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Applications of an Anti-fuzzy Semigroup

1Department of Mathematics, Manakula Vinayagar Institute of Technology, Kalitheerthal Kuppam, Puducherry 605 107, India2Department of Management Studies, Manakula Vinayagar Institute of Technology, Kalitheerthal Kuppam, Puducherry 605 107, India.3Department of Mathematics, Measi Academy of Architecture, Royapettah, Chennai 600014, Tamil Nadu, India.
* Corresponding Author: S. Sivaramakrishnan. Email:

Annals of Communications in Mathematics 2024, 7 (4), 430-438. https://doi.org/10.62072/acm.2024.070409
Received: 17 Oct 2024 |
Accepted: 19 Dec 2024 |
Published: 31 Dec 2024

Abstract

This paper introduces the ”anti fuzzy semigroup,” a novel algebraic structure that integrates the concepts of semigroups and anti fuzzy sets. We demonstrate, through a specific example, how a Kinship system can be represented as an anti fuzzy semigroup, effectively capturing the relationships between managers and subordinates. This appli- cation underscores the potential of anti fuzzy semigroups to model complex hierarchical structures and relationships within organizational settings. Furthermore, we investigate the representation of DNA sequences using this framework. We delve into the algebraic properties of anti fuzzy semigroups, proving that the union of two such semigroups always results in another anti fuzzy semigroup. However, we provide a counterexample to demon- strate that the intersection of two anti fuzzy semigroups may not necessarily preserve the anti fuzzy semigroup property. Finally, the Cartesian product of two anti fuzzy semigroups forms an anti fuzzy semigroup.

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Cite This Article

S. Sivaramakrishnan, P. Baskaran, P. Balaji.
Applications of an Anti-fuzzy Semigroup.
Annals of Communications in Mathematics
2024,
7 (4):
430-438.
https://doi.org/10.62072/acm.2024.070409

Creative Commons License
Copyright © 2024 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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