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Interactive Fuzzy Goal Programming Based on Jacobian Matrix to Solve Decentralized Bi-level Multi-objective Fractional Programming Problems

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Abstract

This paper attempts to shed light on solving decentralized bi-level multi-objective fractional programming problems (DBL-MOFPP) with single decision maker at the first level and multiple decision makers at the second level. In this paper, we proposed a fuzzy goal programming (FGP) based on Jacobian matrix for DBL-MOFPP. In the proposed approach, membership functions are associated for the fuzzy goals of all objectives at two levels and they are linearized using a Jacobian matrix. Then FGP approach is used to achieve highest degree of each of the membership goals by obtaining the most satisfactory solution for all decision makers. We used known numerical example and practical application in order to show the efficiency and superiority of the proposed approach. Sensitivity analysis with variation of tolerance values on decision functions is performed to present how the solution is sensitive to the change of tolerance values.

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Authors and Affiliations

  1. Industrial Engineering Department, Erciyes University, 38039, Kayseri, Turkey

    M. Duran Toksarı & Yasemin Bilim

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  1. M. Duran Toksarı
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  2. Yasemin Bilim
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Correspondence to M. Duran Toksarı.

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Toksarı, M.D., Bilim, Y. Interactive Fuzzy Goal Programming Based on Jacobian Matrix to Solve Decentralized Bi-level Multi-objective Fractional Programming Problems. Int. J. Fuzzy Syst. 17, 499–508 (2015). https://doi.org/10.1007/s40815-015-0036-1

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  • DOI: https://doi.org/10.1007/s40815-015-0036-1

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