Almost Bi-Î“-Ideals and Fuzzy Almost Bi-Î“-Ideals of Î“-Semigroups

Simuen, Anusorn; Abdullah, Saleem; Yonthanthum, Winita; Chinram, Ronnason

doi:10.29020/nybg.ejpam.v13i3.3759

Cited by 6 publications

(6 citation statements)

References 7 publications

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“…al [3] studied the almost bi-quasi-interior ideal and fuzzy almost bi-quasi-interior ideal in semigroups. Moreover, related research to various types of almost ideals has been studied in other algebraic structures (see, e.g., [9,11,12,[14][15][16][17]). Recently N. Sarasit et al [13] studied almost ternary subsemirings.…”

Section: Introductionmentioning

confidence: 99%

Applications of Bipolar Fuzzy Almost Ideals in Semigroups

Khamrot,

Gaketem

2024

Int. J. Anal. Appl.

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Section: Introductionmentioning

confidence: 99%

Applications of Bipolar Fuzzy Almost Ideals in Semigroups

Khamrot,

Gaketem

2024

Int. J. Anal. Appl.

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“…Research on various types of almost ideals and fuzzy almost ideals has also been conducted in specialized areas such as Γ -semigroups [7,18,19], ordered semigroups [20,23], ternary semigroups [22], semihypergroups [6,13,15,21,24], and LA-semihypergroups [14], including studies on bipolar fuzzy sets [9,10].…”

Section: Introductionmentioning

confidence: 99%

Characterization of almost filters and their fuzzifications of semigroups

Khamrot,

Chinram,

Gaketem

2024

J. Math. Computer Sci.

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“…Simuen, Wattanatripop and Chinram [19] using the concepts of quasi Γ-ideals in Γ-semigroups and almost Γ-ideals in Γ-semigroups, studied the basic properties of both almost quasi Γ-ideals and fuzzy almost quasi Γ-ideals of Γsemigroups. Moreover, they gave the remarkable relationship between almost quasi-Γ-ideals and their fuzzification.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, they gave the remarkable relationship between almost quasi-Γ-ideals and their fuzzification. In addition, Simuen, Abdullah, Yonthanthum and Chinram [18] introduced the concepts of almost bi Γ-ideals and fuzzy almost bi-Γ-ideals of Γ-semigroups. Also, they gave some properties and investigated relationship between almost bi Γ-ideals of Γsemigroups and their fuzzification.…”

Section: Introductionmentioning

confidence: 99%

Almost Interior Gamma-ideals and Fuzzy Almost Interior Gamma-ideals in Gamma-semigroups

Jantanan¹,

Simuen²,

Yonthanthum³

et al. 2021

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Ideal theory plays an important role in studying in many algebraic structures, for example, rings, semigroups, semirings, etc. The algebraic structure Γ-semigroup is a generalization of the classical semigroup. Many results in semigroups were extended to results in Γ-semigroups. Many results in ideal theory of Γ-semigroups were widely investigated. In this paper, we first focus to study some novel ideals of Γ-semigroups. In Section 2, we define almost interior Γ-ideals and weakly almost interior Γ-ideals of Γ-semigroups by using the concept ideas of interior Γ-ideals and almost Γ-ideals of Γ-semigroups. Every almost interior Γ-ideal of a Γ-semigroup S is clearly a weakly almost interior Γ-ideal of S but the converse is not true in general. The notions of both almost interior Γ-ideals and weakly almost interior Γ-ideals of Γ-semigroups are generalizations of the notion of interior Γ-ideal of a Γ-semigroup S. We investigate basic properties of both almost interior Γ-ideals and weakly almost interior Γ-ideals of Γ-semigroups. The notion of fuzzy sets was introduced by Zadeh in 1965. Fuzzy set is an extension of the classical notion of sets. Fuzzy sets are somewhat like sets whose elements have degrees of membership. In the remainder of this paper, we focus on studying some novelties of fuzzy ideals in Γ-semigroups. In Section 3, we introduce fuzzy almost interior Γ-ideals and fuzzy weakly almost interior Γ-ideals of Γ-semigroups. We investigate their properties. Finally, we give some relationship between almost interior Γ-ideals [weakly almost interior Γ-ideals] and fuzzy almost interior Γ-ideals [fuzzy weakly almost interior Γ-ideals] of Γ-semigroups.

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Almost Bi-Î“-Ideals and Fuzzy Almost Bi-Î“-Ideals of Î“-Semigroups

Abstract: In this paper, we introduce the notions of almost bi-Γ-ideals and fuzzy almost bi-Γ-ideals of Γ-semigroups and give properties of them. Moreover, we investigate relationship between almost bi-Γ-ideals and fuzzy almost bi-Γ-ideals.

Cited by 6 publications

References 7 publications

Applications of Bipolar Fuzzy Almost Ideals in Semigroups

Applications of Bipolar Fuzzy Almost Ideals in Semigroups

Characterization of almost filters and their fuzzifications of semigroups

Almost Interior Gamma-ideals and Fuzzy Almost Interior Gamma-ideals in Gamma-semigroups

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