article

Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system

Authors:

Chen WuAuthors Info & Claims

Information Sciences—Informatics and Computer Science, Intelligent Systems, Applications: An International Journal, Volume 207

Pages 66 - 78

https://doi.org/10.1016/j.ins.2012.03.023

Published: 01 November 2012 Publication History

Abstract

Rough set is a useful tool to deal with partition related uncertainty, granularity, and incompleteness of knowledge. Although the classical rough set is constructed on the basis of an indiscernibility relation, it can also be generalized by using some weaker binary relations. In this paper, a systematic approach is used to study the generalized rough sets in six coverings and pure reflexive neighborhood system. After two steps, relationships among generalized rough sets in six coverings and pure reflexive neighborhood system are obtained. The first step is to study the generalized rough sets in six coverings, and to get relationships between every two covering rough set models. The second step is to study the relationships between generalized rough sets in each covering and in pure reflexive neighborhood system. The inclusion relations or equivalence relations among the seven upper/lower approximations could be acquired. Finally, the accuracy measures of generalized rough sets in six coverings and that in pure reflexive neighborhood system are compared. The relationships among seven accuracy measures are also obtained. Some illustrative examples are employed to demonstrate our arguments.

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cover image Information Sciences: an International Journal

Information Sciences: an International Journal Volume 207, Issue

November, 2012

98 pages

ISSN:0020-0255

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Copyright © Elsevier Inc. © 2012.

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Elsevier Science Inc.

United States

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Published: 01 November 2012

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Cited By

Zhang XLi JLi W(2022)A new mechanism of rule acquisition based on covering rough setsApplied Intelligence10.1007/s10489-021-03067-x52:11(12369-12381)Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s10489-021-03067-x
Liu G(2019)Using one axiom to characterize rough set and fuzzy rough set approximationsInformation Sciences: an International Journal10.1016/j.ins.2012.10.004223(285-296)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.ins.2012.10.004
Zhao FLi L(2018)Axiomatization on generalized neighborhood system-based rough setsSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-017-2957-022:18(6099-6110)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1007/s00500-017-2957-0
Wang PLi Q(2017)The rough membership function based on C 10 ¯ and its applicationsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-15160832:1(279-289)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.3233/JIFS-151608
Zhou XZhao BHan S(2016)Roughness in m-semilattices Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/IFS-15200330:4(2331-2338)Online publication date: 1-Jan-2016
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Yan SYan LWu J(2016)Rough data-deduction based on the upper approximationInformation Sciences: an International Journal10.1016/j.ins.2016.09.011373:C(308-320)Online publication date: 10-Dec-2016
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Salehi SSelamat AFujita H(2015)Systematic mapping study on granular computingKnowledge-Based Systems10.1016/j.knosys.2015.02.01880:C(78-97)Online publication date: 1-May-2015
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Zhang YLi CLin MLin Y(2015)Relationships between generalized rough sets based on covering and reflexive neighborhood systemInformation Sciences: an International Journal10.1016/j.ins.2015.05.023319:C(56-67)Online publication date: 20-Oct-2015
https://dl.acm.org/doi/10.1016/j.ins.2015.05.023
Wang ZWang HFeng QShu L(2015)The approximation number function and the characterization of covering approximation spaceInformation Sciences: an International Journal10.1016/j.ins.2015.02.002305:C(196-207)Online publication date: 1-Jun-2015
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Li TGu SWu W(2015)Knowledge Spaces and Reduction of Covering Approximation SpacesRough Sets and Knowledge Technology10.1007/978-3-319-25754-9_15(164-174)Online publication date: 20-Nov-2015
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