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In this paper, an optimization model with a linear objective functionsubjected to a system of fuzzy relation equations (FRE) is studied where thefeasible region is defined by the Dombi t-norm. Dombi family of t-normsincludes a parametric family of continuous strict t-norms, whose members areincreasing functions of the parameter. This family of t-norms covers the wholespectrum of t-norms when the parameter is changed from zero to infinity. Sincethe feasible solutions set of FREs is non-convex and 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, based on some theoretical properties of the problem, amodified branch-and-bound solution technique is presented, which solves theproblem by considering a few number of feasible paths. After presenting oursolution procedure, a concrete example is included for illustration purpose.

A fast method for solving the linear optimization p roblem subjected to simplified Dombi fuzzy relational equations