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Bi-Level Linear Fuzzy Fractional Programming Problem Under Trapezoidal Fuzzy Environment: A Solution Approach

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Proceedings of International Joint Conference on Advances in Computational Intelligence (IJCACI 2022)

Part of the book series: Algorithms for Intelligent Systems ((AIS))

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Abstract

This paper proposes a method to solve a bi-level linear fuzzy fractional programming problem comprising all its constants and coefficients expressed in form of trapezoidal fuzzy numbers. Fuzzy \(\alpha , \beta \)-cuts are respectively used in the objective functions and constraints to equivalently transform the bi-level fuzzy optimization into bi-level interval valued form. Subsequently, a bi-level bi-objective linear fractional programming problem is generated. Change of variable method is implemented to construct linear fuzzy membership functions at upper and lower level. Fuzzy goal programming eliminating over deviations from aspiration level of fuzzy membership functions along with a proposed modified linearization process of fractional functions are together used to determine the compromise solution of the problem. To illustrate and justify the feasibility of the proposed method, an existing numerical problem is solved and the results obtained are comparatively analyzed.

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Author information

Authors and Affiliations

  1. Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar, 751024, Odisha, India

    Sujit Maharana & Suvasis Nayak

Authors
  1. Sujit Maharana
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  2. Suvasis Nayak
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Correspondence to Suvasis Nayak .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Jahangirnagar University, Dhaka, Bangladesh

    Mohammad Shorif Uddin

  2. Department of Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

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Maharana, S., Nayak, S. (2023). Bi-Level Linear Fuzzy Fractional Programming Problem Under Trapezoidal Fuzzy Environment: A Solution Approach. In: Uddin, M.S., Bansal, J.C. (eds) Proceedings of International Joint Conference on Advances in Computational Intelligence. IJCACI 2022. Algorithms for Intelligent Systems. Springer, Singapore. https://doi.org/10.1007/978-981-99-1435-7_38

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