Maximizing a monomial geometric objective function subject to bipolar max-product fuzzy relation constraints

Article type: Research Article

Authors: Aliannezhadi, Samaneh | Ardalan, Shadi Shahab | Abbasi Molai, Ali^*

Affiliations: School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran

Correspondence: [*] Corresponding author. Ali Abbasi Molai, School of Mathematics and Computer Sciences, Damghan University, P.O. Box 36715-364, Damghan, Iran. Tel.: +98 9126933771; Fax: +98 23 35220092; E-mail: a_abbasimolai@du.ac.ir.

Abstract: In this paper, the problem of maximizing a monomial geometric objective function subject to bipolar max-product fuzzy relation constraints is studied. First of all, it is shown that the bipolar max-product Fuzzy Relation Inequality (FRI) system can equivalently be converted to a bipolar max-product Fuzzy Relation Equation (FRE) system. Hence, the structure of feasible domain of the problem is determined in the case of the bipolar max-product FRE system. It is shown that its solution set is non-convex, in a general case. Some sufficient conditions are proposed for solution existence of its feasible domain. An algorithm is designed to solve the optimization problem with regard to the structure of its feasible domain and the properties of the objective function. Its importance is also illustrated by an application example in the area of economics and covering problem. Some numerical examples are given to illustrate the above points.

Keywords: Bipolar fuzzy relation equation, max-product composition, non-convex optimization, bipolar variables

DOI: 10.3233/JIFS-151820

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 337-350, 2017