Neutrosophic fuzzy set and its application in decision making

Fuzzy set (FS) is used to tackle the uncertainty using the membership grade, whereas neutrosophic set (NS) is used to tackle uncertainty using the truth, indeterminacy and falsity membership grades which are considered as independent. In this paper, we introduce the notion of neutrosophic fuzzy set (NFS) by combining FS with NS, which gives rise to some new concepts. Since NFS finds some difficulties to deal with some real life problems due to the nonstandard interval of neutrosophic components, we introduce single valued NFS (SVNFS) which is considered as an instance of NFS. Some set theoretic operations of SVNFS are proposed and their properties are derived. We also propose the distance measures between two SVNFSs. Then a decision making approach is presented using similarity measures based on distance measures. Finally, we emonstrate the proposed approach using a numerical example.