FRE paths for finding the minimal solutions of the linear optimization problems subjected to Einstein-product-FREs

In this paper, an optimization model with a linear objective function subject to a system of fuzzy relation equations (FRE) is studied where the feasible region is defined by the Einstein product t-norm. Since the finding of all minimal solutions is an NP-hard problem, designing an efficient solution procedure for solving such problems is not a trivial job. Firstly, the feasible domain is characterized and then the problem is solved with a modified branch-and-bound solution technique based on a new solution set that includes the minimal solutions. After presenting our solution procedure, a concrete example is included for illustration purposes.

Keywords:

Fuzzy relational equations , linear optimization , strict t-norm , Einstein product t-norm ,