Ordered fuzzy rings and substructures: Operations, homomor-phisms, and convex structures
نویسندگان
1 School of Mathematical Sciences & Center for Applied Mathematics, Guangxi Minzu University, Nanning 530006, P.R. China.
2 School of Mathematical Sciences & Center for Applied Mathematics, Guangxi Minzu University, Nanning 530006, P.R. China.
3 Guangxi Colleges and Universities Engineering Research Center, Guangxi Minzu University, Nanning 530006, P.R. China.
4 Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan.
doi
10.22105/jfea.2025.529956.1956چکیده
This study advances the theoretical framework of ordered fuzzy rings (OFRs) by examining the structural relationships among ordered fuzzy subrings (OFSRs) and ordered fuzzy ideals (OF Is). The motivation stems from the need to extend classical ring theory into fuzzy and partially ordered settings, enabling algebraic reasoning under uncertainty. Methodologically, the paper develops ordered fuzzy operations (OFOs)—fuzzy addition and multiplication defined on partially ordered sets—and investigates the behaviors of zero divisors, homomorphisms, closure properties, and convex substructures. Building upon these foundations, the work formulates and proves the first, second, and third isomorphism theorems within the ordered fuzzy context. The results establish how order-preserving operations interact with convexity in OF SRs, offering new insights into kernels, images, intersections, and quotient constructions. Overall, the findings provide a rigorous basis for the algebraic study of fuzzy systems and open pathways for applications in decision sciences, control theory, and artificial intelligence, where representing graded uncertainty is essential.
