Abstract
Rough set theory and neutrosophic set theory are mathematical models to deal with incomplete and vague information. These two theories can be combined into a framework for modeling and processing incomplete information in information systems. Thus, the neutrosophic rough set hybrid model gives more precision, flexibility and compatibility to the system as compared to the classic and fuzzy models. In this research study, we develop neutrosophic rough digraphs based on the neutrosophic rough hybrid model. Moreover, we discuss regular neutrosophic rough digraphs, and we solve decision-making problems by using our proposed hybrid model. Finally, we give a comparison analysis of two hybrid models, namely, neutrosophic rough digraphs and rough neutrosophic digraphs.
Highlights
The concept of a neutrosophic set, which generalizes fuzzy sets [1] and intuitionistic fuzzy sets [2], was proposed by Smarandache [3] in 1998, and it is defined as a set about the degree of truth, indeterminacy, and falsity
Neutrosophic set and rough set are two different theories to deal with uncertainty and imprecise and incomplete information
It is necessary to develop hybrid models by incorporating the advantages of many other different mathematical models dealing with uncertainty
Summary
The concept of a neutrosophic set, which generalizes fuzzy sets [1] and intuitionistic fuzzy sets [2], was proposed by Smarandache [3] in 1998, and it is defined as a set about the degree of truth, indeterminacy, and falsity. Algorithms 2018, 11, 59 and Sayed et al, [18] introduced rough neutrosophic digraphs, in which they have approximated neutrosophic set under the influence of a crisp equivalence relation. We apply another hybrid set model, neutrosophic rough, to graph theory. We deal with regular neutrosophic rough digraphs and solve the decision-making problem by using our proposed hybrid model. Our paper is organized as follows: Firstly, we develop the notion of neutrosophic rough digraphs and present some numerical examples. We describe novel applications of our proposed hybrid decision-making method.
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