Amin Ghodousian - Faculty of Engineering Science, University of Tehran, Tehran, Iran
Alireza Norouzi Azad - Department of Engineering Science, University of Tehran, Tehran, Iran
Zahra Boreiri - Department of Engineering Science, University of Tehran, Tehran, Iran

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.

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