A modified TOPSIS approach for solving stochastic fuzzy multi-level multi-objective fractional decision making problem
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A modified TOPSIS approach for solving stochastic fuzzy multi‑level multi‑objective fractional decision making problem M. A. El Sayed1 · Ibrahim A. Baky1,2 · Pitam Singh3 Accepted: 4 June 2020 © Operational Research Society of India 2020
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 lefthand 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 𝛼-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. Keywords Multi-level optimization · Multi-objective programming · TOPSIS · Fractional programming · Chance constrained programming · Fuzzy sets
* M. A. El Sayed [email protected] Ibrahim A. Baky [email protected] Pitam Singh [email protected] 1
Department of Basic Engineering Sciences, Faculty of Engineering, Benha University, Elqalyoubia, Egypt
2
Department of Mathematics, Faculty of Sciences, Tabuk University, Tabuk, Saudi Arabia
3
Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad Prayagraj 211004, India
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1 Introduction Multi-level programming problems (MLPP) emerge in multi-leveled associations including numerous decision leaders (DL) to settle decentralized programming issues where each DL controls a lot of choice factors autonomously [1–5]. DL must have a bargaining and agreeable inspiration for assurance of an answer for the general advantage of the association at which each DL gains a minimum standard of achievement. In the course of the most recent couple of years, fast improvement in thinking through MLPP [1, 3, 6–11] has been seen and a lot of strategies have been displayed. The utilization of the idea of the fuzzy set theory to MLPP for getting satisfactory choices was first displayed by Lai in [5]. Interactive fuzzy programming for bi-level fractional programming problems was exhibited in [12]. Fuzzy goal programming (FGP) algorithm was created by Baky for solving MLPP [3]. MLPP were starting late focused by Chen and Chen [6]. FGP model and fuzzy goals of the top level decision variables for solving MLPP has been introduced by Pramanik and Roy [8]. Th
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