbb{R}}^{n} $ to the set of intuitionistic fuzzy numbers. By using the concept of epigraph, the characterization of intuitionistic convex fuzzy mappings is also discussed. Different types of intuitionistic convex (concave) fuzzy mappings are defined and their properties are investigated. Then, we discuss some applications of intuitionistic fuzzy convex mappings in fuzzy optimization. Additionally, some variational inequalities, known as intuitionistic fuzzy variational inequality and intuitionistic fuzzy variational mixed inequalities, are introduced. The results obtained in this paper can be regarded as refinements and extensions of previously established results.

Keywords

• intuitionistic fuzzy numbers
• intuitionistic convex fuzzy mappings
• intuitionistic quasi-convex fuzzy mappings
• global minimum
• intuitionistic fuzzy variational inequalities