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New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets
- Source :
- Symmetry, Vol 10, Iss 6, p 187 (2018), Symmetry, Volume 10, Issue 6, Pages: 187
- Publication Year :
- 2018
- Publisher :
- MDPI AG, 2018.
-
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.
- Subjects :
- Physics and Astronomy (miscellaneous)
generalized De Morgan algebra
General Mathematics
Score
02 engineering and technology
01 natural sciences
Combinatorics
0103 physical sciences
0202 electrical engineering, electronic engineering, information engineering
Computer Science (miscellaneous)
Order (group theory)
soft set
totally dependent-neutrosophic soft set
De Morgan algebra
Mathematics
Complement (set theory)
010308 nuclear & particles physics
Intersection (set theory)
lcsh:Mathematics
lcsh:QA1-939
totally dependent-neutrosophic set
Chemistry (miscellaneous)
Algebraic operation
neutrosophic set
020201 artificial intelligence & image processing
Soft set
Universe (mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 10
- Issue :
- 6
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....6554e432b156620f76409ea420d43bff