TY - JOUR
T1 - Granular representation of OWA-based fuzzy rough sets
AU - Palangetić, Marko
AU - Cornelis, Chris
AU - Greco, Salvatore
AU - Słowiński, Roman
N1 - Funding Information:
Marko Palangetić and Chris Cornelis would like to thank Odysseus project from Flanders Research Foundation ( FWO ), grant G0H9118N for funding their research. Salvatore Greco wishes to acknowledge the support of the Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR) - PRIN 1576 2017 , project “Multiple Criteria Decision Analysis and Multiple Criteria Decision Theory”, grant 2017CY2NCA . The research of Roman Słowiński was supported by the Polish Ministry of Education and Science , grant no. 0311/SBAD/0709 .
Funding Information:
Marko Palangeti? and Chris Cornelis would like to thank Odysseus project from Flanders Research Foundation (FWO), grant G0H9118N for funding their research. Salvatore Greco wishes to acknowledge the support of the Ministero dell'Istruzione, dell'Universit? e della Ricerca (MIUR) - PRIN 1576 2017, project ?Multiple Criteria Decision Analysis and Multiple Criteria Decision Theory?, grant 2017CY2NCA. The research of Roman S?owi?ski was supported by the Polish Ministry of Education and Science, grant no. 0311/SBAD/0709.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/4/26
Y1 - 2021/4/26
N2 - Granular representations of crisp and fuzzy sets play an important role in rule induction algorithms based on rough set theory. In particular, arbitrary fuzzy sets can be approximated using unions of simple fuzzy sets called granules. These granules, in turn, have a straightforward interpretation in terms of human-readable fuzzy “if…, then…” rules. In this paper, we are considering a fuzzy rough set model based on ordered weighted average (OWA) aggregation over considered values. We show that this robust extension of the classical fuzzy rough set model, which has been applied successfully in various machine learning tasks, also allows for a granular representation. In particular, we prove that when approximations are defined using a directionally convex t-norm and its residual implicator, the OWA-based lower and upper approximations are definable as unions of fuzzy granules. This result has practical implications for rule induction from such fuzzy rough approximations.
AB - Granular representations of crisp and fuzzy sets play an important role in rule induction algorithms based on rough set theory. In particular, arbitrary fuzzy sets can be approximated using unions of simple fuzzy sets called granules. These granules, in turn, have a straightforward interpretation in terms of human-readable fuzzy “if…, then…” rules. In this paper, we are considering a fuzzy rough set model based on ordered weighted average (OWA) aggregation over considered values. We show that this robust extension of the classical fuzzy rough set model, which has been applied successfully in various machine learning tasks, also allows for a granular representation. In particular, we prove that when approximations are defined using a directionally convex t-norm and its residual implicator, the OWA-based lower and upper approximations are definable as unions of fuzzy granules. This result has practical implications for rule induction from such fuzzy rough approximations.
KW - Fuzzy rough sets
KW - Granular computing
KW - Ordered weighted average
KW - Rule induction
UR - http://www.scopus.com/inward/record.url?scp=85105282963&partnerID=8YFLogxK
U2 - 10.1016/j.fss.2021.04.018
DO - 10.1016/j.fss.2021.04.018
M3 - Article
AN - SCOPUS:85105282963
SN - 0165-0114
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
ER -