EXTENDING THE ROUGHNESS OF THE DATA VIA TRANSITIVE CLOSURES OF SIMILARITY INDEXES

F.X. Bertran, N. Clara and J.C. Ferrer
Additional contact information
J.C. Ferrer: Girona University

Fuzzy Economic Review, 2007, vol. XII, issue 2, 75-84

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.

Keywords: Indiscernibility relation; rough sets; fuzzy similarity index; fuzzy relation; transitive closure (search for similar items in EconPapers)
JEL-codes: G17 (search for similar items in EconPapers)
Date: 2007
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:fzy:fuzeco:v:xii:y:2007:i:2:p:75-84

Access Statistics for this article

More articles in Fuzzy Economic Review from International Association for Fuzzy-set Management and Economy (SIGEF) Contact information at EDIRC.
Bibliographic data for series maintained by Aurelio Fernandez ( this e-mail address is bad, please contact ).