Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition
Applied and Computational Mathematics
Volume 4, Issue 1-2, January 2015, Pages: 20-30
Received: Dec. 21, 2014; Accepted: Jan. 19, 2015; Published: Feb. 8, 2015
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Authors
Z‎. ‎ Valizadeh-Gh, Department of Mathematics‎, ‎Roudehen Branch‎, ‎Islamic Azad University‎, ‎Roudehen‎, ‎Iran
E‎. ‎Khorram, Faculty of Mathematics and Computer Science,‎ Amirkabir University of Technology, ‎Tehran‎, ‎Iran
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Abstract
‎In this paper‎, ‎linear fractional multi-objective optimization problems subject to a system of fuzzy relational equations (FRE) using the max-average composition are considered‎. ‎First‎, ‎some theorems and results are presented to thoroughly identify and reduce the feasible set of the fuzzy relation equations‎. ‎Next‎, ‎the linear fractional multi-objective optimization problem is converted to a linear one using Nykowski and Zolkiewski's approach‎. ‎Then‎, ‎the efficient solutions are obtained by applying the improved ε-constraint method‎. ‎‎Finally‎, ‎the proposed method is effectively tested by solving a consistent test problem‎.
Keywords
Fuzzy Relational Equation, The Max-Average Composition, Linear Fractional Multi-Objective Optimization Problems, The Improved ε-Constraint Method‎
To cite this article
Z‎. ‎ Valizadeh-Gh, E‎. ‎Khorram, Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition, Applied and Computational Mathematics. Special Issue:New Advances in Fuzzy Mathematics: Theory, Algorithms, and Applications. Vol. 4, No. 1-2, 2015, pp. 20-30. doi: 10.11648/j.acm.s.2015040102.15
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