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Article | Open Access

SR-fuzzy subalgebras and ideals in BCK/BCI-algebras

Ashutosh Pradhan1, G. Muhiuddin2( ), Rajesh Kumar Shukla3, Tami Alsubie2
Department of Applied Science and Humanities, Invertis University, Bareilly 243123, India.
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia.
Faculty of Engineering and Technology, Invertis University, Bareilly 243123, India.
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Abstract

This paper introduces the concepts of SR-fuzzy subalgebras and ideals within the framework of BCK/BCI-algebras. SR-fuzzy subalgebras are defined and illustrated with various examples to elucidate their structure and behaviour under different operations in BCK/BCI-algebras. The research explores the properties of SR-fuzzy subalgebras and ideals, investigating their interrelationships and establishing that every SR-fuzzy ideal is an SR-fuzzy subalgebra, although the reverse is not necessarily true. Conditions under which an SR-fuzzy subalgebra qualifies as an SR-fuzzy ideal are also discussed. Through various examples, this paper illustrates these concepts and highlights potential areas for further exploration. This study contributes to the expanding literature on fuzzy sets and their applications in algebraic structures, offering insights that may benefit future research endeavours.

Keywords

SR-fuzzy setBCK/BCI-algebrasSR-fuzzy BCK/BCI-subalgebrasSR-fuzzy BCK/BCI-algebras ideals

References

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Fuzzy Information and Engineering
Volume 17 Issue 4,
December 2025
Pages 395-407
DOI: 10.26599/FIE.2025.9270068

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Cite this article:
Pradhan A, Muhiuddin G, Shukla RK, et al. SR-fuzzy subalgebras and ideals in BCK/BCI-algebras. Fuzzy Information and Engineering, 2025, 17(4): 395-407. https://doi.org/10.26599/FIE.2025.9270068

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Received: 19 December 2024
Revised: 23 March 2025
Accepted: 20 April 2025
Published: 12 December 2025
© The Author(s) 2025.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).