Title: Solving multi-objective linear fractional programming problem based on Stanojevic's normalisation technique under fuzzy environment
Authors: Indrani Maiti; Tarni Mandal; Surapati Pramanik; Sapan Kumar Das
Addresses: Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, India ' Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, India ' Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, P.O. Naraynpur, North 24 Paraganas, 743126, India ' Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, India
Abstract: The fuzzy linear fractional programming (FLFP) problem has always been a subject of keen interest, and a rigorous research has also been done on it. However, due to some limitation of these methods, they cannot be applied to solving multi-objective linear fractional programming (MOLFP) problem with fuzzy coefficients and fuzzy variables. To overcome these limitations, Taylor series approximation and normalisation technique is applied in this problem. In this paper, we deal with the concept of α-cuts which are employed to defuzzify the problem. We also formulate the membership function of each objective function is linearised using first order Taylor series approximation and normalisation technique. Normalisation technique is employed to ensure that the range of the reduced membership function belongs to [0, 1]. Then fuzzy goal programming is applied to solve the formulated problem so that the negative deviational variables are minimised. Finally, the fruitfulness of the proposed algorithm is illustrated through numerical examples as compared to other methods.
Keywords: fuzzy number; fuzzy goal programming; FGP; multi-objective linear fractional programming problem; Taylor series; normalisation; crisp functions.
International Journal of Operational Research, 2021 Vol.42 No.4, pp.543 - 564
Received: 24 Mar 2019
Accepted: 09 Jun 2019
Published online: 04 Jan 2022 *