Fuzzy Sets and Fuzzy Algebras

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "A: Algebra and Logic".

Deadline for manuscript submissions: closed (30 April 2025) | Viewed by 508

Special Issue Editor


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Guest Editor
Department of Mathematics, University of Houston-Downtown, Houston, TX 77002, USA
Interests: algebras of logic; universal algebras; non-classical algebras; non-classical logic including fuzzy algebra, fuzzy logic, hyper structures, and applications; division algebras and the Brauer groups

Special Issue Information

Dear Colleagues,

We are pleased to invite you to contribute to this Special Issue on “Fuzzy Sets and Fuzzy Algebras” with an original research article focusing on all aspects of fuzzy sets theory.

In mathematics, fuzzy sets have given rise to new research topics in category theory, topology, and algebra. In addition, fuzzy sets have strong logical connections and play a central role in multi-valued logics. Thus, several algebras are associated with these logics (e.g. MV-algebras, BL-algebras, MTL-algebras, Gödel algebras, residuated lattices, etc.) and are integral parts of fuzzy sets and algebras. Furthermore, fuzzy sets have a wide range of applications in various fields, thanks to their ability to handle uncertainty and imprecision. In this Special Issue, contributions on fuzzy sets from the point of view of fundamental mathematics or applications are all welcome.

Dr. Jean Bernard Nganou
Guest Editor

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Keywords

  • Boolean algebras
  • MV-algebras
  • BL-algebras
  • MTL-algebras
  • Gödel algebras
  • residuated lattices
  • circuit switching

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Published Papers (1 paper)

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Research

20 pages, 322 KiB  
Article
Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm
by Ravikumar Bandaru, Tahsin Oner, Neelamegarajan Rajesh and Amal S. Alali
Mathematics 2025, 13(8), 1282; https://doi.org/10.3390/math13081282 - 14 Apr 2025
Viewed by 211
Abstract
In this paper, we explore the application of fuzzy set theory in the context of triangular norms, with a focus on strong Sheffer stroke NMV-algebras. We introduce the concepts of T-fuzzy subalgebras and T-fuzzy filters, analyze their properties, and provide several [...] Read more.
In this paper, we explore the application of fuzzy set theory in the context of triangular norms, with a focus on strong Sheffer stroke NMV-algebras. We introduce the concepts of T-fuzzy subalgebras and T-fuzzy filters, analyze their properties, and provide several illustrative examples. Our study demonstrates that T-fuzzy subalgebras and filters generalize classical subalgebras and filters, with level subsets preserving algebraic structures under t-norms. Notably, T-fuzzy sets exhibit strong closure properties, and homomorphisms between SSNMV-algebras extend naturally to fuzzy settings. Furthermore, we examine the relationships between T-fuzzy subalgebras (or filters) and their classical counterparts, as well as their corresponding level subsets and homomorphisms. These results contribute to refined uncertainty modeling in logical systems, with potential applications in fuzzy control and AI. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Algebras)
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