A uniform framework for rough approximations based on generalized quantifiers

Tuan Fang Fan, Churn Jung Liau*, Duen-Ren Liu

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The rough set theory provides an effective tool for decision analysis in the way of extracting decision rules from information systems. The rule induction process is based on the definitions of lower and upper approximations of the decision class. The condition attributes of the information system constitute an indiscernibility relation on the universe of objects. An object is in the lower approximation of the decision class if all objects indiscernible with it are in the decision class and it is in the upper approximation of the decision class if some objects indiscernible with it are in the decision class. Various generalizations of rough set theory have been proposed to enhance the capability of the theory. For example, variable precision rough set theory is used to improve the robustness of rough set analysis and fuzzy rough set approach is proposed to deal with vague information. In this paper, we present a uniform framework for different variants of rough set theory by using generalized quantifiers. In the framework, the lower and upper approximations of classical rough set theory are defined with universal and existential quantifiers respectively, whereas variable precision rough approximations correspond to probability quantifiers. Moreover, fuzzy rough set approximations can be defined by using different fuzzy quantifiers. We show that the framework can enhance the expressive power of the decision rules induced by rough set-based decision analysis.

Original languageEnglish
Title of host publicationTransactions on Rough Sets XIX
EditorsAndrzej Skowron, Dominik Ślęzak, Hung Son Nguyen, James F. Peters, Andrzej Skowron, Dominik Ślęzak, Hung Son Nguyen, James F. Peters, Jan G. Bazan, James F. Peters, Andrzej Skowron, Dominik Ślęzak, Hung Son Nguyen, Jan G. Bazan, Jan G. Bazan
PublisherSpringer Verlag
Pages1-16
Number of pages16
ISBN (Print)9783662478141, 9783662478141, 9783662478141
DOIs
StatePublished - 1 Jan 2015
EventInternational Workshop on Rough Set Applications, RSA 2012, held as a part of Federated Conference on Computer Science and Information Systems, FedCSIS 2012 - Wroclaw, Poland
Duration: 9 Sep 201212 Sep 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8988
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Workshop on Rough Set Applications, RSA 2012, held as a part of Federated Conference on Computer Science and Information Systems, FedCSIS 2012
CountryPoland
CityWroclaw
Period9/09/1212/09/12

Keywords

  • Fuzzy cardinality
  • Fuzzy set
  • Rough set
  • Variable precision rough set

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