Abstract
To handle indeterminate and incomplete data, neutrosophic logic/set/probability were established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry as the truth and the falsehood look the same and behave in a symmetrical way with respect to the indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The idea of neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough (NSR) lower and upper approximations. Properties of suggested approximations are proposed and subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate the feasibility of the newly rough set model with decision making problems involving neutrosophic soft set. Finally, a discussion on the features and limitations of the proposed model is provided.
Highlights
The limitation of deterministic research is currently recognized in areas of management, social sciences, operations research and economics
The equivalence relation is a very stringent condition which limits the applications of rough sets in the real world
We start by reviewing the concepts of rough set, neutrosophic set and soft set
Summary
The limitation of deterministic research is currently recognized in areas of management, social sciences, operations research and economics Uncertain theories such as probability, fuzzy sets [1], intuitionistic fuzzy sets [2], vague sets [3] and theory of interval mathematics [4] are applied in realms which are ambiguous and uncertain. This section further defines neutrosophic soft rough set approximations. NSR-set concepts include neutrosophic soft rough (NSR) definability, neutrosophic soft rough (NSR)-membership function, neutrosophic soft rough (NSR)-membership relations, neutrosophic soft rough (NSR)-inclusion relations and neutrosophic soft rough (NSR)-equality relations Properties of these concepts are proven and examples provided. We outline future work and draw conclusions to this work
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