A decomposition of fuzzy relations

Author

Pedrycz, Witold ; Hirota, Kaoru ; Sessa, Salvatore

Author_Institution

Dept. of Electr. & Comput. Eng., Alberta Univ., Edmonton, Alta., Canada

Volume

31

Issue

4

fYear

2001

fDate

8/1/2001 12:00:00 AM

Firstpage

657

Lastpage

663

Abstract

This study is concerned with a decomposition of fuzzy relations, that is their representation with the aid of a certain number of fuzzy sets. We say that some fuzzy sets decompose an original fuzzy refraction if the sum of their Cartesian products approximate the given fuzzy relation. The theoretical underpinnings of the problem are presented along with some linkages with Boolean matrices (such as a Schein rank). Subsequently, we reformulate the decomposition of fuzzy relations as a problem of numeric optimizing and propose a detailed learning scheme leading to a collection of decomposing fuzzy sets. The role of the decomposition in a general class of data compression problems (including those of image compression and rule-based system condensation) is formulated and discussed in detail

Keywords

Boolean functions; data compression; fuzzy logic; fuzzy set theory; image coding; knowledge based systems; matrix algebra; Boolean matrices; Cartesian products; Schein rank; data compression; fuzzy relation; fuzzy relations decomposition; fuzzy sets; image compression; rule-based system condensation; Calculus; Councils; Couplings; Data compression; Fuzzy control; Fuzzy sets; Fuzzy systems; Image coding; Knowledge based systems; Matrix decomposition;

fLanguage

English

Journal_Title

Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on

Publisher

ieee

ISSN

1083-4419

Type

jour

DOI

10.1109/3477.938269

Filename

938269