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Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach

Author

Listed:
  • M. S. Osman

    (El Asher University)

  • O. E. Emam

    (Helwan University)

  • M. A. El Sayed

    (Benha University)

Abstract

In this paper, a fuzzy goal programming (FGP) approach is considered for solving stochastic fuzzy multi-level multi-objective fractional programming (ML-MOFP) problem. In the developed stochastic fuzzy ML-MOFP model the fractional objective function coefficients and scalars are represented by fuzzy parameters. Moreover, in the constraints, the right-hand sides are independent random variable with known distribution function while both the left-hand side coefficients and the tolerance measures are considered to be fuzzy parameters. Therefore, the chance-constrained approach with dominance possibility criteria and the α-cut approach are utilized to transform the stochastic fuzzy ML-MOFP problem to its equivalent deterministic-crisp problem. Then, the membership functions for the defined fuzzy goals are setup. Also, in the proposed FGP model, a linearization procedures for the membership goals of the objective functions is developed. Hence, the FGP approach is used to achieve the highest degree of each of the membership goals by minimizing the sum of the negative deviational variables. Finally, an algorithm to clarify the developed FGP approach, as well as Illustrative numerical example, are presented.

Suggested Citation

  • M. S. Osman & O. E. Emam & M. A. El Sayed, 2017. "Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 816-840, December.
    • Handle: RePEc:spr:opsear:v:54:y:2017:i:4:d:10.1007_s12597-017-0307-8
    DOI: 10.1007/s12597-017-0307-8
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    References listed on IDEAS

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    1. Lachhwani, Kailash, 2015. "Modified FGP approach for multi-level multi objective linear fractional programming problems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1038-1049.
    2. Ahlatcioglu, Mehmet & Tiryaki, Fatma, 2007. "Interactive fuzzy programming for decentralized two-level linear fractional programming (DTLLFP) problems," Omega, Elsevier, vol. 35(4), pages 432-450, August.
    3. Pramanik, Surapati & Roy, Tapan Kumar, 2007. "Fuzzy goal programming approach to multilevel programming problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1151-1166, January.
    4. Arora, S.R. & Gupta, Ritu, 2009. "Interactive fuzzy goal programming approach for bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 194(2), pages 368-376, April.
    5. Romero, Carlos, 2001. "Extended lexicographic goal programming: a unifying approach," Omega, Elsevier, vol. 29(1), pages 63-71, February.
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    Cited by:

    1. Hawaf AbdAlhakim & O. E. Emam & A. A. Abd El-Mageed, 2019. "Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(2), pages 367-389, June.
    2. M. A. El Sayed & Ibrahim A. Baky & Pitam Singh, 2020. "A modified TOPSIS approach for solving stochastic fuzzy multi-level multi-objective fractional decision making problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1374-1403, December.
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    4. Kailash Lachhwani, 2021. "Solving the general fully neutrosophic multi-level multiobjective linear programming problems," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1192-1216, December.
    5. Zhang, Fan & Cai, Yanpeng & Tan, Qian & Wang, Xuan, 2021. "Spatial water footprint optimization of crop planting: A fuzzy multiobjective optimal approach based on MOD16 evapotranspiration products," Agricultural Water Management, Elsevier, vol. 256(C).

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