Abstract
The aim of this paper is to study a class of nonconvex optimization problems with fuzzy objective functions under granular differentiability concept. In order to get it, we give the definition of granular preinvex fuzzy functions and discuss its fascinating characteristics. In particular, two necessary and sufficient conditions for granular differentiable fuzzy functions to be granular preinvex are proved. As an application of granular preinvex fuzzy functions, we study a class of nonconvex fuzzy optimization problems with constraints, and obtain the existence of the optimal solution by solving the fuzzy variational inequalities. In addition, the developed theory is illustrated by some numerical examples.
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