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arXiv · 2207.06373

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

Amin Ghodousian·Sara Zal
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Abstract

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.

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Amin Ghodousian, Sara Zal. 2022-06-30. A fast method for solving the linear optimization p roblem subjected to simplified Dombi fuzzy relational equations. https://arxiv.org/abs/2207.06373

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