A decomposition of fuzzy relations

Witold Pedrycz; Kaoru Hirota; Salvatore Sessa

doi:10.1109/3477.938269

A decomposition of fuzzy relations

Witold Pedrycz^*, Kaoru Hirota, Salvatore Sessa

^*Corresponding author for this work

Research output: Contribution to journal › Letter › peer-review

23 Citations (Scopus)

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 relation 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 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.

Original language	English
Pages (from-to)	657-663
Number of pages	7
Journal	IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume	31
Issue number	4
DOIs	https://doi.org/10.1109/3477.938269
Publication status	Published - Aug 2001
Externally published	Yes

Keywords

Data compression
Decomposition
Fuzzy relations
Max-t composition
Schein rank of Boolean matrices

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10.1109/3477.938269

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AB - 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 relation 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 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.

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A decomposition of fuzzy relations

Abstract

Keywords

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