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.
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2019, Vol. 32 
