Open AccessArticle

On Pythagorean normal subbisemiring of bisemiring

and

K. Arulmozhi²

1Annamalai University, Department of Mathematics, Chidambaram, 608002, India.

* Corresponding Author: M. Palanikumar. Email: palanimaths86@gmail.com

Annals of Communications in Mathematics 2021, 4 (1), 63-72. https://doi.org/10.62072/acm.2021.040107

Received: 28 December 2021 |

Accepted: 11 March 2021 |

Published: 31 March 2021

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ABSTRACT.

We discuss the notion of Pythagorean subbisemiring, level sets of Pythagorean subbisemirings and Pythagorean normal subbisemiring of a bisemiring and investigate some of the properties related to subbisemirings. The fuzzy subset

\[
L = (\mu_{S}^{P}, \, \omega_{S}^{P})
\]

is a Pythagorean subbisemiring if and only if all non-empty level set

\[
L_{(\alpha,\beta)} \, (\alpha,\beta \in (0,1])
\]

is a subbisemiring. The Cartesian product of two Pythagorean subbisemirings is also Pythagorean subbisemiring. The homomorphic image and preimage of Pythagorean subbisemiring is also Pythagorean subbisemiring. To illustrate our results and examples are given.

Keywords

bisemiring; homomorphism; Normal; Subbisemiring

Cite This Article

M. Palanikumar, K. Arulmozhi.

On Pythagorean normal subbisemiring of bisemiring.

Annals of Communications in Mathematics

2021,

4 (1):

63-72.

https://doi.org/10.62072/acm.2021.040107

Copyright © 2021 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/).