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Pessimistic Multigranulation Roughness of a Fuzzy Set Based on Soft Binary Relations over Dual Universes and Its Application

Author

Listed:
  • Jamalud Din

    (Department of Mathematics, Quaid-I-Azam University, Islamabad 44230, Pakistan)

  • Muhammad Shabir

    (Department of Mathematics, Quaid-I-Azam University, Islamabad 44230, Pakistan)

  • Ye Wang

    (Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, China
    Department of Mathematics, Huzhou University, Huzhou 313000, China)

Abstract

The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application.

Suggested Citation

  • Jamalud Din & Muhammad Shabir & Ye Wang, 2022. "Pessimistic Multigranulation Roughness of a Fuzzy Set Based on Soft Binary Relations over Dual Universes and Its Application," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:541-:d:745541
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