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Exploring θ-Translation and θ-Multiplication: A Graphical Analysis in Fuzzy Z-Algebra and Q-Fuzzy Z-Algebra |
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PP: 1-11 |
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doi:10.18576/amis/200101
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Author(s) |
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Suleiman Ibrahim Mohammad,
M. Premkumar,
N. Raja,
V. Helan Sinthiya,
K. Malathi,
M. Joel Jaikumar Madhuram,
P. Shanmugavel,
Asokan Vasudevan,
Mohammad Faleh Ahmmad Hunitie,
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Abstract |
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| In this paper, we introduce new notations for algebraic structures, specifically θ-T and θ-M, and explore their properties through graphical analysis within the framework of Z-subalgebras of Z-algebras. The study provides a comprehensive discussion of the algebraic properties associated with these structures and includes illustrative examples to enhance understanding. Building on this foundation, we further extend the definitions of θ-T and θ-M to the domain of Z-ideals of Z-algebras, employing graphical analysis to demonstrate their various group-theoretical properties. These extensions offer deeper insights into the interplay between these algebraic structures and their graphical representations. Moreover, we introduce and formalize the concepts of θ -translations and θ-multiplications within the framework of Z-ideals of Q-fuzzy Z-algebras. Using graphical analysis, we provide a detailed exploration of their properties, offering a fresh perspective on how these new constructs behave within the broader context of Q-fuzzy Z-algebras. By delving into their algebraic characteristics, we reveal significant relationships and properties that contribute to the advancement of algebraic theory. The graphical approach employed throughout this paper not only facilitates a better understanding of the underlying structures but also aids in visualizing complex relationships and operations. Through rigorous analysis and the integration of examples, we highlight the utility of these notations and their potential applications in algebraic studies. This work sets the stage for further exploration and development of similar structures in advanced algebraic systems, establishing a foundation for future research in this field.
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