Rough Entropy and Knowledge Granularity Based on Cartesian Product of Double Universes
DENG Qie1,2, ZHANG Xianyong1,2, YANG Jilin2, CHEN Shuai1,2
1.School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066; 2.Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066
Abstract According to the Cartesian product,the covering space on two-dimensional direct product universe is constructed, and the corresponding rough entropy and knowledge granularity are investigated. Firstly, two single-universe covering spaces are induced by double-universes approximate space, and two-dimensional covering space is constructed.Then, the rough entropy and knowledge granularity based on double-universes are positioned at a single-universe covering space, and the two measures are determined in covering spaces on symmetrical single-universe and compositive two-dimensional universe by structural simulation and granular replacement. For the three sets of double metrics, the double-metrics sum, supremum and infimum, granulation monotonicity and three-way linear combination are achieved. Finally, data simulation and simulation experiment verify the effectiveness of the measure construction and the theoretical properties.
Fund:Supported by National Natural Science Foundation of China(No.61673258), Sichuan Science and Technology Foundation(No.19YYJC2845), Sichuan Youth Science and Technology Foundation(No. 2017JQ0046)
Corresponding Authors:
ZHANG Xianyong, Ph.D., professor. His research inte-rests include rough set, granular computing and data mining.
About author:: DENG Qie, master student. Her research interests include rough set and granular computing.YANG Jilin, Ph.D., associate professor. Her research interests include rough set and fuzzy set.CHEN Shuai, master student. His research interests include rough set and data mining.
DENG Qie,ZHANG Xianyong,YANG Jilin等. Rough Entropy and Knowledge Granularity Based on Cartesian Product of Double Universes[J]. , 2019, 32(11): 975-986.
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2019, Vol. 32 
