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A Novel Limit of Bipolar K-Q Group Acting on θ-Subgroup, Normal Subgroup, and Homomorphism of θ-Fuzzy Subgroup |
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PP: 1335-1343 |
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doi:10.18576/amis/190608
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Author(s) |
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Suleiman Shelash Mohammad,
Premkumar Munusamy,
A. Prasanna,
Hanan Jadallah,
N. Raja,
R Selvakumari,
M. Venkatachalam,
P. Shanmugavel,
Asokan Vasudevan,
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Abstract |
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| In this paper, we introduce and define the concept of a Bipolar K-Q Group acting on a θ-fuzzy subset, along with its associated algebraic properties. The study begins by examining the fundamental notion of a Bipolar K-Q Group acting on θ-fuzzy subgroups, shedding light on their structural and theoretical attributes. We then extend the discussion to Bipolar K-Q Groups acting on θ -fuzzy cosets, providing a detailed analysis of their algebraic properties and significance. These concepts are instrumental in exploring the interplay between group theory and fuzzy logic. Furthermore, we present a new notation: the Bipolar K-Q Group acting on a θ -fuzzy normal subgroup. This notion is further investigated in the context of quotient groups, particularly with respect to homomorphisms. We demonstrate various group-theoretical properties, including normality, compatibility, and structural relationships, to highlight the robustness of this framework. The paper provides a comprehensive foundation for understanding the algebraic behavior of these new group structures, offering insights into their broader theoretical and practical applications. By combining the principles of fuzzy logic and algebraic groups, this work advances the mathematical study of uncertainty and creates opportunities for future research in related areas of Mathematics. |
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