Necessary and Sufficient Optimality Conditions for Fuzzy Variational Problems of Several Dependent Variables in Terms of Fuzzy Granular Derivatives

Abstract

This paper is intended to investigate fuzzy variational problems of several dependent variables. Firstly, we establish both necessary and sufficient optimality conditions for fundamental fuzzy variational problems and fuzzy variational problems with natural boundary conditions. Then, the necessary and sufficient optimality conditions for fuzzy variational problems with isoperimetric constraints and holonomic constraints are discussed. Some examples are given to illustrate our results.