Int-soft ideals over the soft sets in ordered semigroups

Muhiuddin, G.; Mahboob, Ahsan

doi:10.3934/math.2020159

Cited by 20 publications

(9 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, Jun et al [14] applied the theory of fuzzy soft sets to BCK/BCI-algebras and introduced the notion of fuzzy soft BCK/BCI-algebras (briefly, FSB-algebras) and related notions. Moreover, Muhiuddin et al studied and applied the soft set theory to the different algebraic structures on various aspects (see, e.g., [15][16][17][18][19][20][21][22][23]). Also, some related concepts based on the present work are studied in [24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Generalization of Fuzzy Soft $BCK / BCI$ -Algebras

Alam

Muhiuddin

Obeidat

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

In this paper, the notions of ∈ , ∈ ∨ q -fuzzy soft BCK / BCI -algebras and ∈ , ∈ ∨ q -fuzzy soft sub- BCK / BCI -algebras are introduced, and related properties are investigated. Furthermore, relations between fuzzy soft BCK / BCI -algebras and ∈ , ∈ ∨ q -fuzzy soft BCK / BCI -algebras are displayed. Moreover, conditions for an ∈ , ∈ ∨ q -fuzzy soft BCK / BCI -algebra to be a fuzzy soft BCK / BCI -algebra are provided. Also, the union, the extended intersection, and the “AND”-operation of two ∈ , ∈ ∨ q -fuzzy soft (sub-) BCK / BCI -algebras are discussed, and a characterization of an ∈ , ∈ ∨ q -fuzzy soft BCK / BCI -algebra is established.

show abstract

Section: Introductionmentioning

confidence: 99%

Generalization of Fuzzy Soft $BCK / BCI$ -Algebras

Alam

Muhiuddin

Obeidat

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…e concept of union-soft semigroups, unionsoft l-ideals, union-soft r-ideals, and union-soft semiprime soft sets have been considered by [10]. In addition, Muhiuddin et al studied the soft set theory on various aspects (see, for example, [11][12][13][14][15][16][17][18][19][20][21]). For more related concepts, the readers are referred to [22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

(m, n)-Ideals in Semigroups Based on Int-Soft Sets

Muhiuddin

Alanazi

2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, and topological spaces. This provides sufficient motivation to researchers to review various concepts and results from the realm of abstract algebra in the broader framework of fuzzy setting. In this paper, we introduce the notions of int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals of semigroups by generalizing the concept of int-soft bi-ideals, int-soft right ideals, and int-soft left ideals in semigroups. In addition, some of the properties of int-soft m , n -ideal, int-soft m , 0 -ideal, and int-soft 0 , n -ideal are studied. Also, characterizations of various types of semigroups such as m , n -regular semigroups, m , 0 -regular semigroups, and 0 , n -regular semigroups in terms of their int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals are provided.

show abstract

“…For some recent papers on ordered semigroups or ordered Gamma-semigroups, the reader can look at [7][8][9][10] in References.…”

Section: Introductionmentioning

confidence: 99%

On orderedΓ-hypersemigroups and their relation to lattice ordered semigroups

Kehayopulu¹

2021

Turk J Math

View full text Add to dashboard Cite

The concept of Γ-hypersemigroup has been introduced in [5], in which it has been shown that various results on Γ-hypersemigroups can be obtained directly as corollaries of more general results from the theory of le-semigroups (i.e. lattice ordered semigroups having a greatest element) or poe-semigroups. As a continuation of the paper mentioned above, in the present paper, the concept of ordered Γ-hypersemigroups has been introduced, and their relation to lattice ordered semigroups is given. It has been shown that although the results on ordered Γ-hypersemigroups cannot be obtained as corollaries to the corresponding results of le or poe-semigroups, still the main idea comes from the le-semigroups or poe-semigroups, and the proofs go along the lines of the le or poe-semigroups.

show abstract

Int-soft ideals over the soft sets in ordered semigroups

Cited by 20 publications

References 16 publications

Generalization of Fuzzy Soft $BCK / BCI$ -Algebras

Generalization of Fuzzy Soft $BCK / BCI$ -Algebras

(m, n)-Ideals in Semigroups Based on Int-Soft Sets

On orderedΓ-hypersemigroups and their relation to lattice ordered semigroups

Contact Info

Product

Resources

About

Int-soft ideals over the soft sets in ordered semigroups

Cited by 20 publications

References 16 publications

Generalization of Fuzzy Soft BCK / BCI -Algebras

Generalization of Fuzzy Soft BCK / BCI -Algebras

(m, n)-Ideals in Semigroups Based on Int-Soft Sets

On orderedΓ-hypersemigroups and their relation to lattice ordered semigroups

Contact Info

Product

Resources

About

Generalization of Fuzzy Soft $BCK / BCI$ -Algebras

Generalization of Fuzzy Soft $BCK / BCI$ -Algebras