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Extending the roughness of the data via transitive closures of similarity indexes

One main assumption in the theory of rough sets applied to information tables is that the elements that exhibit the same information are indiscernible (similar) and form blocks that can be understood as elementary granules of knowledge about the universe. We propose a variant of this concept defining a measure of similarity between the elements of the universe in order to consider that two objects can be indiscernible even though they do not share all the attribute values because the knowledge is partial or uncertain. The set of similarities define a matrix of a fuzzy relation satisfying reflexivity and symmetry but transitivity thus a partition of the universe is not attained. This problem can be solved calculating its transitive closure what ensure a partition for each level belonging to the unit interval [0,1]. This procedure allows generalizing the theory of rough sets depending on the minimum level of similarity accepted. This new point of view increases the rough character of the data because increases the set of indiscernible objects. Finally, we apply our results to a not real application to be capable to remark the differences and the improvements between this methodology and the classical one

¬© Fuzzy Economic Review, 2007, vol.12, n√ļm. 2, p.75-84

SIGEF. Facultat de Ciències Econòmiques i Empresarials

Author: Bertran i Roura, Xavier
Clara i Lloret, Narcís
Ferrer i Comalat, Joan Carles
Date: 2007
Abstract: One main assumption in the theory of rough sets applied to information tables is that the elements that exhibit the same information are indiscernible (similar) and form blocks that can be understood as elementary granules of knowledge about the universe. We propose a variant of this concept defining a measure of similarity between the elements of the universe in order to consider that two objects can be indiscernible even though they do not share all the attribute values because the knowledge is partial or uncertain. The set of similarities define a matrix of a fuzzy relation satisfying reflexivity and symmetry but transitivity thus a partition of the universe is not attained. This problem can be solved calculating its transitive closure what ensure a partition for each level belonging to the unit interval [0,1]. This procedure allows generalizing the theory of rough sets depending on the minimum level of similarity accepted. This new point of view increases the rough character of the data because increases the set of indiscernible objects. Finally, we apply our results to a not real application to be capable to remark the differences and the improvements between this methodology and the classical one
Format: application/pdf
ISSN: 1136-0593
Document access: http://hdl.handle.net/10256/9372
Language: eng
Publisher: SIGEF. Facultat de Ciències Econòmiques i Empresarials
Collection: Reproducció digital del document publicat a: http://search.proquest.com/docview/229091806
Articles publicats (D-EM)
Is part of: ¬© Fuzzy Economic Review, 2007, vol.12, n√ļm. 2, p.75-84
Rights: Tots els drets reservats
Subject: Conjunts borrosos
Fuzzy sets
Conjunts aproximats
Rough sets
Title: Extending the roughness of the data via transitive closures of similarity indexes
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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