Arithmetic Operations Of Neutrosophic Sets Interval Neutrosophic Sets And Rough Neutrosophic Sets
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Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets
In approximation theory, neutrosophic set and logic show an important role. They are generalizations of intuitionistic fuzzy set and logic respectively. Based on neutrosophy, which is a new branch of philosophy, every idea X, has an opposite denoted as anti (X) and their neutral which is denoted as neut (X). These are the main features of neutrosophic set and logic. This chapter is based on the basic concepts of neutrosophic set as well as some of their hybrid structures. In this chapter, we define and study the notion of neutrosophic set and their basic properties. Moreover, interval-valued neutrosophic set are studied with some of their properties. Finally, we define rough neutrosophic sets.
Algebraic operations on new interval neutrosophic vague sets
The interval neutrosophic set plays an important role to handle indeterminacy and inconsistency of information during decision making process. Recently, the interval neutrosophic vague sets have been proposed as an extension of the neutrosophic sets. Similar with other sets, this newly proposed set have to fulfill some algebraic operations. This paper aims to present algebraic operations for the interval neutrosophic vague sets. Some algebraic operations on interval neutrosophic vague set are introduced. Specifically, algebraic operations of addition, multiplication, scalar multiplication and power for the interval neutrosophic vague sets are presented. In addition, several related examples are also presented together with supporting proofs.
Some New Operations of (𝜶, 𝜷, 𝜸) Interval Cut Set of Interval Valued Neutrosophic Sets
In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties.