### Abstract

A neutrosophic set was proposed as an approach to study neutral uncertain information. It is characterized through three memberships, T, I and F, such that these independent functions stand for the truth, indeterminate, and false-membership degrees of an object. The neutrosophic set presents a symmetric form since truth enrolment T is symmetric to its opposite false enrolment F with respect to indeterminacy enrolment I that acts as an axis of symmetry. The neutrosophic set was further extended to a Q-neutrosophic soft set, which is a hybrid model that keeps the features of the neutrosophic soft set in dealing with uncertainty, and the features of a Q-fuzzy soft set that handles two-dimensional information. In this study, we discuss some operations of Q-neutrosophic soft sets, such as subset, equality, complement, intersection, union, AND operation, and OR operation. We also define the necessity and possibility operations of a Q-neutrosophic soft set. Several properties and illustrative examples are discussed. Then, we define the Q-neutrosophic-set aggregation operator and use it to develop an algorithm for using a Q-neutrosophic soft set in decision-making issues that have indeterminate and uncertain data, followed by an illustrative real-life example.

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

Article number | 139 |

Journal | Symmetry |

Volume | 11 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2019 |

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### Keywords

- Decision making
- Neutrosophic set
- Q-neutrosophic set
- Q-neutrosophic soft set
- Soft set

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- Mathematics(all)
- Physics and Astronomy (miscellaneous)

### Cite this

*Symmetry*,

*11*(2), [139]. https://doi.org/10.3390/sym11020139

**An approach toward a Q-neutrosophic soft set and its application in decision making.** / Qamar, Majdoleen Abu; Hassan, Nasruddin.

Research output: Contribution to journal › Article

*Symmetry*, vol. 11, no. 2, 139. https://doi.org/10.3390/sym11020139

}

TY - JOUR

T1 - An approach toward a Q-neutrosophic soft set and its application in decision making

AU - Qamar, Majdoleen Abu

AU - Hassan, Nasruddin

PY - 2019/2/1

Y1 - 2019/2/1

N2 - A neutrosophic set was proposed as an approach to study neutral uncertain information. It is characterized through three memberships, T, I and F, such that these independent functions stand for the truth, indeterminate, and false-membership degrees of an object. The neutrosophic set presents a symmetric form since truth enrolment T is symmetric to its opposite false enrolment F with respect to indeterminacy enrolment I that acts as an axis of symmetry. The neutrosophic set was further extended to a Q-neutrosophic soft set, which is a hybrid model that keeps the features of the neutrosophic soft set in dealing with uncertainty, and the features of a Q-fuzzy soft set that handles two-dimensional information. In this study, we discuss some operations of Q-neutrosophic soft sets, such as subset, equality, complement, intersection, union, AND operation, and OR operation. We also define the necessity and possibility operations of a Q-neutrosophic soft set. Several properties and illustrative examples are discussed. Then, we define the Q-neutrosophic-set aggregation operator and use it to develop an algorithm for using a Q-neutrosophic soft set in decision-making issues that have indeterminate and uncertain data, followed by an illustrative real-life example.

AB - A neutrosophic set was proposed as an approach to study neutral uncertain information. It is characterized through three memberships, T, I and F, such that these independent functions stand for the truth, indeterminate, and false-membership degrees of an object. The neutrosophic set presents a symmetric form since truth enrolment T is symmetric to its opposite false enrolment F with respect to indeterminacy enrolment I that acts as an axis of symmetry. The neutrosophic set was further extended to a Q-neutrosophic soft set, which is a hybrid model that keeps the features of the neutrosophic soft set in dealing with uncertainty, and the features of a Q-fuzzy soft set that handles two-dimensional information. In this study, we discuss some operations of Q-neutrosophic soft sets, such as subset, equality, complement, intersection, union, AND operation, and OR operation. We also define the necessity and possibility operations of a Q-neutrosophic soft set. Several properties and illustrative examples are discussed. Then, we define the Q-neutrosophic-set aggregation operator and use it to develop an algorithm for using a Q-neutrosophic soft set in decision-making issues that have indeterminate and uncertain data, followed by an illustrative real-life example.

KW - Decision making

KW - Neutrosophic set

KW - Q-neutrosophic set

KW - Q-neutrosophic soft set

KW - Soft set

UR - http://www.scopus.com/inward/record.url?scp=85061866564&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061866564&partnerID=8YFLogxK

U2 - 10.3390/sym11020139

DO - 10.3390/sym11020139

M3 - Article

AN - SCOPUS:85061866564

VL - 11

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 2

M1 - 139

ER -