Pythagorean Fuzzy \(\hat{Z}\)-Subalgebras in \(\hat{Z}\)-Algebraic Systems

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DOI: https://doi.org/10.28924/2291-8639-24-2026-36
Published: Feb 19, 2026
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K. P. Shanmugapriya, P. Hemavathi, R. Vinodkumar, Aiyared Iampan, Pythagorean Fuzzy \(\hat{Z}\)-Subalgebras in \(\hat{Z}\)-Algebraic Systems, Int. J. Anal. Appl., 24 (2026), 36.

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K. P. Shanmugapriya, P. Hemavathi, R. Vinodkumar, Aiyared Iampan

Abstract

The idea of Pythagorean fuzzy sets was developed to improve the standard fuzzy set and intuitionistic fuzzy set theories by providing a more robust approach to handling uncertainty. This method provides greater flexibility in demonstrating membership, ensuring that the square sum of the degrees of membership and non-membership is maintained. This study examines how to incorporate Pythagorean fuzzy sets into the structure of the \(\hat{Z}\)-algebra, focusing on the properties of \(\hat{Z}\)-subalgebras. Pythagorean fuzzy \(\hat{Z}\)-subalgebras are a new notion that builds on traditional \(\hat{Z}\)-subalgebra structures. The purpose is to make algebra more creative when the conditions are uncertain. Significant developments in algebraic structures provide the theoretical basis for these fuzzy substructures. In addition, the Pythagorean fuzzy \(\hat{Z}\)-subalgebras under \(\hat{Z}\)-algebra homomorphism are examined, especially in relation to image and pre-image mappings.

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