Generalization of Rough Bi-ideals in Quantales Based on Cores of Successor Classes Under Fuzzy Relations
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.
Authors
- Muhammad Murtaza Yousaf (ORCID: https://orcid.org/0000-0001-9578-8811)
- Maasoomah Sadaf (ORCID: https://orcid.org/0000-0002-1689-0824)
- Ghazala Akram (ORCID: https://orcid.org/0000-0003-0288-9299)
- Karim K. Ahmed (ORCID: https://orcid.org/0000-0003-0414-4960)
- Homan Emadifar (ORCID: https://orcid.org/0000-0002-8034-1475)
- Saqib Mazher Qurashi (ORCID: https://orcid.org/0000-0002-4732-3320)
- Abeer S. Khalifa (ORCID: https://orcid.org/0000-0003-4431-0353)
- Muhammad Zubair Raza (ORCID: https://orcid.org/0009-0003-0673-6852)
- Muhammad Abdaal Bin Iqbal (ORCID: https://orcid.org/0009-0001-2075-9028)
- Hafiz Muhammad Awais
Institutions
- University of the Punjab (PK)
- Government College University, Faisalabad (PK)
- Technical and Vocational University (IR)
- Saveetha University (IN)
- German University in Cairo (EG)
Publication Details
- Journal
- International Journal of Computational Intelligence Systems
- Published
- 2025-11-11
- DOI
- https://doi.org/10.1007/s44196-025-01027-8
- Primary Topic
- Fuzzy and Soft Set Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00