On the resolution and Linear programming problems subjected by Aczel-Alsina Fuzzy relational equations

Aczel-Alsina t-norm belongs to the family of strict t-norms that are the most applied fuzzy operators invarious fuzzy modelling problems. In this paper, we study a linear optimization problem where thefeasible region is formed as a system of fuzzy relational equations (FRE) defined by the Aczel-Alsinat-norm. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutionsis an NP-hard problem, conventional methods may not be directly employed. The resolution of thefeasible region is completely investigated. Based on some theoretical properties of the problem, analgorithm is presented to find all the optimal solutions, and finally an example is described to illustratethis algorithm.

Keywords:

Fuzzy relational equations , linear optimization , strict t-norm , Aczel-Alsina t-norm