| Title of paper:
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On the translational invariant intuitionistic fuzzy subset of a Γ-ring
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| Author(s):
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| Hem Lata
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| Research Scholar, Lovely Professional University, Phagwara, Punjab, India
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| goyalhema1986@gmail.com
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| P. K. Sharma
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| Post Graduate, Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
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| pksharma@davjalandhar.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 1, pages 11–22
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| DOI:
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https://doi.org/10.7546/nifs.2022.28.1.11-22
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| Download:
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 PDF (212 Kb Kb, File info)
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| Abstract:
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In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring 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 Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we prove that every homomorphic image of a prime ideal of a Γ-ring generated by an Aγ-prime element and translational invariant and f-invariant intuitionistic fuzzy subset is also a prime ideal.
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| Keywords:
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Γ-Ring, Translational invariant intuitionistic fuzzy subset (TIIFS), f-invariant intuitionistic fuzzy subset, Aγ-unit, Aγ-prime element.
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| AMS Classification:
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16Y99, 03F55, 03G25
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