DocumentCode :
1090961
Title :
Fuzzy Rough Sets: The Forgotten Step
Author :
De Cock, Martine ; Cornelis, Chris ; Kerre, Etienne E.
Author_Institution :
Dept. of Appl. Math. & Comput. Sci., Ghent Univ., Gent
Volume :
15
Issue :
1
fYear :
2007
Firstpage :
121
Lastpage :
130
Abstract :
Traditional rough set theory uses equivalence relations to compute lower and upper approximations of sets. The corresponding equivalence classes either coincide or are disjoint. This behaviour is lost when moving on to a fuzzy T-equivalence relation. However, none of the existing studies on fuzzy rough set theory tries to exploit the fact that an element can belong to some degree to several "soft similarity classes" at the same time. In this paper we show that taking this truly fuzzy characteristic into account may lead to new and interesting definitions of lower and upper approximations. We explore two of them in detail and we investigate under which conditions they differ from the commonly used definitions. Finally we show the possible practical relevance of the newly introduced approximations for query refinement
Keywords :
approximation theory; equivalence classes; fuzzy set theory; fuzzy systems; rough set theory; equivalence classes; fuzzy T-equivalence relation; fuzzy rough sets; query refinement; soft similarity classes; Computer science; Fuzzy set theory; Fuzzy sets; Fuzzy systems; Humans; Mathematics; Rough sets; Set theory; Terminology; Uncertainty; Fuzzy rough set; lower and upper approximation; query refinement; transitivity;
fLanguage :
English
Journal_Title :
Fuzzy Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
1063-6706
Type :
jour
DOI :
10.1109/TFUZZ.2006.889762
Filename :
4088982
Link To Document :
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