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Solution of Fully Bipolar Fuzzy Linear Programming Models

Author

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  • Muhammad Athar Mehmood
  • Muhammad Akram
  • Majed G. Alharbi
  • Shahida Bashir

Abstract

The Yin-Yang bipolar fuzzy set is a powerful mathematical tool for depicting fuzziness and vagueness. We first extend the concept of crisp linear programming problem in a bipolar fuzzy environment based on bipolar fuzzy numbers. We first define arithmetic operations of unrestricted bipolar fuzzy numbers and multiplication of an unrestricted trapezoidal bipolar fuzzy number (TrBFN) with non-negative TrBFN. We then propose a method for solving fully bipolar fuzzy linear programming problems (FBFLPPs) with equality constraints in which the coefficients are unrestricted triangular bipolar fuzzy numbers and decision variables are nonnegative triangular bipolar fuzzy numbers. Furthermore, we present a method for solving FBFLPPs with equality constraints in which the coefficients and decision variables are unrestricted TrBFNs. The FBFLPP is transformed into a crisp linear programming problem, and then, it is solved to achieve the exact bipolar fuzzy optimal solution. We illustrate the proposed methodologies with several numerical examples.

Suggested Citation

  • Muhammad Athar Mehmood & Muhammad Akram & Majed G. Alharbi & Shahida Bashir, 2021. "Solution of Fully Bipolar Fuzzy Linear Programming Models," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-31, April.
    • Handle: RePEc:hin:jnlmpe:9961891
    DOI: 10.1155/2021/9961891
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    Cited by:

    1. Muhammad Shabir & Ahmad N. Al-Kenani & Fawad Javed & Shahida Bashir, 2022. "An Efficient Approach to Approximate Fuzzy Ideals of Semirings Using Bipolar Techniques," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    2. Figueroa–García, Juan Carlos & Hernández, Germán & Franco, Carlos, 2022. "A review on history, trends and perspectives of fuzzy linear programming," Operations Research Perspectives, Elsevier, vol. 9(C).
    3. Shahida Bashir & Sundas Shahzadi & Ahmad N. Al-Kenani & Muhammad Shabir, 2021. "Regular and Intra-Regular Semigroups in Terms of m -Polar Fuzzy Environment," Mathematics, MDPI, vol. 9(17), pages 1-18, August.

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