Linear optimization problems subjected to Lukasiewicz fuzzy relational equations

In this paper, we study a linear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the Lukasiewicz t-norm. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutions is an NP-hard problem, conventional methods may not be directly employed. The resolution of the feasible region is completely investigated. Based on some theoretical properties of the problem, an algorithm is presented to find all the optimal solutions, and finally an example is described to illustrate this algorithm.

Keywords:

Fuzzy relational equations , linear optimization , strict t-norm , Lukasiewicz t-norm.