caa a22 4500 605468966 CHVBK 20210128100319.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s00500-014-1387-5 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1387-5 Complement information entropy for uncertainty measure in fuzzy rough set and its applications [Elektronische Daten] [Junyang Zhao, Zhili Zhang, Chongzhao Han, Zhaofa Zhou] Uncertainty measure is an important tool for analyzing imprecise and ambiguous data. Some information entropy models in rough set theory have been defined for various information systems. However, there are relatively few studies on evaluating uncertainty in fuzzy rough set. In this paper, we propose a new complement information entropy model in fuzzy rough set based on arbitrary fuzzy relation, which takes inner-class and outer-class information into consideration. The corresponding definitions of complement conditional entropy, complement joint entropy, complement mutual information and complement information granularity are also presented. The properties of these definitions are analyzed, which show complement information entropy shares some similar properties with Shannon's entropy. Moreover, a generalized information entropy model is proposed by introducing probability distribution into fuzzy approximate space. This model can be used to measure uncertainty of data with the different sample distributions. Applications of the proposed entropy measures in feature importance evaluation and feature selection are studied with data set experiments. Experimental results show that the proposed method is effective and adaptable to different classifiers. Springer-Verlag Berlin Heidelberg, 2014 Uncertainty measure nationallicence Information entropy nationallicence Fuzzy relation nationallicence Fuzzy rough set nationallicence Information granularity nationallicence Zhao Junyang Ministry of Education Key Lab For Intelligent Networks and Network Security (MOE KLINNS Lab), Institute of Integrated Automation, School of Electronic and Information Engineering, Xi'an Jiaotong University, 710049, Xi'an, China aut Zhang Zhili Xi'an Research Inst. of Hi-tech Hongqing Town, 710025, Xi'an, China aut Han Chongzhao Ministry of Education Key Lab For Intelligent Networks and Network Security (MOE KLINNS Lab), Institute of Integrated Automation, School of Electronic and Information Engineering, Xi'an Jiaotong University, 710049, Xi'an, China aut Zhou Zhaofa Xi'an Research Inst. of Hi-tech Hongqing Town, 710025, Xi'an, China aut Soft Computing Springer Berlin Heidelberg 19/7(2015-07-01), 1997-2010 1432-7643 19:7<1997 2015 19 500 https://doi.org/10.1007/s00500-014-1387-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1387-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhao Junyang Ministry of Education Key Lab For Intelligent Networks and Network Security (MOE KLINNS Lab), Institute of Integrated Automation, School of Electronic and Information Engineering, Xi'an Jiaotong University, 710049, Xi'an, China aut NATIONALLICENCE 700 1- Zhang Zhili Xi'an Research Inst. of Hi-tech Hongqing Town, 710025, Xi'an, China aut NATIONALLICENCE 700 1- Han Chongzhao Ministry of Education Key Lab For Intelligent Networks and Network Security (MOE KLINNS Lab), Institute of Integrated Automation, School of Electronic and Information Engineering, Xi'an Jiaotong University, 710049, Xi'an, China aut NATIONALLICENCE 700 1- Zhou Zhaofa Xi'an Research Inst. of Hi-tech Hongqing Town, 710025, Xi'an, China aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/7(2015-07-01), 1997-2010 1432-7643 19:7<1997 2015 19 500