Geometric programming problem with single-term exponents subject to max-product fuzzy relational equations

Authors:
Xuegang Zhou;Rashida Ahat
Affiliations:
Department of Applied Mathematics, GuangDong University of Finance, Guangzhou, Guangdong, 510521, China;School of Mathematics and System Science of Xinjiang University, Wulumuqi, Xinjiang, 830046, China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

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Abstract

In this paper, an optimization model for minimizing an objective function with single-term exponents subject to fuzzy relational equations specified in max-product composition is presented. The solution set of such a fuzzy relational equation is a non-convex set. First, we present some properties for the optimization problem under the assumptions of both negative and nonnegative exponents in the objective function. Second, an efficient procedure is developed to find an optimal solution without looking for all the potential minimal solutions and without using the value matrix. An example is provided to illustrate the procedure.