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An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems

Author

Listed:
  • Salma Iqbal

    (Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan
    These authors contributed equally to this work.)

  • Naveed Yaqoob

    (Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan
    These authors contributed equally to this work.)

  • Muhammad Gulistan

    (Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada
    These authors contributed equally to this work.)

Abstract

The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree α of α level sets, the max-min problem is solved in this interactive technique using Zimmermann’s min operator method. By using the updating technique of degree α , we can solve DM from the set of α -cut optimal solutions based on the membership function and non-membership function. Fuzzy numbers based on α -cut analysis bestowing the degree α given by DM can first be used to classify fuzzy Diophantine inside the coefficients. After this, a crisp multi-objective non-linear fractional programming problem (MONLFPP) is created from a Diophantine fuzzy nonlinear programming problem (DFNLFPP). Additionally, the MONLFPP can be reduced to a single-objective nonlinear programming problem (NLPP) using the idea of fuzzy mathematical programming, which can then be solved using any suitable NLPP algorithm. The suggested approach is demonstrated using a numerical example.

Suggested Citation

  • Salma Iqbal & Naveed Yaqoob & Muhammad Gulistan, 2023. "An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems," Mathematics, MDPI, vol. 11(15), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3383-:d:1209170
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Sujeet Kumar Singh & Shiv Prasad Yadav, 2016. "A new approach for solving intuitionistic fuzzy transportation problem of type-2," Annals of Operations Research, Springer, vol. 243(1), pages 349-363, August.
    3. Sakawa, Masatoshi & Nishizaki, Ichiro & Uemura, Yoshio, 2001. "Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: A case study," European Journal of Operational Research, Elsevier, vol. 135(1), pages 142-157, November.
    4. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
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