A Kind of Nonlinear and Non-convex Optimization Problems under Mixed Fuzzy Relational Equations Constraints with Max-min and Max-average Composition

In this paper, a kind of nonlinear and non-convex optimization problems under the constraints expressed by a system of mixed fuzzy relation equations with max-min and max-average composition is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this optimization problem is given based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem. Finally, numerical examples are provided to illustrate our algorithms.