Optimality Guidelines for the Fuzzy Multi-Objective Optimization under the Assumptions of Vector Granular Convexity and Differentiability

In this research, we investigate a novel class of granular type optimality guidelines for the fuzzy multi-objective optimizations based on guidelines of vector granular convexity and granular differentiability. Firstly, the concepts of vector granular convexity is introduced to the vector fuzzy-valued function. Secondly, several properties of vector granular convex fuzzy-valued functions are provided. Thirdly, the granular type Karush-Kuhn-Tucker(KKT) optimality guidelines are derived for the fuzzy multi-objective optimizations.