Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2010-08-01

Journal: COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 60

Issue: 3

Page Number: 442-463

ISSN: 0898-1221

Key Words: L-fuzzy set; n-dimensional fuzzy set; Finite valued fuzzy set; Cut set; Decomposition theorem; Representation theorem

Abstract: The connections among the n-dimensional fuzzy set, Zadeh fuzzy set and the finite-valued fuzzy set are established in this paper. The n-dimensional fuzzy set, a special L-fuzzy set, is first defined. It is pointed out that the n-dimensional fuzzy set is a generalization of the Zadeh fuzzy set, the interval-valued fuzzy set, the intuitionistic fuzzy set, the interval-valued intuitionistic fuzzy set and the three dimensional fuzzy set. Then, the definitions of cut set on n-dimensional fuzzy set and n-dimensional vector level cut set of Zadeh fuzzy set are presented. The cut set of the n-dimensional fuzzy set and n-dimensional vector level set of the Zadeh fuzzy set are both defined as n + 1-valued fuzzy sets. It is shown that a cut set defined in this way has the same properties as a normal cut set of the Zadeh fuzzy set. Finally, by the use of these cut sets, decomposition and representation theorems of the n-dimensional fuzzy set and new decomposition and representation theorems of the Zadeh fuzzy set are constructed. (C) 2010 Elsevier Ltd. All rights reserved.