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Granular representation of OWA-based fuzzy rough sets

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Abstract
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.
Keywords
fuzzy rough sets, granular computing, ordered weighted average, rule induction

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MLA
Palangetić, Marko, et al. “Granular Representation of OWA-Based Fuzzy Rough Sets.” FUZZY SETS AND SYSTEMS, 2021, doi:10.1016/j.fss.2021.04.018.
APA
Palangetić, M., Cornelis, C., Greco, S., & Słowiński, R. (2021). Granular representation of OWA-based fuzzy rough sets. FUZZY SETS AND SYSTEMS. https://doi.org/10.1016/j.fss.2021.04.018
Chicago author-date
Palangetić, Marko, Chris Cornelis, Salvatore Greco, and Roman Słowiński. 2021. “Granular Representation of OWA-Based Fuzzy Rough Sets.” FUZZY SETS AND SYSTEMS. https://doi.org/10.1016/j.fss.2021.04.018.
Chicago author-date (all authors)
Palangetić, Marko, Chris Cornelis, Salvatore Greco, and Roman Słowiński. 2021. “Granular Representation of OWA-Based Fuzzy Rough Sets.” FUZZY SETS AND SYSTEMS. doi:10.1016/j.fss.2021.04.018.
Vancouver
1.
Palangetić M, Cornelis C, Greco S, Słowiński R. Granular representation of OWA-based fuzzy rough sets. FUZZY SETS AND SYSTEMS. 2021;
IEEE
[1]
M. Palangetić, C. Cornelis, S. Greco, and R. Słowiński, “Granular representation of OWA-based fuzzy rough sets,” FUZZY SETS AND SYSTEMS, 2021.
@article{8707734,
  abstract     = {{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.}},
  author       = {{Palangetić, Marko and Cornelis, Chris and Greco, Salvatore and Słowiński, Roman}},
  issn         = {{0165-0114}},
  journal      = {{FUZZY SETS AND SYSTEMS}},
  keywords     = {{fuzzy rough sets,granular computing,ordered weighted average,rule induction}},
  language     = {{eng}},
  pages        = {{19}},
  title        = {{Granular representation of OWA-based fuzzy rough sets}},
  url          = {{http://dx.doi.org/10.1016/j.fss.2021.04.018}},
  year         = {{2021}},
}

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