Table of Content
Mohamed E. Elnair
Open AccessArticleA Novel Approach to Filters in BL-algebras Through Bipolar Fuzzy Set Theory
Ashutosh Pradhan, Deena Al-Kadi, G. Muhiuddin* and Mohamed E. Elnair
Annals of Communications in Mathematics 2024,
7 (4),
478-484
DOI: https://doi.org/10.62072/acm.2024.070414
AbstractThis paper introduces a novel approach to the study of filters in BL-algebras by leveraging the principles of bipolar fuzzy set theory and investigating some of their properties. Filters are essential in the structural analysis of BL-algebras, affecting their properties and applications across various fields. Moreover, Bipolar-valued fuzzy filters generated by a fuzzy set are discussed. By integrating bipolar fuzzy set concepts, we provide a new framework that enhances the representation of uncertainty and vagueness inherent in filter operations. We explore the foundational aspects of bipolar fuzzy sets and demonstrate their applicability in defining and characterizing filters within BL-algebras. Our findings highlight the potential of bipolar fuzzy set theory to enrich the understanding of filters in BL-algebras.
Open AccessArticleProperties of Hybrid Structures in Groupoids
B. Elavarasan, G. Muhiuddin, K. Porselvi, Mohamed E. Elnair and Taif Alshehri
Annals of Communications in Mathematics 2025,
8 (4),
515-529
DOI: https://doi.org/10.62072/acm.2025.080408
ABSTRACT. Classical mathematical methods are insufficient for resolving certain issues in real-life human problems due to the uncertainty of the data. Researchers from around the world have created innovative mathematical models, like soft and fuzzy set theories, to model the uncertainties that arise in different areas. Jun recently developed a hybrid structure that combined fuzzy and soft set concepts. The hybrid structure principle is applied to groupoids in this paper, and the properties of hybrid ideals and hybrid subgroupoids in groupoids are also described. Furthermore, the notions of hybrid subgroups, hybrid normal subgroups, and hybrid cosets in a group, as well as their key properties, are discussed. In addition, we show that any member of the collection of hybrid cut sets of a hybrid normal subgroup of a group G is a normal subgroup of G in the traditional sense. Finally, we obtain a finite-group hybrid version of Lagrange’s theorem.