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.

Recently, vague sets and neutrosophic sets have received great attention among the scholars and have been applied in many applications. But, the actual theoretical impacts of the combination of these two sets in dealing uncertainties are still not fully explored until now. In this paper, a new generalized mathematical model called interval neutrosophic vague sets is proposed, which is a combination of vague sets and interval neutrosophic sets and a generalization of interval neutrosophic vague sets. Some definitions of interval neutrosophic vague set such as union, complement and intersection are presented. Furthermore, the basic operations, the derivation of its properties and related example are included.

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.

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties. The notions of the (a, β, g) interval cut set of interval valued neutrosophic sets and the (a, β, g) strong interval cut set of interval valued neutrosophic sets are put forward. Some related properties have been established with proof, examples and counter examples.

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties.

In this paper, we introduce the notion of interval-valued neutrosophic UP-subalgebras (resp., interval-valued neutrosophic near UP- lters, interval-valued neutrosophic UP- lters, interval-valued neutrosophic UP-ideals, and interval-valued neutrosophic strong UP-ideals) of UP-algebras, proved some results, and their generalizations. Furthermore, we discuss the relations between interval-valued neutrosophic UP-subalgebras (resp., interval-valued neutrosophic near UP- lters, interval-valued neutrosophic UP- lters, interval-valued neutrosophic UP-ideals, and interval-valued neutrosophic strong UP- ideals) and their level subsets.

Vague sets and neutrosophic sets play an inevitable role in the developing scenario of mathematical world. In this modern era of artificial intelligence most of the real life situations are found to be immersed with unclear data. Even the newly developed concepts are found to fail with such problems. So new sets like Plithogenic and new combinations like neutrosophic vague arose. Classical set theory dealt with single universe and can be studied by taking it’s subsets.

This book presents the advancements and applications of neutrosophics, which are generalizations of fuzzy logic, fuzzy set, and imprecise probability. The neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics are increasingly used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, physics.In the last chapter a soft semantic Web Services agent framework is proposed to facilitate the registration and discovery of high quality semantic Web Services agent. The intelligent inference engine module of soft semantic Web Services agent is implemented using interval neutrosophic logic.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: Neutrosophic Soft Fixed Points, Selection of Alternative under the Framework of Single-Valued Neutrosophic Sets, Application of Single Valued Trapezoidal Neutrosophic Numbers in Transportation Problem.