Cluster techniques are used in hotspot spatial analysis to detect hotspots as areas on the map; an extension of the Fuzzy C-means that the clustering algorithm has been applied to locate hotspots on the map as circular areas; it represents a good trade-off between the accuracy in the detection of the hotspot shape and the computational complexity. However, this method does not measure the reliability of the detected hotspots and therefore does not allow us to evaluate how reliable the identification of a hotspot of a circular area corresponding to the detected cluster is; a measure of the reliability of hotspots is crucial for the decision maker to assess the need for action on the area circumscribed by the hotspots. We propose a method based on the use of De Luca and Termini’s Fuzzy Entropy that uses this extension of the Fuzzy C-means algorithm and measures the reliability of detected hotspots. We test our method in a disease analysis problem in which hotspots corresponding to areas where most oto-laryngo-pharyngeal patients reside, within a geographical area constituted by the province of Naples, Italy, are detected as circular areas. The results show a dependency between the reliability and fluctuation of the values of the degrees of belonging to the hotspots.

中文翻译：

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基于模糊熵的空间热点可靠性

在热点空间分析中使用聚类技术将热点检测为地图上的区域；Fuzzy C的扩展表示聚类算法已应用于在地图上将热点定位为圆形区域；它代表了热点形状检测的准确性与计算复杂性之间的良好折衷。然而，该方法不能测量所检测到的热点的可靠性，因此不能允许我们评估与所检测到的簇相对应的圆形区域的热点识别的可靠性。衡量热点可靠性的方法对于决策者评估对热点所限区域采取行动的必要性至关重要。我们提出了一种基于De Luca和Termini模糊熵的使用方法，该方法使用Fuzzy C-means算法的这种扩展并测量检测到的热点的可靠性。我们在疾病分析问题中测试了我们的方法，在该问题中，将由意大利那不勒斯省构成的地理区域中与大多数耳喉咽部患者居住的区域相对应的热点检测为圆形区域。结果表明，可靠性和归属度值的波动之间存在依赖性。