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空间密度算子及其应用研究

张发明,刘娴,杨红暾   

  1. 南昌大学经济管理学院, 南昌  330031
  • 出版日期:2019-12-25 发布日期:2020-03-20

张发明,刘娴,杨红暾. 空间密度算子及其应用研究[J]. 系统科学与数学, 2019, 39(12): 2041-2056.

ZHANG Faming,LIU Xian,YANG Hongtun. Spatital Density Operator and Its Application[J]. Journal of Systems Science and Mathematical Sciences, 2019, 39(12): 2041-2056.

Spatital Density Operator and Its Application

ZHANG Faming ,LIU Xian ,YANG Hongtun   

  1. School of Economics and Management, Nanchang University, Nanchang 330031
  • Online:2019-12-25 Published:2020-03-20

为在信息集结过程中体现空间时序数据的分布特征,提出了一种新的集结方法,即空间密度算子.该算子首先构建了融合灰色关联度和相似度思想的空间贴近度,并在此基础上利用直接聚类法对空间时序数据进行聚类;然后在组内和组间信息基础上,以信息偏差最小为原则确定组内权重,以规模密度及属性密度为基准确定组间密度权重;最后提出空间密度加权算术平均算子(SDWA)和空间密度加权几何平均算子(SDWGA)这两种新算子,对空间时序数据进行集结,得到最终评价结果.通过性质分析,发现该算子具有置换不变性、幂等性、介值性和单调性等特征.进一步,文末用一个算例来验证方法的可行性和有效性.

In order to reflect the distribution characteristics of time series multi-dimensional data in the process of information aggregation, this paper proposes a new way of information aggregation-spatial density operator. Firstly, spatial closeness is put forward with the grey correlation degree and its similarity, and a simple method of time series multi-dimensional data clustering is put forward with the idea of closeness. Then, according to the characteristics of the results of the intra-group and the inter-group clustering, the intra-group weights are determined based on the minimum information deviation principle, and the inter-group weights are determined based on the attribute density and the scale density. Finally, two new operators are put forward, which are respectively the spatial density weighted arithmetic mean operator (SDWA) and the spatial surface density weighted geometric mean operator (SDWGA), to aggregate time series multi-dimensional data. So the final evaluation results can be obtained. By properties analysis, it is found that the operator has the characteristics of substitution invariance, idempotency, medianity and monotonicity. In addition, an example is proposed to verify feasibility and effectiveness of this method.

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