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.
| Published in |
Applied and Computational Mathematics (Volume 4, Issue 1-2)
This article belongs to the Special Issue New Advances in Fuzzy Mathematics: Theory, Algorithms, and Applications |
| DOI | 10.11648/j.acm.s.2015040102.15 |
| Page(s) | 20-30 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Fuzzy Relational Equation, The Max-Average Composition, Linear Fractional Multi-Objective Optimization Problems, The Improved ε-Constraint Method
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APA Style
Z. Valizadeh-Gh, E. Khorram. (2015). Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition. Applied and Computational Mathematics, 4(1-2), 20-30. https://doi.org/10.11648/j.acm.s.2015040102.15
ACS Style
Z. Valizadeh-Gh; E. Khorram. Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition. Appl. Comput. Math. 2015, 4(1-2), 20-30. doi: 10.11648/j.acm.s.2015040102.15
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Download@article{10.11648/j.acm.s.2015040102.15,
author = {Z. Valizadeh-Gh and E. Khorram},
title = {Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition},
journal = {Applied and Computational Mathematics},
volume = {4},
number = {1-2},
pages = {20-30},
doi = {10.11648/j.acm.s.2015040102.15},
url = {https://doi.org/10.11648/j.acm.s.2015040102.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2015040102.15},
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.},
year = {2015}
}
TY - JOUR T1 - Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition AU - Z. Valizadeh-Gh AU - E. Khorram Y1 - 2015/02/08 PY - 2015 N1 - https://doi.org/10.11648/j.acm.s.2015040102.15 DO - 10.11648/j.acm.s.2015040102.15 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 20 EP - 30 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.s.2015040102.15 AB - 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. VL - 4 IS - 1-2 ER -
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