  In this paper, we introduce a type of latticized optimization problem whose
objective function is the maximum component function and the feasible region is
defined as a system of fuzzy relational equalities (FRE) defined by the Dombi
t-norm. Dombi family of t-norms includes a parametric family of continuous
strict t-norms, whose members are increasing functions of the parameter. This
family of t-norms covers the whole spectrum of t-norms when the parameter is
changed from zero to infinity. Since the feasible solutions set of FREs is
non-convex and 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. Some necessary and sufficient conditions are derived to determine
the feasibility of the problem. The feasible solution set is characterized in
terms of a finite number of closed convex cells. An algorithm is presented for
solving this nonlinear problem. It is proved that the algorithm can find the
exact optimal solution and an example is presented to illustrate the proposed
algorithm.
