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Rough JU-Algebras in Quantales Via Core Successor Classes Based on Fuzzy Relations
Research Article - Volume: 1, Issue: 1, 2026 (September)
Rough JU-Algebras in Quantales Via Core Successor Classes Based on Fuzzy Relations Download PDF

Muhammad Yousaf1*, Chadaphorn Kodsueb2

1Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
2School of Mathematical Sciences and Geoinformatics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand

*Correspondence to: Muhammad Yousaf, Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan, E-mail:

Received: July 25, 2026; Manuscript No: JMPM-26-1420; Editor Assigned: July 28, 2026; PreQc No: JMPM-26-1420 (PQ); Reviewed: July 31, 2026; Revised: August 06, 2026; Manuscript No: JMPM-26-1420 (R); Published: September 22, 2026

ABSTRACT

Fuzzy sets (FSs), rough sets (RSs), quantales, and core successor classes (CSCs) are mathematical tools that are applicable in real-world situations with imprecise and ambiguous data. In this research, we propose the novel idea of RSs on -algebra in quantales that are based on CSCs under fuzzy relations (FRs). The following article contains a notion that has never been introduced before. This merges the -algebras and RSs in quantales to provide a new approach for reducing uncertainty in various fields. We develop a mathematical model for approximate substructures on -algebras via CSCs, based on which options can be evaluated in a situation where the information is imprecise. The proposed approach is a recommended technique for coping with ambiguity and uncertainty in multiple fields. Applications in different fields are described, and theoretical foundations of rough -algebras are explored. Our findings demonstrate the effectiveness of the suggested strategy in handling ambiguity.

Keywords: Rough sets, Fuzzy Sets, Algebra, Quantales, Core Successor Classes.

Citation: Yousaf M, Kodsueb C (2026). Rough JU-Algebras in Quantales Via Core Successor Classes Based on Fuzzy Relations. J. Math. Phys. Mech. Vol.1 Iss.1, September (2026), pp:24-44.
Copyright: © 2026 Muhammad Yousaf, Chadaphorn Kodsueb. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.