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A fuzzy linear programming model with fuzzy parameters and decision variables

Author

Listed:
  • Saber Saati
  • Madjid Tavana
  • Adel Hatami-Marbini
  • Elham Hajiakhondi

Abstract

Linear programming (LP) is an optimisation technique most widely used for optimal allocation of limited resources amongst competing activities. Precise data are fundamentally indispensable in standard LP problems. However, the observed values of the data in real-world problems are often imprecise or vague. Fuzzy set theory has been extensively used to represent ambiguous, uncertain or imprecise data in LP by formalising the inaccuracies inherent in human decision-making. We propose a new method for solving fuzzy LP (FLP) problems in which the right-hand side parameters and the decision variables are represented by fuzzy numbers. A new fuzzy ranking model and a new supplementary variable are utilised in the proposed FLP method to obtain the fuzzy and crisp optimal solutions by solving one LP model. Moreover, we introduce an alternative model with deterministic variables and parameters derived from the proposed FLP model. Interestingly, the result of the alternative model is identical to the crisp solution of the proposed FLP model. We use a numerical example from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedure.

Suggested Citation

  • Saber Saati & Madjid Tavana & Adel Hatami-Marbini & Elham Hajiakhondi, 2015. "A fuzzy linear programming model with fuzzy parameters and decision variables," International Journal of Information and Decision Sciences, Inderscience Enterprises Ltd, vol. 7(4), pages 312-333.
    • Handle: RePEc:ids:ijidsc:v:7:y:2015:i:4:p:312-333
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    Cited by:

    1. Namrata Rani & Vandana Goyal & Deepak Gupta, 2022. "FGP approach and Rouben ranking function to bi-level multi-objective quadratic fractional problem with trapezoidal fuzzy numbers and soft fuzzy constraints," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(1), pages 113-122, February.

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