An Approach toward a Q-Neutrosophic Soft Set and Its Application in Decision Making

• Main Authors: Majdoleen Abu Qamar, Nasruddin Hassan
• Format: Article
• Language: English
• Published: MDPI AG 2019-01-01
• Series: Symmetry
• Subjects: decision making; neutrosophic set; Q-neutrosophic set; Q-neutrosophic soft set; soft set
• Online Access: https://www.mdpi.com/2073-8994/11/2/139

A neutrosophic set was proposed as an approach to study neutral uncertain information. It is characterized through three memberships, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>T</mi> <mo>,</mo> <mi>I</mi> </mrow> </semantics> </math> </inline-formula> and <i>F</i>, 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 <i>T</i> is symmetric to its opposite false enrolment <i>F</i> with respect to indeterminacy enrolment <i>I</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.