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In this paper, an optimization model with a linear objective function subjectto a system of fuzzy relation equations (FRE) is studied where the feasibleregion is defined by the Lukasiewicz t-norm. Since the finding of all minimalsolutions is an NP-hard problem, designing an efficient solution procedure forsolving such problems is not a trivial job. Firstly, the feasible domain ischaracterized and then the problem is solved with a modified branch-and-boundsolution technique based on a new solution set that includes the minimalsolutions. After presenting our solution procedure, a concrete example isincluded for illustration purposes.

A branch and bound technique for finding the minimal solutions of the linear optimization problems subjected to Lukasiewicz