Bipolar Fuzzy Implicative Ideals of BCK-Algebras

Muhiuddin, G.; Al-Kadi, Deena

doi:10.1155/2021/6623907

Cited by 17 publications

(20 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…e concept of "quasi-coincidence" of an interval-valued fuzzy point together with "belongingness" within an interval-valued fuzzy set were used in the studies made by Ma et al in [17,18], where they discussed properties of some types of (∈, ∈ ∨q)-interval-valued fuzzy ideals of BCI-algebras. Also, in [19][20][21][22][23][24], some more general ideas on bipolar fuzzy sets' related ideals were considered. e m-polar fuzzy set, an extension of the bipolar fuzzy set, was introduced by Chen et al [25] in 2014.…”

Section: Introductionmentioning

confidence: 99%

Interval-Valued $m$ -Polar Fuzzy Positive Implicative Ideals in $B C K$ -Algebras

Muhiuddin

Al-Kadi

Mahboob³

et al. 2021

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

In this paper, the notion of interval-valued m -polar fuzzy positive implicative ideals in BCK-algebras is presented. Then, the relationships between interval-valued m -polar fuzzy positive implicative ideals and interval-valued m -polar fuzzy ideals are investigated. After that, the concepts of interval-valued m -polar ∈ , ∈ ∨ q κ ˜ -fuzzy positive implicative ideals and interval-valued m -polar ∈ , ∈ ∨ q κ ˜ -fuzzy ideals are defined and some equivalent conditions are provided. Furthermore, we show that interval-valued m -polar ∈ , ∈ ∨ q κ ˜ -fuzzy positive implicative ideals are interval-valued m -polar ∈ , ∈ ∨ q κ ˜ -fuzzy ideals, but the converse need not be true in general and an example is given in this aim.

show abstract

Section: Introductionmentioning

confidence: 99%

Interval-Valued $m$ -Polar Fuzzy Positive Implicative Ideals in $B C K$ -Algebras

Muhiuddin

Al-Kadi

Mahboob³

et al. 2021

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Meng [6] studied about fuzzy implicative ideals in 𝐵𝐶𝐾-algebras in 1997. Moreover, Muhiuddin and Al-Kadi [7] introduced bipolar fuzzy implicative ideals in 𝐵𝐶𝐾-algebras. They discussed about the relationship between a bipolar fuzzy ideal and bipolar fuzzy implicative ideal.…”

Section: Introductionmentioning

confidence: 99%

Multipolar Intuitionistic Fuzzy Ideal in B-Algebras

Amigo

Hidayat

Krisnawati

2022

CAUCHY

View full text Add to dashboard Cite

In this paper, we study with the definition of B-algebras, commutative B-algebras and fuzzy ideal in B-algebras. We consider the terminology of multipolar intuitionistic fuzzy ideal. We propose about multipolar intuitionistic fuzzy ideal in B-algebras and some related properties. Then, we discuss about theorems and propositions which contain some conditions for a multipolar intuitionistic fuzzy set become a multipolar intuitionistic fuzzy ideal in B-algebras.

show abstract

“…Sarwar et al [19] applied Bipolar fuzzy soft information in hypergraph setting. Muhiuddin and Al-Kadi [20] introduced the notion of bipolar fuzzy implicative ideals of a BCK-algebra and determined several properties.…”

Section: Introductionmentioning

confidence: 99%

Domination of Bipolar Fuzzy Graphs in Various Settings

Gong

Hua

Gao

2021

Int J Comput Intell Syst

View full text Add to dashboard Cite

Bipolar fuzzy sets are used to describe the positive and negative of the uncertainty of objects, and the bipolar fuzzy graphs are used to characterize the structural relationship between uncertain concepts in which the vertices and edges are assigned positive and negative membership function values to feature the opposite uncertainty elevation. The dominating set is the control set of vertices in the graph structure and it occupies a critical position in graph analysis. This paper mainly contributes to extending the concept of domination in the fuzzy graph to the bipolar frameworks and obtaining the related expanded concepts of a variety of bipolar fuzzy graphs. Meanwhile, the approaches to obtain the specific dominating sets are presented. Finally, a numeral example on city data in Yunnan Province is presented to explain the computing of domination in bipolar fuzzy graph in the specific application.

show abstract

Bipolar Fuzzy Implicative Ideals of BCK-Algebras

Cited by 17 publications

References 28 publications

Interval-Valued $m$ -Polar Fuzzy Positive Implicative Ideals in $B C K$ -Algebras

Interval-Valued $m$ -Polar Fuzzy Positive Implicative Ideals in $B C K$ -Algebras

Multipolar Intuitionistic Fuzzy Ideal in B-Algebras

Domination of Bipolar Fuzzy Graphs in Various Settings

Contact Info

Product

Resources

About

Bipolar Fuzzy Implicative Ideals of BCK-Algebras

Cited by 17 publications

References 28 publications

Interval-Valuedm-Polar Fuzzy Positive Implicative Ideals inBCK-Algebras

Interval-Valuedm-Polar Fuzzy Positive Implicative Ideals inBCK-Algebras

Multipolar Intuitionistic Fuzzy Ideal in B-Algebras

Domination of Bipolar Fuzzy Graphs in Various Settings

Contact Info

Product

Resources

About

Interval-Valued $m$ -Polar Fuzzy Positive Implicative Ideals in $B C K$ -Algebras

Interval-Valued $m$ -Polar Fuzzy Positive Implicative Ideals in $B C K$ -Algebras