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A modified TOPSIS approach for solving stochastic fuzzy multi-level multi-objective fractional decision making problem

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Abstract

This paper presents a new modified technique for order preference by similarity to ideal solution (M-TOPSIS) approach for unraveling stochastic fuzzy multi-level multi-objective fractional decision making problem (ML-MOFDM) problem. In the proposed model the coefficients and the scalars of the fractional objectives have a fuzzy nature. The right-hand sides are stochastic parameters also, both of the left-hand side coefficients and the tolerance measures are fuzzy kind. In this manner, the deterministic-crisp ML-MOFDM model of stochastic fuzzy ML-MOFDM can be gotten utilizing chance constrained strategy with predominance plausibility criteria and the \( \alpha \)-cut methodology. In literature, almost all works on multi-level fractional programming are the crisp version, in which they convert the fractional functions into a linear one using a first order Taylor series which causes rounding off error. The proposed M-TOPSIS approach presents a new method for solving such problem without approximating or changing the nature of the problem. An algorithm to clear up the M-TOPSIS approach, just as illustrative numerical model is displayed.

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Authors and Affiliations

  1. Department of Basic Engineering Sciences, Faculty of Engineering, Benha University, Elqalyoubia, Egypt

    M. A. El Sayed & Ibrahim A. Baky

  2. Department of Mathematics, Faculty of Sciences, Tabuk University, Tabuk, Saudi Arabia

    Ibrahim A. Baky

  3. Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad Prayagraj, 211004, India

    Pitam Singh

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  1. M. A. El Sayed
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  2. Ibrahim A. Baky
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  3. Pitam Singh
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Correspondence to M. A. El Sayed.

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Appendices

Appendix 1: Lingo programming screen shot for the numerical example

figure b

Appendix 2: Lingo programming screen shot for the application problem

figure c

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El Sayed, M.A., Baky, I.A. & Singh, P. A modified TOPSIS approach for solving stochastic fuzzy multi-level multi-objective fractional decision making problem. OPSEARCH 57, 1374–1403 (2020). https://doi.org/10.1007/s12597-020-00461-w

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