New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Setsopen access
- Authors
- Zhang, Xiaohong; Bo, Chunxin; Smarandache, Florentin; Park, Choonkil
- Issue Date
- Jun-2018
- Publisher
- MDPI
- Keywords
- neutrosophic set; soft set; totally dependent-neutrosophic set; totally dependent-neutrosophic soft set; generalized De Morgan algebra
- Citation
- SYMMETRY-BASEL, v.10, no.6, pp.1 - 17
- Indexed
- SCIE
SCOPUS
- Journal Title
- SYMMETRY-BASEL
- Volume
- 10
- Number
- 6
- Start Page
- 1
- End Page
- 17
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/149932
- DOI
- 10.3390/sym10060187
- ISSN
- 2073-8994
- 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.
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