### Abstract

Neutrosophic set theory was initiated as a method to handle indeterminate uncertain data. It is identified via three independent memberships represent truth T, indeterminate I and falsity F membership degrees of an element. As a generalization of neutrosophic set theory, Q-neutrosophic set theory was established as a new hybrid model that keeps the features of Q-fuzzy soft sets which handle two-dimensional information and the features of neutrosophic soft sets in dealing with uncertainty. Different extensions of fuzzy sets have been already implemented to several algebraic structures, such as groups, symmetric groups, rings and lie algebras. Group theory is one of the most essential algebraic structures in the field of algebra. The inspiration of the current work is to broaden the idea of Q-neutrosophic soft set to group theory. In this paper the concept of Q-neutrosophic soft groups is presented. Numerous properties and basic attributes are examined. We characterize the thought of Q-level soft sets of a Q-neutrosophic soft set, which is a bridge between Q-neutrosophic soft groups and soft groups. The concept of Q-neutrosophic soft homomorphism is defined and homomorphic image and preimage of a Q-neutrosophic soft groups are investigated. Furthermore, the cartesian product of Q-neutrosophic soft groups is proposed and some relevant properties are explored.

Original language | English |
---|---|

Pages (from-to) | 114-130 |

Number of pages | 17 |

Journal | Neutrosophic Sets and Systems |

Volume | 27 |

Publication status | Published - 1 Jan 2019 |

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### Keywords

- Group
- Neutrosophic group
- Neutrosophic set
- Neutrosophic soft group
- Q-neutrosophic set
- Q-neutrosophic soft set
- Soft group

### ASJC Scopus subject areas

- Logic
- Applied Mathematics

### Cite this

*Neutrosophic Sets and Systems*,

*27*, 114-130.

**Characterizations of group theory under Q-neutrosophic soft environment.** / Abu Qamar, Majdoleen; Hassan, Nasruddin.

Research output: Contribution to journal › Article

*Neutrosophic Sets and Systems*, vol. 27, pp. 114-130.

}

TY - JOUR

T1 - Characterizations of group theory under Q-neutrosophic soft environment

AU - Abu Qamar, Majdoleen

AU - Hassan, Nasruddin

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Neutrosophic set theory was initiated as a method to handle indeterminate uncertain data. It is identified via three independent memberships represent truth T, indeterminate I and falsity F membership degrees of an element. As a generalization of neutrosophic set theory, Q-neutrosophic set theory was established as a new hybrid model that keeps the features of Q-fuzzy soft sets which handle two-dimensional information and the features of neutrosophic soft sets in dealing with uncertainty. Different extensions of fuzzy sets have been already implemented to several algebraic structures, such as groups, symmetric groups, rings and lie algebras. Group theory is one of the most essential algebraic structures in the field of algebra. The inspiration of the current work is to broaden the idea of Q-neutrosophic soft set to group theory. In this paper the concept of Q-neutrosophic soft groups is presented. Numerous properties and basic attributes are examined. We characterize the thought of Q-level soft sets of a Q-neutrosophic soft set, which is a bridge between Q-neutrosophic soft groups and soft groups. The concept of Q-neutrosophic soft homomorphism is defined and homomorphic image and preimage of a Q-neutrosophic soft groups are investigated. Furthermore, the cartesian product of Q-neutrosophic soft groups is proposed and some relevant properties are explored.

AB - Neutrosophic set theory was initiated as a method to handle indeterminate uncertain data. It is identified via three independent memberships represent truth T, indeterminate I and falsity F membership degrees of an element. As a generalization of neutrosophic set theory, Q-neutrosophic set theory was established as a new hybrid model that keeps the features of Q-fuzzy soft sets which handle two-dimensional information and the features of neutrosophic soft sets in dealing with uncertainty. Different extensions of fuzzy sets have been already implemented to several algebraic structures, such as groups, symmetric groups, rings and lie algebras. Group theory is one of the most essential algebraic structures in the field of algebra. The inspiration of the current work is to broaden the idea of Q-neutrosophic soft set to group theory. In this paper the concept of Q-neutrosophic soft groups is presented. Numerous properties and basic attributes are examined. We characterize the thought of Q-level soft sets of a Q-neutrosophic soft set, which is a bridge between Q-neutrosophic soft groups and soft groups. The concept of Q-neutrosophic soft homomorphism is defined and homomorphic image and preimage of a Q-neutrosophic soft groups are investigated. Furthermore, the cartesian product of Q-neutrosophic soft groups is proposed and some relevant properties are explored.

KW - Group

KW - Neutrosophic group

KW - Neutrosophic set

KW - Neutrosophic soft group

KW - Q-neutrosophic set

KW - Q-neutrosophic soft set

KW - Soft group

UR - http://www.scopus.com/inward/record.url?scp=85071698453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071698453&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85071698453

VL - 27

SP - 114

EP - 130

JO - Neutrosophic Sets and Systems

JF - Neutrosophic Sets and Systems

SN - 2331-6055

ER -