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Pessimistic Multigranulation Rough Set of Intuitionistic Fuzzy Sets Based on Soft Relations

Author

Listed:
  • Muhammad Zishan Anwar

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

  • Ahmad N. Al-Kenani

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

  • Shahida Bashir

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

  • Muhammad Shabir

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

Abstract

Qian presented multigranulation rough set (MGRS) models based on Pawlak’s rough set (RS) model. There are two types of MGRS models, named optimistic MGRS and pessimistic MGRS. Recently, Shabir et al. presented an optimistic multigranulation intuitionistic fuzzy rough set (OMGIFRS) based on soft binary relations. This paper explores the pessimistic multigranulation intuitionistic fuzzy rough set (PMGIFRS) based on soft relations combined with a soft set (SS) over two universes. The resulting two sets are lower approximations and upper approximations with respect to the aftersets and foresets. Some basic properties of this established model are studied. Similarly, the MGRS of an IFS based on multiple soft relations is presented and some algebraic properties are discussed. Finally, an example is presented that illustrates the importance of the proposed decision-making algorithm.

Suggested Citation

  • Muhammad Zishan Anwar & Ahmad N. Al-Kenani & Shahida Bashir & Muhammad Shabir, 2022. "Pessimistic Multigranulation Rough Set of Intuitionistic Fuzzy Sets Based on Soft Relations," Mathematics, MDPI, vol. 10(5), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:685-:d:756039
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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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    1. 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.

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