Optimization of partially monotonic functions subject to bipolar fuzzy relation equations

A method to solve a latticed optimization problem constrained by a bipolar fuzzy relation equation is presented in this paper, under the hypothesis of a partially monotonic objective function. The solving strategy consists of transforming the problem into optimizing an order-preserving function in all arguments subject to another bipolar fuzzy relation equation. As a result, all the solutions of the original optimization problem can be deduced from the extremal elements of the feasible domain of the transformed problem. The presented approach embraces the particular case of linear optimization constrained by bipolar fuzzy relation equations.