Role of Homomorphism and Cartesian Product over Fuzzy PMS-algebras

Selvam, P.M.Sithar; Nagalakshmi, K.T.

doi:10.22457/ijfma.v11n1a5

Cited by 1 publication

(2 citation statements)

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“…Let S be a nonempty subset of a PMS-algebra X. Then S is called a PMS-subalgebra of X if x * y ∈ S, for all x, y ∈ S. Definition 2.3 ( [7,9]). Let X and Y be any two PMS-algebras.…”

Section: Preliminariesmentioning

confidence: 99%

“…Sithar Selvam and Nagalakshmi [7] fuzzified PMS-subalgebras and PMS ideals in PMS-algebra. In the same year, Sithar Selvam and Nagalakshmi [9] also introduced the concept of homomorphism and Cartesian product of fuzzy PMS-algebra and set up some properties. In our earlier paper [4], we introduced the notion of fuzzy PMS-subalgebra in PMS-algebra and studied some of its properties.…”

Section: Introductionmentioning

confidence: 99%

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On Homomorphism and Cartesian Products of Intuitionistic Fuzzy PMS-subalgebra of a PMS-algebra

2023

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In this paper, we introduce the notion of intuitionistic fuzzy PMS-subalgebras under homomorphism and Cartesian product and investigate several properties. We study the homomorphic image and inverse image of the intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, which are also intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, and find some other interesting results. Furthermore, we also prove that the Cartesian product of intuitionistic fuzzy PMS- subalgebras is again an intuitionistic fuzzy PMS-subalgebra and characterize it in terms of its level sets. Finally, we consider the strongest intuitionistic fuzzy PMS-relations on an intuitionistic fuzzy set in a PMS-algebra and demonstrate that an intuitionistic fuzzy PMS-relation on an intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra if and only if the corresponding intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra of a PMS-algebra.

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“…Let S be a nonempty subset of a PMS-algebra X. Then S is called a PMS-subalgebra of X if x * y ∈ S, for all x, y ∈ S. Definition 2.3 ( [7,9]). Let X and Y be any two PMS-algebras.…”

Section: Preliminariesmentioning

confidence: 99%