Intuitionistic fuzzy variational inequalities and their applications

Tareq Saeed; Tareq Saeed

doi:10.3934/math.20241634

AIMS Mathematics

2024, Volume 9, Issue 12: 34289-34310. doi: 10.3934/math.20241634

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Research article

Intuitionistic fuzzy variational inequalities and their applications

Tareq Saeed ^,

Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 05 August 2024 Revised: 28 October 2024 Accepted: 14 November 2024 Published: 05 December 2024
MSC : 62G10, 62G20, 62N05

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.
Citation: Tareq Saeed. Intuitionistic fuzzy variational inequalities and their applications[J]. AIMS Mathematics, 2024, 9(12): 34289-34310. doi: 10.3934/math.20241634

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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.

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