A Class of BCI-Algebra and Quasi-Hyper BCI-Algebra

As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced by Mohseni Takallo, Borzooei and Jun, and it is applied to BCK/BCI-algebras. In this article, MBJ-neutrosophic set is used to study commutative ideal in BCI-algebras. The concept of closed MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal is introduced and their properties and relationships are studied. The conditions for an MBJ-neutrosophic ideal to be a commutative MBJ-neutrosophic ideal are given. The conditions for an MBJ-neutrosophic ideal to be a closed MBJ-neutrosophic ideal are provided. Characterization of a commutative MBJ-neutrosophic ideal is established. Finally, the extension property for a commutative MBJ-neutrosophic ideal is founded.

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“…Example 1. Consider a BCI-algebra X = {0, 1, a, b, c} with the binary operation * which is given in Table 1 (see [11]).…”

Section: Commutative Mbj-neutrosophic Ideals Of Bci-algebrasmentioning

confidence: 99%

Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures

2021

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“…Let U = {0, x, b, c, d} be a set with a binary operation * , which is given in Table 2. Then, U is a BCI-algebra (see [2]). Define a 3-polar intuitionistic fuzzy set ( ξ, ) on U as follows:…”

Section: K-polar Intuitionistic Fuzzy P-idealsmentioning

confidence: 99%

“…BCI-algebras are a generalization of BCK-algebras, and they originated from two sources: set theory and propositional calculi. See the books [2,3] for more information on BCK/BCI-algebras. Fuzzy sets were first introduced by Zadeh [4], in which the membership degree is represented by only one function-the truth function.…”

Section: Introductionmentioning

confidence: 99%

A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets

et al. 2020

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In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

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“…Zhang and Y.D. Du proposed introducing a quasi-minimal element into BCI-algebra and proved the adjoint semigroup of QM-BCI-algebra is a commutative Clifford semigroup in [13]. As another generalization of BCI-algebra, BZ-algebra was first proposed by Ye (see [14]).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, they gave the concepts of anti-grouped hyper BZ-algberas as well as generalized anti-grouped hyper BZ-algebras and discussed the connection between them and BZ-algebras. Additionally, in [13], X.H. Zhang and Y.D.…”

Section: Introductionmentioning

confidence: 99%

QM-BZ-Algebras and Quasi-Hyper BZ-Algebras

Zhang

2022

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BZ-algebra, as the common generalization of BCI-algebra and BCC-algebra, is a kind of important logic algebra. Herein, the new concepts of QM-BZ-algebra and quasi-hyper BZ-algebra are proposed and their structures and constructions are studied. First, the definition of QM-BZ-algebra is presented, and the structure of QM-BZ-algebra is obtained: Each QM-BZ-algebra is KG-union of quasi-alter BCK-algebra and anti-grouped BZ-algebra. Second, the new concepts of generalized quasi-left alter (hyper) BZ-algebras and QM-hyper BZ-algebra are introduced, and some characterizations of them are investigated. Third, the definition of quasi-hyper BZ-algebra is proposed, and the relationships among BZ-algebra, hyper BZ-algebra, quasi-hyper BCI-algebra, and quasi-hyper BZ-algebra are discussed. Finally, several special classes of quasi-hyper BZ-algebras are studied in depth and the following important results are proved: (1) an anti-grouped quasi-hyper BZ-algebra is an anti-grouped BZ-algebra; (2) every generalized anti-grouped quasi-hyper BZ-algebra corresponds to a semihypergroup.

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A Class of BCI-Algebra and Quasi-Hyper BCI-Algebra

Cited by 19 publications

References 22 publications

Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures

Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures

A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets

QM-BZ-Algebras and Quasi-Hyper BZ-Algebras

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