About Rough Neutrosophic Soft Sets Theory and Study Their Properties

Abstract

Earlier fuzzy set, vague set, intuitionistic fuzzy set, L fuzzy set etc are used as a mathematical tools for solving problems based on uncertainties or ambiguous in nature. But due to more complexity involves in problems exist in nature, traditional tools are unable to handle those in a systematic manner. So we need a tool which is more flexible to handle those problems. Which leads to the invention of soft set which was introduced by Molodtsov in 1999. Soft set (SS) theory is a mathematical tool deals with parametric data which are imprecise in nature. Ithis a generalization of fuzzy set theory. On the other hand Rough set (RS) theory and Neutrosophic set (NS) theory both rising as a powerful tool to handle these uncertain, incomplete, inconsistent and imprecise information in an effective manner. Actually Neutrosophic set is a generalization of intuitionistic fuzzy set. Sometimes it is not possible to handle all sorts of uncertain problems with a single mathematical tool. Fusion of two or more mathematical tools give rise to a new mathematical concept which gives an idea how to solve such type of problems in a more sophisticated ways. Which leads to the introduction of fuzzy soft set, rough soft set, intuitionistic fuzzy soft set, soft rough set etc. Neutrosophic soft set (NSS) was established by combining the concept of Soft set and Neutrosophic set. In this paper, using the concept of Rough set and Neutrosophic soft set a new concept known as Rough neutrosophic soft set (RNSS) is developed. Some properties and operations on them are introduced.