ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS

Jomal Josen; Sunil Jacob John; Baıju Thankachan

ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS

Abstract

One recent generalization of Zadeh's fuzzy sets is the concept of multidimensional fuzzy sets. This work extends this concept further by introducing a generalized form of multidimensional fuzzy algebra. By focusing on multidimensional t-norms and t-conorms, we develop a comprehensive theory. This includes the notion of strong multidimensional fuzzy algebras and explores their properties, such as multidimensional groupoids, monoids, and groups. Additionally, we introduce equivalence relations on the collection of all multidimensional fuzzy sets and present an example of specific monoids within this collection. Finally, we demonstrate how a group structure can be imposed on a subcollection of orderless multidimensional fuzzy sets.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Logic, Set Theory, Lattices and Universal Algebra

Journal Section

Research Article

Authors

Jomal Josen This is me
0009-0009-5450-120X
India

Sunil Jacob John
0000-0002-6333-2884
India

Baıju Thankachan ^*
0000-0002-5558-1581
India

Publication Date

January 8, 2026

Submission Date

November 14, 2024

Acceptance Date

May 20, 2025

Published in Issue

Year 2026 Volume: 16 Number: 1

IZ

https://izlik.org/JA63BX44DL

Cite

RIS / Bibtex

APA

Josen, J., John, S. J., & Thankachan, B. (2026). ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS. TWMS Journal of Applied and Engineering Mathematics, 16(1), 1-15. https://izlik.org/JA63BX44DL

AMA

1.Josen J, John SJ, Thankachan B. ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS. JAEM. 2026;16(1):1-15. https://izlik.org/JA63BX44DL

Chicago

Josen, Jomal, Sunil Jacob John, and Baıju Thankachan. 2026. “ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS”. TWMS Journal of Applied and Engineering Mathematics 16 (1): 1-15. https://izlik.org/JA63BX44DL.

EndNote

Josen J, John SJ, Thankachan B (January 1, 2026) ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS. TWMS Journal of Applied and Engineering Mathematics 16 1 1–15.

IEEE

[1]J. Josen, S. J. John, and B. Thankachan, “ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS”, JAEM, vol. 16, no. 1, pp. 1–15, Jan. 2026, [Online]. Available: https://izlik.org/JA63BX44DL

ISNAD

Josen, Jomal - John, Sunil Jacob - Thankachan, Baıju. “ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS”. TWMS Journal of Applied and Engineering Mathematics 16/1 (January 1, 2026): 1-15. https://izlik.org/JA63BX44DL.

JAMA

1.Josen J, John SJ, Thankachan B. ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS. JAEM. 2026;16:1–15.

MLA

Josen, Jomal, et al. “ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 1, Jan. 2026, pp. 1-15, https://izlik.org/JA63BX44DL.

Vancouver

1.Jomal Josen, Sunil Jacob John, Baıju Thankachan. ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS. JAEM [Internet]. 2026 Jan. 1;16(1):1-15. Available from: https://izlik.org/JA63BX44DL