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Parametric Optimization for Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers

Author

Listed:
  • Aliviya Bhowmick

    (Department of Mathematics & Computing, IIT(ISM) Dhanbad, Dhanbad 826004, Jharkhand, India)

  • Snehashish Chakraverty

    (Department of Mathematics, NIT Rourkela, Rourkela 769008, Odisha, India)

  • Subhashish Chatterjee

    (Department of Mathematics & Computing, IIT(ISM) Dhanbad, Dhanbad 826004, Jharkhand, India)

Abstract

This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world problems. To address this gap, an innovative method has been proposed which incorporates fuzzy logic to model the uncertain parameters as TFNs, allowing for a more realistic and flexible representation of the problem space. The proposed method stands out due to its integration of fuzzy arithmetic into the optimization process, enabling the handling of fuzzy constraints and objectives directly. Unlike conventional techniques that rely on crisp approximations or the defuzzification process, the proposed approach maintains the fuzziness throughout the computation, ensuring that the solutions retain their fuzzy characteristics and better reflect the uncertainties present in the input data. In summary, the proposed method has the ability to directly incorporate fuzzy parameters into the optimization framework, providing a more comprehensive solution to FFLP problems. The main findings of this study underscore the method’s effectiveness and its potential for broader application in various fields where decision-making under uncertainty is crucial.

Suggested Citation

  • Aliviya Bhowmick & Snehashish Chakraverty & Subhashish Chatterjee, 2024. "Parametric Optimization for Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers," Mathematics, MDPI, vol. 12(19), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3051-:d:1488720
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    References listed on IDEAS

    as
    1. Saeid Jafarzadeh Ghoushchi & Elnaz Osgooei & Gholamreza Haseli & Hana Tomaskova, 2021. "A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    2. D. Behera & S. Chakraverty, 2013. "Solution to fuzzy system of linear equations with crisp coefficients," Fuzzy Information and Engineering, Springer, vol. 5(2), pages 205-219, June.
    3. D. Behera & S. Chakraverty, 2013. "Solution to Fuzzy System of Linear Equations with Crisp Coefficients," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 5(2), pages 205-219, June.
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