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Open AccessArticle

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.
Symmetry 2018, 10(6), 187; https://doi.org/10.3390/sym10060187
Received: 29 April 2018 / Revised: 21 May 2018 / Accepted: 28 May 2018 / Published: 30 May 2018
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
MDPI and ACS Style

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. https://doi.org/10.3390/sym10060187

AMA Style

Zhang X, Bo C, Smarandache F, Park C. New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets. Symmetry. 2018; 10(6):187. https://doi.org/10.3390/sym10060187

Chicago/Turabian Style

Zhang, Xiaohong; Bo, Chunxin; Smarandache, Florentin; Park, Choonkil. 2018. "New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets" Symmetry 10, no. 6: 187. https://doi.org/10.3390/sym10060187

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