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Soft Relations Applied to the Substructures of Quantale Module and Their Approximation

Author

Listed:
  • Saqib Mazher Qurashi
  • Khushboo Zahra Gilani
  • Muhammad Shabir
  • Muhammad Gulzar
  • Ashraful Alam

Abstract

This research article offers a study on a new relation of rough sets and soft sets with an algebraic structure quantale module by using soft reflexive and soft compatible relations. The lower approximation and upper approximation of subsets of quantale module are utilized by aftersets and foresets. As a sequel of this relation, different characterizations of rough soft substructures of quantale modules are obtained. To ensure the results, soft reflective and soft compatible relations are focused and these are interpreted by aftersets and foresets. Furthermore, the algebraic relations between upper (lower) approximation of substructures of quantale module and the upper (lower) approximations of their homomorphic images with the help of quantale module homomorphism are examined. In comparison with the different type of approximations in different type of algebraic structures, it is concluded that this new study is much better.

Suggested Citation

  • Saqib Mazher Qurashi & Khushboo Zahra Gilani & Muhammad Shabir & Muhammad Gulzar & Ashraful Alam, 2022. "Soft Relations Applied to the Substructures of Quantale Module and Their Approximation," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:9073503
    DOI: 10.1155/2022/9073503
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    References listed on IDEAS

    as
    1. Qimei Xiao & Qingguo Li, 2012. "Generalized Lower and Upper Approximations in Quantales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Nabilah Abughazalah & Naveed Yaqoob & Kiran Shahzadi & naeem jan, 2021. "Topological Structures of Lower and Upper Rough Subsets in a Hyperring," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, April.
    3. Qimei Xiao & Qingguo Li, 2012. "Generalized Lower and Upper Approximations in Quantales," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, February.
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