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Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making

Author

Listed:
  • Muhammad Zishan Anwar

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

  • Shahida Bashir

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

  • Muhammad Shabir

    (Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan)

  • Majed G. Alharbi

    (Department of Mathematics, College of Science and Arts, Almithnab, Qassim University, Buridah 51931, Saudi Arabia)

Abstract

Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example.

Suggested Citation

  • Muhammad Zishan Anwar & Shahida Bashir & Muhammad Shabir & Majed G. Alharbi, 2021. "Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making," Mathematics, MDPI, vol. 9(20), pages 1-22, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2587-:d:656862
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    References listed on IDEAS

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    1. Muhammad Zishan Anwar & Shahida Bashir & Muhammad Shabir, 2021. "An Efficient Model for the Approximation of Intuitionistic Fuzzy Sets in terms of Soft Relations with Applications in Decision Making," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-19, October.
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    Cited by:

    1. Sorin Nădăban, 2022. "Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)," Mathematics, MDPI, vol. 10(17), pages 1-3, September.

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