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<p>In quantales, algebraic structures that use fuzzy relations and cores of&#xa0;successor class, the notion of upper and lower approximation bi-ideals is introduced. In quantales with upper and lower approximations, we present illustrations of bi-ideals, interior ideals, quasi-ideals, (m, n)-ideals, and (m, n)-quasi-ideal and explore the features of these bi-ideals by expanding the concept of left and right ideals. Furthermore, we develop semi-prime bi-ideals and prime bi-ideals with upper and lower approximations, and we investigate their properties in quotient quantales. This work aims to improve our understanding of these algebraic structures to minimize uncertainty in a variety of domains.</p>

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Generalization of Rough Bi-ideals in Quantales Based on Cores of Successor Classes Under Fuzzy Relations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月11日

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  • Muhammad Yousaf,
  • Saqib Mazher Qurashi,
  • Hafiz Muhammad Awais,
  • Muhammad Abdaal Bin Iqbal,
  • Muhammad Zubair Raza,
  • Maasoomah Sadaf,
  • Ghazala Akram,
  • Homan Emadifar,
  • Abeer S. Khalifa,
  • Karim K. Ahmed

摘要

In quantales, algebraic structures that use fuzzy relations and cores of successor class, the notion of upper and lower approximation bi-ideals is introduced. In quantales with upper and lower approximations, we present illustrations of bi-ideals, interior ideals, quasi-ideals, (m, n)-ideals, and (m, n)-quasi-ideal and explore the features of these bi-ideals by expanding the concept of left and right ideals. Furthermore, we develop semi-prime bi-ideals and prime bi-ideals with upper and lower approximations, and we investigate their properties in quotient quantales. This work aims to improve our understanding of these algebraic structures to minimize uncertainty in a variety of domains.