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An Efficient Approach to Approximate Fuzzy Ideals of Semirings Using Bipolar Techniques

Author

Listed:
  • Muhammad Shabir

    (Department of Mathematics, Quaid-e-Azam University Islamabad, Islamabad 44000, Pakistan)

  • Ahmad N. Al-Kenani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia)

  • Fawad Javed

    (Department of Mathematics, Quaid-e-Azam University Islamabad, Islamabad 44000, Pakistan)

  • Shahida Bashir

    (Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan)

Abstract

The bipolar fuzzy (BF) set is an extension of the fuzzy set used to solve the uncertainty of having two poles, positive and negative. The rough set is a useful mathematical technique to handle vagueness and impreciseness. The major objective of this paper is to analyze the notion of approximation of BF ideals of semirings by combining the theories of the rough and BF sets. Then, the idea of rough approximation of BF subsemirings (ideals, bi-ideals and interior ideals) of semirings is developed. In addition, semirings are characterized by upper and lower rough approximations using BF ideals. Further, it is seen that congruence relations (CRs) and complete congruence relations (CCRs) play fundamental roles for rough approximations of bipolar fuzzy ideals. Therefore, their associated properties are investigated by means of CRs and CCRs.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1009-:d:776451
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    References listed on IDEAS

    as
    1. Shahida Bashir & Medhit Fatima & Muhammad Shabir, 2019. "Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    2. 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.
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