A New Type of Fuzzy Prime Subset in Ordered Semigroups

Mahboob, Ahsan; Muhiuddin, G.

doi:10.1142/s1793005721500368

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…Moreover, researchers have delved into the studies of fuzzy quotient algebras. In subsequent works, scholars primarily focused on exploring fuzzy ideals in semigroups [15][16][17][18]. Zhou, Chen, and Chang [19] introduced the concepts of L-fuzzy ideals and L-fuzzy subalgebras.…”

Section: Introductionmentioning

confidence: 99%

Ideals and Homomorphism Theorems of Fuzzy Associative Algebras

Yang,

Zhou

2024

Mathematics

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Based on the definitions of fuzzy associative algebras and fuzzy ideals, it is proven that the intersections of fuzzy subalgebras are fuzzy subalgebras, and the intersections of fuzzy ideals are fuzzy ideals. Moreover, we prove that the kernels of fuzzy homomorphisms are fuzzy ideals. Using fuzzy ideals, the quotient structures of fuzzy associative algebras are constructed, their corresponding properties are discussed, and their homomorphism theorems are proven.

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Section: Introductionmentioning

confidence: 99%

Ideals and Homomorphism Theorems of Fuzzy Associative Algebras

Yang,

Zhou

2024

Mathematics

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“…In 2021 T. Gaketem [4], studied interval valued fuzzy almost (m, n)-bi-ideal in semigroups. A. Mahboob and G. Muhiuddin [7] studied a fuzzy prime subset in ordered semigroups.…”

Section: Introductionmentioning

confidence: 99%

On Interval Valued Fuzzy Bi-interior Ideals in Semigroups

Gaketem

Prommai²

2023

Eur. J. Pure Appl. Math.

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Characterizations of generalized fuzzy ideals in ordered semigroups

Davvaz

Chinram

Lekkoksung

et al. 2023

IFS

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Ideals play an essential part in studying ordered semigroups. There are several generalizations of ideals that are used to investigate ordered semigroups. It was known that (m, n)-ideals and n-interior ideals are an abstraction of bi-ideals and interior ideals, respectively. This paper introduces a generality of (m, n)-ideals and n-interior ideals, so-called (α, β)-fuzzy (m, n)-ideals and (α, β)-fuzzy n-interior ideals. Furthermore, we discuss our current notions with those that already exist. We examine connections between (m, n)- (resp., n-interior) ideals and (α, β)-fuzzy (m, n)- (resp., n-interior) ideals. A characterization of (α, β)-fuzzy (m, n)- (resp., n-interior) ideals, by a particular product, in ordered semigroups is provided. We demonstrate that our results generalize the known results through specific settings.

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A New Type of Fuzzy Prime Subset in Ordered Semigroups

Cited by 4 publications

References 17 publications

Ideals and Homomorphism Theorems of Fuzzy Associative Algebras

Ideals and Homomorphism Theorems of Fuzzy Associative Algebras

On Interval Valued Fuzzy Bi-interior Ideals in Semigroups

Characterizations of generalized fuzzy ideals in ordered semigroups

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