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Symmetry 2018, 10(6), 187; https://doi.org/10.3390/sym10060187

New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets

1
School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China
2
College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China
3
College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China
4
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
5
Department of Mathematics, Hanyang University, Seoul 04763, Korea
*
Author to whom correspondence should be addressed.
Received: 29 April 2018 / Revised: 21 May 2018 / Accepted: 28 May 2018 / Published: 30 May 2018
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Abstract

The purpose of the paper is to study new algebraic operations and fundamental properties of totally dependent-neutrosophic sets and totally dependent-neutrosophic soft sets. First, the in-coordination relationships among the original inclusion relations of totally dependent-neutrosophic sets (called type-1 and typ-2 inclusion relations in this paper) and union (intersection) operations are analyzed, and then type-3 inclusion relation of totally dependent-neutrosophic sets and corresponding type-3 union, type-3 intersection, and complement operations are introduced. Second, the following theorem is proved: all totally dependent-neutrosophic sets (based on a certain universe) determined a generalized De Morgan algebra with respect to type-3 union, type-3 intersection, and complement operations. Third, the relationships among the type-3 order relation, score function, and accuracy function of totally dependent-neutrosophic sets are discussed. Finally, some new operations and properties of totally dependent-neutrosophic soft sets are investigated, and another generalized De Morgan algebra induced by totally dependent-neutrosophic soft sets is obtained. View Full-Text
Keywords: neutrosophic set; soft set; totally dependent-neutrosophic set; totally dependent-neutrosophic soft set; generalized De Morgan algebra neutrosophic set; soft set; totally dependent-neutrosophic set; totally dependent-neutrosophic soft set; generalized De Morgan algebra
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Zhang, X.; Bo, C.; Smarandache, F.; Park, C. New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets. Symmetry 2018, 10, 187.

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