Neutrosophic Fuzzy Soft Matrix Theory and Its Application in Group Decision Making

Abstract

In 2020, Sujit et al. introduced the notion of the neutrosophic fuzzy set (NFS) to deal with uncertainty under a fuzzy environment where the fuzzy membership grade of every element of the field of the domain is associated with three independent neutrosophic components, namely truth, indeterminacy, and falsity membership grade. The main focus of the chapter is to introduce a neutrosophic fuzzy soft set (NFSS) to deal with uncertainty parametrically, and it gives the approximate solution to the problem. NFSS is a mixture of a neutrosophic set, fuzzy sets, and soft sets. So, it can be treated as a hybrid structure that gives more flexibility to solve multi-criteria decision-making problems under a fuzzy environment. NFSS evolved as an extension of fuzzy set, soft set, neutrosophic set, etc. Then the authors propose an algorithmic approach for group decision-making (GDM) problems using a neutrosophic fuzzy soft matrix (NFSM) and its related properties. Finally, an illustrative example shows the applicability of the proposed approach.