Xiaohong Zhang

Young Bae Jun

Rajab Ali Borzooei

In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods).

Q-Filters of Quantum B-Algebras and Basic Implication Algebras

Jie Meng

BCK-algebras

Florentin Smarandache

Madad Khan

Seok-Zun Song

The notion of (i; j; k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.

Length Neutrosophic Subalgebras of BCK/BCI-Algebras

 Florentin Smarandache

 Hashem Bordbar

The notion of neutrosophic set theory developed by Smarandache (see[1] and[2]) is a more general platform which extends the concepts of classic and fuzzy set, intuitionistic fuzzy set and interval valued (intuitionistic) fuzzy set, and is applied to various parts.

Neutrosophic permeablevaluesandenergeticsubsetswithapplicationsin BCK/BCI-algebras

Seon Jeong Kim

Saeid and Jun introduced the notion of neutrosophic points, and studied neutrosophic subalgebras of several types in BCK=BCI-algebras by using the notion of neutrosophic points.

Generalizations of Neutrosophic Subalgebras in BCK=BCI-Algebras Based on Neutrosophic Points

Hashem Bordbar

The notion of neutrosophic set (NS) theory developed by Smarandache is a more general platform that extends the concepts of classic and fuzzy sets, intuitionistic fuzzy sets, and interval-valued (intuitionistic) fuzzy sets and that is applied to various parts: pattern recognition, medical diagnosis, decision-making problems, and so on

Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-Algebras

Conditions for a neutrosophic set to be a (q, ∈∨q)-neutrosophic subalgebra are considered.

Neutrosophic subalgebras of several types in BCK/BCI-algebras

Mehmat Ali Ozturk

The notions of a commutative (Ɛ, Ɛ)-neutrosophic ideal and a commutative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of a commutative (Ɛ, Ɛ)-neutrosophic ideal are obtained. Relations between commutative (Ɛ, Ɛ)-neutrosophic ideal and (Ɛ, Ɛ)-neutrosophic ideal are discussed.

Commutative falling neutrosophic ideals in BCK-algebras

Generalized neutrosophic set is introduced, and applied it to BCK/BCI-algebras. The notions of generalized neutrosophic subalgebras and generalized neutrosophic ideals in BCK/BCI-algebras are introduced, and related properties are investigated. Characterizations of generalized neu- trosophic subalgebra/ideal are considered. Relation between generalized neutrosophic subalgebra and generalized neutrosophic ideal is discussed. In a BCK-algebra, conditions for a generalized neutrosophic subalgebra to be a generalized neutrosophic ideal are provided. Conditions for a gen- eralized neutrosophic set to be a generalized neutrosophic ideal are also provided. Homomorphic image and preimage of generalized neutrosophic ideal are considered.

Novel Extension of Neutrosophic Sets and Its Application in BCK/BCI-Algebras

In the fuzzy set which is introduced by Zadeh, the membership degree is expressed by only one function so called the truth function. As a generalization of fuzzy set, intuitionistic fuzzy set is introduced by Atanassove by using membership function and nonmembership function.

Polarity of generalized neutrosophic subalgebras in BCK/BCI-algebras

In this paper, we introduce a more general form of neutrosophic ideal, and investigate their properties.

A General Model of Neutrosophic Ideals in Bck/Bci-Algebras Based on Neutrosophic Points

Rajab Ali Borzooei 

 Xiaohong Zhang 

The concept of a commutative generalized neutrosophic ideal in a BCK-algebra is proposed, and related properties are proved. Characterizations of a commutative generalized neutrosophic ideal are considered. Also, some equivalence relations on the family of all commutative generalized neutrosophic ideals in BCK-algebras are introduced, and some properties are investigated.

Commutative Generalized Neutrosophic Ideals in BCK-Algebras

M. Mohseni Takallo

The concepts of a positive implicative BMBJ-neutrosophic ideal is introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a (positive implicative) BMBJ-neutrosophic ideal are provided. Relations between BMBJ-neutrosophic ideal and positive implicative BMBJ-neutrosophic ideal are discussed. Characterizations of positive implicative BMBJ-neutrosophic ideal are displayed.

Positive implicative BMBJ-neutrosophic ideals in BCK-algebras

R. A. Borzooei

The concepts of a BMBJ-neutrosophic subalgebra and a (closed) BMBJ-neutrosophic ideal are introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a BMBJ-neutrosophic ideal in BCK/BCI-algebras are provided. Characterizations of BMBJ-neutrosophic ideal are discussed. Relations between a BMBJ-neutrosophic subalgebra, a BMBJ-neutrosophic subalgebra and a (closed) BMBJ-neutrosophic ideal are considered.

BMBJ-neutrosophic ideals in BCK/BCI-algebras

R.A. Borzooei

Smarandache (F. Smarandache. Neutrosophy, neutrosophic probability, set, and logic, ProQuest Information & Learning, Ann Arbor,Michigan, USA, 105 p., 1998) initiated neutrosophic sets which can be used as a mathematical tool for dealing with indeterminates and inconsistent information.

MBJ-neutrosophic structures and its applications in BCK=BCI-algebras

Kul Hur

Jeong Gon Lee

The notion of positive implicative MBJ-neutrosophic ideal is introduced, and several properties are investigated. Relations between MBJ-neutrosophic ideal and positive implicative MBJ-neutrosophic ideal are discussed. Characterizations of positive implicative MBJ-neutrosophic ideal are displayed.

Positive implicative MBJ-neutrosophic ideals of BCK/BCI-algebras

The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed.

Neutrosophic Quadruple BCK/BCI-Algebras

S. Satham Hussain 

R. Jahir Hussain

A bipolar model is a significant model wherein positive data revels the liked object, while negative data speaks the disliked object. The principle reason for analysing the vague graphs is to demonstrate the stability of few properties in a graph, characterized or to be characterized in using vagueness.

Neutrosophic Bipolar Vague Set and its Application to Neutrosophic Bipolar Vague Graphs

Chang Su Kim

Conditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic set are provided. Conditions for the Punion and the P-intersection of two truth-external (resp. indeterminacy-external and falsity-external) neutrosophic cubic sets to be a truth-internal (resp. indeterminacy-internal and falsity-internal) neutrosophic cubic set are discussed.

Young Bae Jun

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