Basic concepts of neutrosophic crisp sets

Abstract

The world around us is characterized by specificity, ambiguity, and contradiction, which led to a lack of our full knowledge of its facts and events. Therefore, we became in need of a new vision and a logical system that fits our incomplete information. In 1965, the American scientist F. Smarandache presented neutrosophic logic as a generalization of fuzzy logic and intuitive fuzzy logic. He added a new component to the degrees of a membership function and a non-membership function, which is the degree of indeterminacy. The crispneutrosophic sets presented by Ahmed Salama is considered a generalization of the classical set theory, as he developed and introduced new concepts in the fields of mathematics, statistics, computer science, and classical information systems. The purpose of this paper is to introduce basic concepts of neutrosophic crisp sets and give some types and operations on neutrosophic crisp sets. Also, we discussed the relationship between neutrosophic crisp sets and others. Finally, we investigate some properties of neutrosophic crisp sets supported by many theorems and illustrative examples. We can use the new of neutrosophic notions in the following applications: database, networks robots, compiler, and codes.