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Parametric computation of a fuzzy set solution to a class of fuzzy linear fractional optimization problems

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Abstract

The class of fuzzy linear fractional optimization problems with fuzzy coefficients in the objective function is considered in this paper. We propose a parametric method for computing the membership values of the extreme points in the fuzzy set solution to such problems. We replace the exhaustive computation of the membership values—found in the literature for solving the same class of problems—by a parametric analysis of the efficiency of the feasible basic solutions to the bi-objective linear fractional programming problem through the optimality test in a related linear programming problem, thus simplifying the computation. An illustrative example from the field of production planning is included in the paper to complete the theoretical presentation of the solving approach, but also to emphasize how many real life problems may be modelled mathematically using fuzzy linear fractional optimization.

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Acknowledgments

This research was partially supported by the Ministry of Education and Science, Republic of Serbia, Project numbers TR36006 and TR32013. The authors want to express their gratitude to the anonymous referees for their valuable suggestions and remarks.

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Authors and Affiliations

  1. Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, Belgrade, 11001, Serbia

    Bogdana Stanojević

  2. Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, Belgrade, 11000, Serbia

    Milan Stanojević

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  1. Bogdana Stanojević
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  2. Milan Stanojević
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Correspondence to Bogdana Stanojević.

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Stanojević, B., Stanojević, M. Parametric computation of a fuzzy set solution to a class of fuzzy linear fractional optimization problems. Fuzzy Optim Decis Making 15, 435–455 (2016). https://doi.org/10.1007/s10700-016-9232-1

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  • DOI: https://doi.org/10.1007/s10700-016-9232-1

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