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Indexed by:期刊论文

Date of Publication:2009-10-01

Journal:COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:58

Issue:7

Page Number:1349-1359

ISSN No.: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