Solving a linear programming problem with the convex combination of the max–min and the max-average fuzzy relation equations

In this paper, we introduce a fuzzy operator constructed by the convex combination of two known operators, max–min and max-average compositions [H.J. Zimmermann, Fuzzy set theory and it’s application, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999]. This operator contains some propertie...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 180; no. 1; pp. 411 - 418
Main Authors: Ghodousian, A., Khorram, E.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.09.2006
Elsevier
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Fuzzy relation compositions
Fuzzy relation equations
Linear objective function optimization
Mathematical analysis
Mathematics
Sciences and techniques of general use
Fuzzy relation equations
Fuzzy relation compositions
Linear objective function optimization
Operator equation
Linear function
Linear programming
Convex programming
Linear equation
Applied mathematics
Fuzzy relation
Fuzzy set theory
Objective function
Mathematical programming
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:In this paper, we introduce a fuzzy operator constructed by the convex combination of two known operators, max–min and max-average compositions [H.J. Zimmermann, Fuzzy set theory and it’s application, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999]. This operator contains some properties of the two known compositions when it generates the feasible region for linear optimization problems. We investigate linear optimization problems whose feasible region is the fuzzy sets defined with this operator. Thus, firstly, the structure of these fuzzy regions is considered and then a method to solve the linear optimization problems with fuzzy equation constraints regarding this operator is presented.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2005.12.027