Title of paper:

On the translational invariant intuitionistic fuzzy subset of a Γring

Author(s):

Hem Lata

Research Scholar, Lovely Professional University, Phagwara, Punjab, India

goyalhema1986@gmail.com

P. K. Sharma

Post Graduate, Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India

pksharma@davjalandhar.com


Published in:

Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 1, pages 11–22

DOI:

https://doi.org/10.7546/nifs.2022.28.1.1122

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Abstract:

In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γring and generalize some notions of a ring to a Γring. Also, we define ideals of a Γring generated by an intuitionistic fuzzy subset with an element of Γring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γring. Further, we study the properties of homomorphic image and preimage of translational invariant intuitionistic fuzzy subset under the Γring homomorphism and we prove that every homomorphic image of a prime ideal of a Γring generated by an A_{γ}prime element and translational invariant and finvariant intuitionistic fuzzy subset is also a prime ideal.

Keywords:

ΓRing, Translational invariant intuitionistic fuzzy subset (TIIFS), finvariant intuitionistic fuzzy subset, A_{γ}unit, A_{γ}prime element.

AMS Classification:

16Y99, 03F55, 03G25

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