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Scalarizing fuzzy multi-objective linear fractional programming with application

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Abstract

Multi-objective linear fractional programming (MOLFP) is an important field of research. As in several real-world problems, the decision-makers (DMs) need to find a solution to a MOLFP. In making a decision, the DM needs to deal with several imprecise numerical quantities due to fluctuating environments. This work presents a novel fuzzy multi-objective linear fractional programming (FMOLFP) model in an ambiguous environment. Since fuzzy set theory has been shown to be a useful tool to handle decisive parameters’ uncertain nature in several research articles. The proposed model attempts to minimize multiple conflicting objectives, simultaneously having some uncertain/fuzzy parameters. An equivalent crisp MOLFP model has been derived using the arithmetic operations on fuzzy numbers. After that, applying the Charnes-Cooper transformation effectively, the problem reduces to a deterministic multi-objective linear programming (MOLP). The MOLP is scalarized by using Gamma-connective and minimum bounded sum operator techniques to solve to optimality. The proposed algorithm’s computation phase’s basic idea is to transform the FMOLFP into a deterministic MOLP. Then to scalarize the MOLP into a single objective linear problem (LP) to optimize further. Later, the proposed model is applied to solve an integrated production-transportation problem.

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Authors and Affiliations

  1. Indian Institute of Management Jammu, Jammu, 180016, India

    Sujeet Kumar Singh

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Shiv Prasad Yadav

Authors
  1. Sujeet Kumar Singh
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  2. Shiv Prasad Yadav
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Communicated by Anibal Tavares de Azevedo.

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Singh, S.K., Yadav, S.P. Scalarizing fuzzy multi-objective linear fractional programming with application. Comp. Appl. Math. 41, 93 (2022). https://doi.org/10.1007/s40314-022-01798-2

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  • DOI: https://doi.org/10.1007/s40314-022-01798-2

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