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The three-dimensional fuzzy sets and their cut sets
- Source :
-
Computers & Mathematics with Applications . Oct2009, Vol. 58 Issue 7, p1349-1359. 11p. - Publication Year :
- 2009
-
Abstract
- Abstract: In this paper, a new kind of -fuzzy set is introduced which is called the three-dimensional fuzzy set. We first put forward four kinds of cut sets on the three-dimensional fuzzy sets which are defined by the 4-valued fuzzy sets. Then, the definitions of 4-valued order nested sets and 4-valued inverse order nested sets are given. Based on them, the decomposition theorems and representation theorems are obtained. Furthermore, the left interval-valued intuitionistic fuzzy sets and the right interval-valued intuitionistic fuzzy sets are introduced. We show that the lattices constructed by these two special -fuzzy sets are not equivalent to sublattices of lattice constructed by the interval-valued intuitionistic fuzzy sets. Finally, we show that the three-dimensional fuzzy set is equivalent to the left interval-valued intuitionistic fuzzy set or the right interval-valued intuitionistic fuzzy set. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 58
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Computers & Mathematics with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 43872978
- Full Text :
- https://doi.org/10.1016/j.camwa.2009.02.031