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Multi-Granulation Rough Set for Incomplete Interval-Valued Decision Information Systems Based on Multi-Threshold Tolerance Relation

by Bingyan Lin 1,† and Weihua Xu 2,*,†
1
School of Sciences, Chongqing University of Technology, Chongqing 400054, China
2
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2018, 10(6), 208; https://doi.org/10.3390/sym10060208
Received: 17 May 2018 / Revised: 4 June 2018 / Accepted: 5 June 2018 / Published: 8 June 2018
A relation is viewed as a granularity from a granular computing perspective. A classic rough set contains only one granularity. A multi-granulation rough set contains multiple granularities, which promotes the applications of classical rough set. Firstly, this paper uses the incomplete interval-valued decision information system (IIVDIS) as research object and constructs two rough set models in the light of single granularity rough set model for applying the rough set theory to real life more widely, which are optimistic multi-granulation rough set (OMGRS) model and pessimistic multi-granulation rough set (PMGRS) model in the IIVDIS. Secondly, we design two algorithms to compute the roughness and the degree of dependence that are two tools for measuring uncertainty of rough set. Finally, several experiments are performed on six UCI data sets to verify the validity of the proposed theorems. View Full-Text
Keywords: multi-threshold tolerance relation; multi-granulation; incomplete interval-valued decision information system; rough set multi-threshold tolerance relation; multi-granulation; incomplete interval-valued decision information system; rough set
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Lin, B.; Xu, W. Multi-Granulation Rough Set for Incomplete Interval-Valued Decision Information Systems Based on Multi-Threshold Tolerance Relation. Symmetry 2018, 10, 208.

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