Bipolar Valued Fuzzy Ideals of Bf-Algebras

Sabarinathan, S.; Kumar, Dharmendra; Muralikrishna, P.

doi:10.12732/ijpam.v109i4.7

Cited by 3 publications

(4 citation statements)

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“…e bipolar-valued fuzzification has been used to study different notions in BCK/BCI-algebras such as subalgebras and ideals of BCK/BCI-algebras [5], a-ideals of BCI-algebras [6], and more, see the references [7][8][9][10]. Other researches also added their contribution to the study in this field on different branches of algebra in various aspects (see, e.g., [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]). Also, some more general concepts on bipolar fuzzy have been studied in [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Bipolar Fuzzy Implicative Ideals of BCK-Algebras

Muhiuddin

Al-Kadi

2021

Journal of Mathematics

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The notion of bipolar fuzzy implicative ideals of a BCK-algebra is introduced, and several properties are investigated. The relation between a bipolar fuzzy ideal and a bipolar fuzzy implicative ideal is studied. Characterizations of a bipolar fuzzy implicative ideal are given. Conditions for a bipolar fuzzy set to be a bipolar fuzzy implicative ideal are provided. Extension property for a bipolar fuzzy implicative ideal is stated.

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Section: Introductionmentioning

confidence: 99%

Bipolar Fuzzy Implicative Ideals of BCK-Algebras

Muhiuddin

Al-Kadi

2021

Journal of Mathematics

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“…The results of this study can be further expanded to various algebraic structures, such as PF-algebras, semigroups, Γ-semihypergroups, and hemirings (see [18,19,44,46]). Furthermore, the notion of the m-pF set used in this work can be studied according to the thought in [47][48][49][50], which will be the way for much future research.…”

Section: Discussionmentioning

confidence: 97%

“…The first definition of fuzzy ideals in BCK/BCI-algebras was by Xi [13] in 1991. Bipolar information is applied in many algebraic structures-for instance, BCK/BCI-algebras [14][15][16][17], BF-algebras [18], Γ-semihypergroups [19], and hemirings [20]. In many real-life issues, information sometimes comes from m factors (m ≥ 2), that is, multi-attribute data arise which cannot be handled using the existing ideals (e.g., fuzzy ideals, bipolar fuzzy ideals, etc.).…”

Section: Introductionmentioning

confidence: 99%

m-Polar ( α , β ) -Fuzzy Ideals in BCK/BCI-Algebras

Al-Masarwah

Ahmad

2019

Symmetry

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Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years. Hybrid models of fuzzy sets have already been applied to many algebraic structures, such as B C K / B C I -algebras, lie algebras, groups, and symmetric groups. A symmetry of the algebraic structure, mathematically an automorphism, is a mapping of the algebraic structure onto itself that preserves the structure. This paper focuses on combining the concepts of m-polar fuzzy sets and m-polar fuzzy points to introduce a new notion called m-polar ( α , β ) -fuzzy ideals in B C K / B C I -algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, ( α , β ) -fuzzy ideals, and bipolar ( α , β ) -fuzzy ideals in B C K / B C I -algebras. We describe the characterization of m-polar ( ∈ , ∈ ∨ q ) -fuzzy ideals in B C K / B C I -algebras by level cut subsets. Moreover, we define m-polar ( ∈ , ∈ ∨ q ) -fuzzy commutative ideals and explore some pertinent properties.

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“…In 2009, Lee [21] applied the concept of bipolar fuzzy set theory to BCK/BCIalgebras, and introduced the notions of bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras. Recently, the notion of bipolar fuzzy set theory was applied to BCK/BCI-algebras [4,23] and other algebraic structures such that Lie algebras [2], Lie superalgebras [3], hemirings [8] and BF -algebras [27,28], etc. Al-Masarwah and Ahmad [5] introduced the notions of doubt bipolar fuzzy subalgebras and doubt bipolar fuzzy ideals in BCK/BCI-algebras.…”

Section: Introductionmentioning

confidence: 99%