Abstract
Soft sets (SSs), neutrosophic sets (NSs), and rough sets (RSs) are different mathematical models for handling uncertainties, but they are mutually related. In this research paper, we introduce the notions of soft rough neutrosophic sets (SRNSs) and neutrosophic soft rough sets (NSRSs) as hybrid models for soft computing. We describe a mathematical approach to handle decision-making problems in view of NSRSs. We also present an efficient algorithm of our proposed hybrid model to solve decision-making problems.
Highlights
Smarandache [1] initiated the concept of neutrosophic set (NS)
We introduce the notions of soft rough neutrosophic sets (SRNSs) and neutrosophic soft rough sets (NSRSs) as hybrid models for soft computing
We present the constructive definition of soft rough neutrosophic relations (SRNRs) by using a soft relation R from M × M = Ḿ to P (Y × Y = Ý ), where Y is a universal set and M is a set of parameter
Summary
Smarandache [1] initiated the concept of neutrosophic set (NS). Smarandache’s NS is characterized by three parts: truth, indeterminacy, and falsity. Molodtsov [7] introduced the notion of soft set as a novel mathematical approach for handling uncertainties. Feng et al [17] introduced a modification of Pawlak approximation space known as soft approximation space (SAS) in which SAS SRSs were proposed They introduced soft rough fuzzy approximation operators in SAS and initiated a idea of SRFSs, which is an extension of RFSs introduced by Dubois and Prade [18]. Developed a hybrid structure by combining RSs and NSs, called RNSs. developed a hybrid structure by combining RSs and NSs, called RNSs They presented interval valued neutrosophic soft rough sets by combining interval valued neutrosophic soft sets and RSs. Yang et al [29] proposed single valued neutrosophic rough sets (SVNRSs) by combining SVNSs and RSs, and established an algorithm for decision-making problems based on SVNRSs in two universes. We present an efficient algorithm of our proposed hybrid model to solve decision-making problems
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