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A Study of Modules of Fractions Under Fuzzy Sets and Soft Sets

Author

Listed:
  • Saba Ayub

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

  • Waqas Mahmood

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

  • Muhammad Shabir

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

  • Rizwan Gul

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

Abstract

The primary purpose of this paper is to introduce the concept of the fuzzy module of fractions and investigate a relationship between fuzzy modules of fractions and rough sets (RSs). In this respect, first, the concept of the soft module of fractions is introduced. Then, the idea of fuzzy approximations of the FS of a module of fractions is defined by using a soft module of fractions and obtaining a new hybrid model called multi-granulation soft rough FSs (MGSR-FSs) in a module of fractions. Moreover, the idea of a fuzzy upper rough module of fractions is introduced. However, it is important to note that the fuzzy lower approximation of a fuzzy module of fractions is not a fuzzy lower rough module of fractions. Several examples are provided to elaborate on the proposed notions.

Suggested Citation

  • Saba Ayub & Waqas Mahmood & Muhammad Shabir & Rizwan Gul, 2024. "A Study of Modules of Fractions Under Fuzzy Sets and Soft Sets," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 247-271, March.
    • Handle: RePEc:wsi:nmncxx:v:20:y:2024:i:01:n:s1793005724500145
    DOI: 10.1142/S1793005724500145
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