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Browsing Mathematics by Author "Poonam Kumar Sharma"

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    Intuitionistic fuzzy group algebra
    (2025) Poonam Kumar Sharma
    This paper introduces the concept of an intuitionistic fuzzy group algebra associated with a finite group G and an intuitionistic fuzzy group A on G. We establish its structural properties, showing that it simultaneously behaves as an intuitionistic fuzzy algebra and an intuitionistic fuzzy G-module. Extending author’s earlier results on the semi-simplicity of intuitionistic fuzzy G-modules, we explore links to complete reducibility and injectivity. Further, we study intersections, (α, β)-cuts, and homomorphic images of such algebras, and define intuitionistic fuzzy group algebra homomorphisms. Finally, we prove that the class of all intuitionistic fuzzy group algebras forms a category.
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    Intuitionistic fuzzy lattice ordered G-modules
    (Journal of Fuzzy Extension and Applications, 2024) Poonam Kumar Sharma
    The investigation of mathematics underlines accuracy, precision, and flawlessness, yet in numerous genuine circumstances, individuals face equivocalness, ambiguity, imprecision, and so forth. Intuitionistic fuzzy set theory, rough set theory, and soft set theory are three noble techniques in mathematics that are utilised for decision-making in vague and uncertain information systems. Intuitionistic fuzzy algebra-based math plays a huge part in the current era of mathematical research, and it deals with the algebraic concepts and models of intuitionistic fuzzy sets. The investigation of different ordered algebraic structures, like lattice-ordered groups, Riesz spaces, etc., is of great importance in algebra. The theory of lattice-ordered G-modules is very useful in the study of lattice-ordered groups and similar algebraic structures. In this article, the theories of intuitionistic fuzzy sets and lattice-ordered G-modules are synchronised in a reasonable way to develop a novel concept in mathematics, i.e., intuitionistic fuzzy lattice-ordered G-modules, which would pave the way for new researchers in intuitionistic fuzzy mathematics to explore much more in this field.