Cut sets on neutsosophic sets and their properties

This thesis consists of disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and their basic properties. Also, we have put forward in the notions of (ζ,η,θ)- cut interval valued neutrosophic set and (ζ,η,θ)- cut strong interval valued neutrosophic set. These concepts play an important role in interval valued neutrosophic set theory. Moreover, the representation theorem of interval valued neutrosophic sets is proposed by using the concept of level sets. Then, the extension principles of interval valued neutrosophic sets are developed based on the representation theorem. We have established the properties with proof and examples. Finally, some algebraic operations such as addition, substraction, multiplication and division operations over interval valued neutrosophic sets are defined.