Support-Neutrosophic Set: A New Concept in Soft Computing

Abstract

 Today, soft computing is a field that is used
a lot in solving real-world problems, such as problems in
economics, finance, banking... With the aim to serve for
solving the real problem, many new theories and/or tools
which were proposed, improved to help soft computing
used more efficiently. We can mention some theories as
fuzzy sets theory (L. Zadeh, 1965), intuitionistic fuzzy set
(K Atanasov, 1986), neutrosophic set (F. Smarandache
1999). In this paper, we introduce a new notion of support-neutrosophic set (SNS), which is the combination a
neutrosophic set with a fuzzy set. So, SNS set is a direct
extension of fuzzy set and neutrosophic sets (F.
Smarandache). Then, we define some operators on the
support-neutrosophic sets, and investigate some properties
of these operators.