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Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition

Received: 21 December 2014     Accepted: 19 January 2015     Published: 8 February 2015
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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.

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

Keywords

Fuzzy Relational Equation, The Max-Average Composition, Linear Fractional Multi-Objective Optimization Problems, The Improved ε-Constraint Method‎

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Cite This Article
  • 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

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    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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    AMA 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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  • @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}
    }
    

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    T1  - Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition
    AU  - Z‎. ‎ Valizadeh-Gh
    AU  - E‎. ‎Khorram
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    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
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    ER  - 

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