research-article

The approximation set of a vague set in rough approximation space

Authors:

Hong YuAuthors Info & Claims

Information Sciences—Informatics and Computer Science, Intelligent Systems, Applications: An International Journal, Volume 300, Issue C

Pages 1 - 19

https://doi.org/10.1016/j.ins.2014.12.023

Published: 10 April 2015 Publication History

Abstract

Vague set is a further generalization of fuzzy set. In rough set theory, a target concept may be a defined set, fuzzy set or vague set. That the target concept is a defined set or fuzzy set was analyzed in detail in our other papers respectively. In general, we can only get two boundaries of an uncertain concept when we use rough set to deal with the uncertain problems and can not get a useable approximation defined set which is a union set with many granules in Pawlak's approximation space. In order to overcome above shortcoming, we mainly discuss the approximation set of a vague set in Pawlak's approximation space in the paper. Firstly, many preliminary concepts or definitions related to the vague set and the rough set are reviewed briefly. And then, many new definitions, such as 0.5-crisp set, step-vague set and average-step-vague set, are defined one by one. The Euclidean similarity degrees between a vague set and its 0.5-crisp set, step-vague set and average-step-vague set are analyzed in detail respectively. And then, the conclusion that the Euclidean similarity degree between a vague set and its 0.5-crisp set is better than the Euclidean similarity degree between the vague set and the other defined set in the approximation space ( U, R ) is drawn. Afterward, it is proved that average-step-vague set is an optimal step-vague set because the Euclidean similarity degree between a vague set and its average-step-vague set in the approximation space ( U, R ) can reach the maximum value. Finally, the change rules of the Euclidean similarity degree with the different knowledge granularities are discussed, and these rules are in accord with human cognitive mechanism in a multi-granularity knowledge space.

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Cited By

Yang JLuo TZeng LJin X(2022)The cost-sensitive approximation of neighborhood rough sets and granular layer selectionJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-21223442:4(3993-4003)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.3233/JIFS-212234
Yang JZhou WLi S(2021)Similarity measure for multi-granularity rough approximations of vague setsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20061140:1(1609-1621)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.3233/JIFS-200611
Bao YYang HLi S(2019)On characterization of $$(\mathcal {I},{\mathcal {N}})$$(I,N)-single valued neutrosophic rough approximation operatorsSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-018-3613-z23:15(6065-6084)Online publication date: 1-Aug-2019
https://dl.acm.org/doi/10.1007/s00500-018-3613-z
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The approximation set of a vague set in rough approximation space
1. Computing methodologies
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cover image Information Sciences: an International Journal

Information Sciences: an International Journal Volume 300, Issue C

April 2015

193 pages

ISSN:0020-0255

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Copyright © Elsevier Inc.

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Elsevier Science Inc.

United States

Publication History

Published: 10 April 2015

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Cited By

Yang JLuo TZeng LJin X(2022)The cost-sensitive approximation of neighborhood rough sets and granular layer selectionJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-21223442:4(3993-4003)Online publication date: 1-Jan-2022
Yang JZhou WLi S(2021)Similarity measure for multi-granularity rough approximations of vague setsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20061140:1(1609-1621)Online publication date: 1-Jan-2021
Bao YYang HLi S(2019)On characterization of $$(\mathcal {I},{\mathcal {N}})$$(I,N)-single valued neutrosophic rough approximation operatorsSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-018-3613-z23:15(6065-6084)Online publication date: 1-Aug-2019
Mardani ANilashi MAntucheviciene JTavana MBausys RIbrahim O(2017)Recent Fuzzy Generalisations of Rough Sets TheoryComplexity10.1155/2017/16081472017Online publication date: 1-Jan-2017
Zhang JLou YZhang LHao DZhang LMei HZimmermann TCleland-Huang JSu Z(2016)Isomorphic regression testing: executing uncovered branches without test augmentationProceedings of the 2016 24th ACM SIGSOFT International Symposium on Foundations of Software Engineering10.1145/2950290.2950313(883-894)Online publication date: 1-Nov-2016
Zhang XMiao D(2016)Double-quantitative fusion of accuracy and importanceKnowledge-Based Systems10.1016/j.knosys.2015.09.00191:C(219-240)Online publication date: 1-Jan-2016
Huang BGuo CLi HFeng GZhou X(2016)Hierarchical structures and uncertainty measures for intuitionistic fuzzy approximation spaceInformation Sciences: an International Journal10.1016/j.ins.2015.12.005336:C(92-114)Online publication date: 1-Apr-2016
Zhang XMiao D(2016)Quantitative/qualitative region-change uncertainty/certainty in attribute reductionInformation Sciences: an International Journal10.1016/j.ins.2015.11.037334:C(174-204)Online publication date: 20-Mar-2016
Zhang QZhang QWang G(2016)The uncertainty of probabilistic rough sets in multi-granulation spacesInternational Journal of Approximate Reasoning10.1016/j.ijar.2016.06.00177:C(38-54)Online publication date: 1-Oct-2016
Zimmermann TCleland-Huang JSu Z(2016)Proceedings of the 2016 24th ACM SIGSOFT International Symposium on Foundations of Software EngineeringundefinedOnline publication date: 1-Nov-2016

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