Characterizations of group theory under Q-neutrosophic soft environment

Majdoleen Abu Qamar, Nasruddin Hassan

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)114-130
Number of pages17
JournalNeutrosophic Sets and Systems
Volume27
Publication statusPublished - 1 Jan 2019

Fingerprint

Group theory
Soft Set
Group Theory
Set theory
Algebra
Set Theory
Fuzzy sets
Algebraic Structure
Fuzzy Sets
Uncertain Data
Group Ring
Homomorphic
Cartesian product
Hybrid Model
Symmetric group
Level Set
Homomorphism
Lie Algebra
Attribute
Uncertainty

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

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

In: Neutrosophic Sets and Systems, Vol. 27, 01.01.2019, p. 114-130.

Research output: Contribution to journalArticle

Abu Qamar, Majdoleen ; Hassan, Nasruddin. / Characterizations of group theory under Q-neutrosophic soft environment. In: Neutrosophic Sets and Systems. 2019 ; Vol. 27. pp. 114-130.
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