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Fuzzy Fractional Minimal Cost Flow Problem

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Abstract

A new version of fractional minimal cost flow problem with fuzzy arc costs is focused in this study. The fuzzy arc costs are applied as in most of the real-world applications, the parameters have high degree of uncertainty. The goal of this problem is to determine the minimum fuzzy fractional cost of sending and passing a specified flow value into and from a network. A decomposition-based solution methodology is introduced to tackle this problem. The methodology applies Zadeh’s extension principle to decompose the problem to two upper bound and lower bound problems. These problems are capable of being solved for different \(\alpha\)-cut values to construct the fuzzy fractional minimal cost flow value as the objective function value. The efficiency of the proposed solution methodology is studied over some well-known examples of fractional minimal cost flow problem. The obtained results show the superiority of the proposed approach comparing to the methods of the literature.

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Authors and Affiliations

  1. Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran

    Ali Mahmoodirad

  2. Department of Industrial Engineering, Firouzabad Institute of Higher Education, Firouzabad, Fars, Iran

    Sadegh Niroomand

  3. Department of Industrial Engineering, Istanbul Aydin University, Florya, Istanbul, Turkey

    Nima Mirzaei

  4. Department of Industrial Engineering, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran

    Abbas Shoja

Authors
  1. Ali Mahmoodirad
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  2. Sadegh Niroomand
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  3. Nima Mirzaei
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  4. Abbas Shoja
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Correspondence to Ali Mahmoodirad.

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Mahmoodirad, A., Niroomand, S., Mirzaei, N. et al. Fuzzy Fractional Minimal Cost Flow Problem. Int. J. Fuzzy Syst. 20, 174–186 (2018). https://doi.org/10.1007/s40815-017-0293-2

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  • DOI: https://doi.org/10.1007/s40815-017-0293-2

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