  In this paper, an optimization model with a linear objective function
subjected to a system of fuzzy relation equations (FRE) is studied where the
feasible region is 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. Firstly, the feasible domain is
characterized and then, based on some theoretical properties of the problem, a
modified branch-and-bound solution technique is presented, which solves the
problem by considering a few number of feasible paths. After presenting our
solution procedure, a concrete example is included for illustration purpose.
