Abstract
Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems.
Highlights
Smarandache [1] initiated the concept of neutrosophic set (NS)
A neutrosophic soft rough set is a generalization of a neutrosophic rough set, and we introduce the idea of neutrosophic soft rough graphs (NSRGs) that are made by combining NSRSs with graphs and describe different methods of their construction
Rough set theory can be considered as an extension of classical set theory
Summary
Smarandache [1] initiated the concept of neutrosophic set (NS). Smarandache’s NS is characterized by three parts: truth, indeterminacy, and falsity. Zhang et al [16,17] presented the notions of soft rough sets, soft rough intuitionistic fuzzy sets, intuitionistic fuzzy soft rough sets, its application in decision-making, and introduced generalized intuitionistic fuzzy soft rough sets. 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 [20] proposed single valued neutrosophic rough sets (SVNRSs) by combining SVNSs and RSs and defined SVNRSs on two universes and established an algorithm for a decision-making problem based on SVNRSs on two universes. A neutrosophic soft rough set is a generalization of a neutrosophic rough set, and we introduce the idea of neutrosophic soft rough graphs (NSRGs) that are made by combining NSRSs with graphs and describe different methods of their construction. Terminologies and applications not mentioned in the paper, the readers are referred to [27,28,29,30,31,32,33,34,35]
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