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Modified reconstructability analysis for many‐valued functions and relations

Modified reconstructability analysis for many‐valued functions and relations A novel many‐valued decomposition within the framework of lossless reconstructability analysis (RA) is presented. In previous work, modified reconstructability analysis (MRA) was applied to Boolean functions, where it was shown that most Boolean functions not decomposable using conventional reconstructability analysis (CRA) are decomposable using MRA. Also, it was previously shown that whenever decomposition exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. In this paper, MRA is extended to many‐valued logic functions, and logic structures that correspond to such decomposition are developed. It is shown that many‐valued MRA can decompose many‐valued functions when CRA fails to do so. Since real‐life data are often many‐valued, this new decomposition can be useful for machine learning and data mining. Many‐valued MRA can also be applied for the decomposition of relations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Kybernetes Emerald Publishing

Modified reconstructability analysis for many‐valued functions and relations

Kybernetes , Volume 33 (5/6): 15 – Jun 1, 2004

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Publisher
Emerald Publishing
Copyright
Copyright © 2004 Emerald Group Publishing Limited. All rights reserved.
ISSN
0368-492X
DOI
10.1108/03684920410533967
Publisher site
See Article on Publisher Site

Abstract

A novel many‐valued decomposition within the framework of lossless reconstructability analysis (RA) is presented. In previous work, modified reconstructability analysis (MRA) was applied to Boolean functions, where it was shown that most Boolean functions not decomposable using conventional reconstructability analysis (CRA) are decomposable using MRA. Also, it was previously shown that whenever decomposition exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. In this paper, MRA is extended to many‐valued logic functions, and logic structures that correspond to such decomposition are developed. It is shown that many‐valued MRA can decompose many‐valued functions when CRA fails to do so. Since real‐life data are often many‐valued, this new decomposition can be useful for machine learning and data mining. Many‐valued MRA can also be applied for the decomposition of relations.

Journal

KybernetesEmerald Publishing

Published: Jun 1, 2004

Keywords: Data analysis; Cybernetics; Boolean functions

References