Linear optimization with bipolar fuzzy relational equation constraints using the Łukasiewicz triangular norm

This paper discusses the linear optimization problem constrained by a system of bipolar fuzzy relational equations with max- $$T$$ T composition, where the involved triangular norm is the ?ukasiewicz t-norm. Although it is in general NP-hard, such an optimization problem can be reformulated in polynomial time into a 0-1 integer linear optimization problem and then solved taking advantage of well developed techniques in integer optimization.