New Class of Preinvex Fuzzy Mappings and Related Inequalities

Abstract

This study aims to consider new kinds of generalized convex fuzzy mappings (convex-𝘍𝘔), which are called strongly α-preinvex fuzzy mappings. We investigated the characterization of preinvex-𝘍𝘔s using α-preinvex-𝘍𝘔s, which can be viewed as a novel and innovative application. Some different types of strongly α-preinvex-𝘍𝘔s are introduced, and their properties are investigated. Under appropriate conditions, we establish the relationship between strongly α-invex-𝘍𝘔s and strongly α𝑗-monotone fuzzy operators. Then, the minimum of strongly α-preinvex-𝘍𝘔s are characterized by strongly fuzzy α-variational-like inequalities. Results obtained in this paper can be viewed as a refinement and improvement of previously known results.