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Neutrosophic Sets and Logic

Neutrosophic Sets and Logic

Mumtaz Ali, Florentin Smarandache, Luige Vladareanu
Copyright: © 2017 |Pages: 46
ISBN13: 9781522509141|ISBN10: 1522509143|EISBN13: 9781522509158
DOI: 10.4018/978-1-5225-0914-1.ch002
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MLA

Ali, Mumtaz, et al. "Neutrosophic Sets and Logic." Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices, edited by Amal Kumar Adak, et al., IGI Global, 2017, pp. 18-63. https://doi.org/10.4018/978-1-5225-0914-1.ch002

APA

Ali, M., Smarandache, F., & Vladareanu, L. (2017). Neutrosophic Sets and Logic. In A. Adak, D. Manna, & M. Bhowmik (Eds.), Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices (pp. 18-63). IGI Global. https://doi.org/10.4018/978-1-5225-0914-1.ch002

Chicago

Ali, Mumtaz, Florentin Smarandache, and Luige Vladareanu. "Neutrosophic Sets and Logic." In Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices, edited by Amal Kumar Adak, Debashree Manna, and Monoranjan Bhowmik, 18-63. Hershey, PA: IGI Global, 2017. https://doi.org/10.4018/978-1-5225-0914-1.ch002

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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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