On Length and Mean Fuzzy Ideals of Sheffer Stroke Hilbert Algebras

Authors

  • Neelamegarajan Rajesh Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamil 6 Nadu, India
  • Tahsin Oner Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey
  • Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand https://orcid.org/0000-0002-0475-3320
  • Ibrahim Senturk Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5779

Keywords:

Sheffer stroke Hilbert algebra, ideal, length fuzzy ideal, mean fuzzy ideal

Abstract

This paper presents a detailed exploration of Sheffer stroke Hilbert algebras, introducing the innovative concepts of length fuzzy ideals and mean fuzzy ideals within an interval-valued fuzzy framework. These new constructs extend classical ideal theory by incorporating fuzzy logic, providing precise mathematical tools to analyze and measure membership gradations. Specifically, the study establishes critical relationships between length fuzzy ideals and mean fuzzy ideals, their hierarchical subsets, and their implications for algebraic consistency and computational logic. Key findings demonstrate that length fuzzy ideals align closely with interval-valued fuzzy subsets, while mean fuzzy ideals offer a unique averaging perspective for understanding ideal structures. These contributions significantly advance the field of fuzzy algebra, offering theoretical insights and potential applications in computational logic, uncertainty modeling, and algorithmic design.

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Published

2025-01-31

Issue

Vol. 18 No. 1: (January 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Neelamegarajan Rajesh, Tahsin Oner, Aiyared Iampan, I. Senturk

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How to Cite

On Length and Mean Fuzzy Ideals of Sheffer Stroke Hilbert Algebras. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5779. https://doi.org/10.29020/nybg.ejpam.v18i1.5779