Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets

Smarandache, Florentin and Ali, Mumtaz and Khan, Mohsin (2019) Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets. In: Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Studies in Fuzziness and Soft Computing, 369. Springer Nature, Cham, Switzerland, pp. 25-42. ISBN 978-3-030-00044-8


Abstract

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.


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Item Type: Book Chapter (Commonwealth Reporting Category B)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to Published version, in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Date Deposited: 29 Jul 2020 05:16
Last Modified: 31 Aug 2020 22:57
Uncontrolled Keywords: Neutrosophic Set Theory; Rough Neutrosophic Sets; Single and Multi-valued Neutrosophic Sets; Neutrosophic Valued Linguistic Soft Sets; Bipolar Neutrosophic Graphs; Power Aggregation Operators; Similarity Measures in Neutrosophic Sets; Correlation Coefficients of Neutrosophic Sets; Data Envelopment Analysis; Cross-entropy; Multicriteria Decision Making
Fields of Research (2008): 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080201 Analysis of Algorithms and Complexity
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010303 Optimisation
Fields of Research (2020): 46 INFORMATION AND COMPUTING SCIENCES > 4613 Theory of computation > 461399 Theory of computation not elsewhere classified
49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490304 Optimisation
Identification Number or DOI: https://doi.org/10.1007/978-3-030-00045-5_2
URI: http://eprints.usq.edu.au/id/eprint/35670

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