Neutrosophic Sets and Logic

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Author(s): Mumtaz Ali (Quaid-i-azam University Islamabad, Pakistan), Florentin Smarandache (University of New Mexico – Gallup, USA)and Luige Vladareanu (Institute of Solid Mechanics of Romanian Academy, Romania)
Copyright: 2017
Pages: 46
Source title: Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices
Source Author(s)/Editor(s): Amal Kumar Adak (Jafuly Deshpran High School, India), Debashree Manna (Damda Jr. High School, India)and Monoranjan Bhowmik (Vidyasagar Teacher’s Training College, India)
DOI: 10.4018/978-1-5225-0914-1.ch002

Keywords: Artificial Intelligence / Computer Science & IT / Engineering Science Reference

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Abstract

Neutrosophic sets and Logic plays a significant role in approximation theory. It is a generalization of fuzzy sets and intuitionistic fuzzy set. Neutrosophic set is based on the neutrosophic philosophy in which every idea Z, has opposite denoted as anti(Z) and its neutral which is denoted as neut(Z). This is the main feature of neutrosophic sets and logic. This chapter is about the basic concepts of neutrosophic sets as well as some of their hybrid structures. This chapter starts with the introduction of fuzzy sets and intuitionistic fuzzy sets respectively. The notions of neutrosophic set are defined and studied their basic properties in this chapter. Then we studied neutrosophic crisp sets and their associated properties and notions. Moreover, interval valued neutrosophic sets are studied with some of their properties. Finally, we presented some applications of neutrosophic sets in the real world problems.

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