Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2009-10-01

Journal: COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 58

Issue: 7

Page Number: 1349-1359

ISSN: 0898-1221

Key Words: 4-valued fuzzy sets; Three-dimensional fuzzy sets; Cut sets; Decomposition theorems; Representation theorems

Abstract: In this paper, a new kind of L-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 L-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. (C) 2009 Published by Elsevier Ltd