Optimality Conditions for Fuzzy Optimization Problems with Generalized Convexity Under the Granular Concept

In recent years, there has been an increasing interest in uncertainty optimization problems. Fuzzy optimization is one of the methods to study real world uncertainty problems, which contain uncertain data and therefore are not well defined. In addition, although the concept of convexity is an important property of optimization problems, many real life problems do not have a convex structure and cannot be solved by convexity. Therefore, this paper focuses on a class of fuzzy optimization problems with equality and inequality constraints, and introduces a new concept of granular optimal solution to this mathematical planning problem based on the concept of granular differentiability, which are innovative and important for practice and computation. By utilizing the concepts of horizontal membership function and triangular fuzzy function, the problem is no longer treated from one-dimensional interval arithmetic, but from multidimensional granules, which leads to computationally more efficient theoretical results. In the literature [4], Zhang et al. have given KKT optimality conditions for a class of fuzzy inequality constrained problems by combining the concept of granularity convex functions, but this theoretical result cannot deal with non-convex optimization problems. Therefore, we combine the concept of granular pseudoconvex functions to establish the KKT optimality conditions for this class of fuzzy optimization problems. Finally, the development of the theory is illustrated by several numerical examples.