• 论文 •

### 空间密度算子及其应用研究

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

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

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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