Abstract: F-distortion data is a data pair ((x)F,(x)-) composed of F-data (x)F and loss data (x).It has internal dynamic characteristic and can be applied in a class of information system which has loss characteristic of data element.Based on the visualization question of F-distortion data，the concept of F-distortion data circle is proposed by F-distortion data.The geometrical method of identification and recovery for F-distortion data is discussed.The paper gives some theorems such as the positional relation theorem，the identification theorem and the recovery theorem of F-distortion data by the method of F-distortion data circle.Meanwhile，the identification criterion of F-distortion data by the method of F-distortion data circle and the application are provided.F-distortion data circle is a data circle pair (OF,O-) composed of data circle OFand O-.F-distortion data circle provides a geometrical method to research F-distortion data.

Key words: P-sets, F-distortion data, F-distortion data circle, identification-recovery

摘要： F-残缺数据是由F-数据(x)F与损失数据(x)-构成的数据对((x)F,(x)-)，((x)F,(x)-)具有内-动态特性，应用于一类具有数据元减少特征的信息系统。基于F-残缺数据可视化问题，应用F-残缺数据提出F-残缺数据圆概念，讨论F-残缺数据辨识与恢复的几何方法。给出F-残缺数据圆位置关系定理，F-残缺数据的F-残缺数据圆辨识定理与辨识准则;给出F-残缺数据的F-残缺数据圆恢复定理，并给出应用。F-残缺数据圆是由数据圆OF，O-构成的数据圆对(OF,O-)，F-残缺数据圆为研究F-残缺数据提供了一种几何方法。

关键词: P-集合, F-残缺数据, F-残缺数据圆, 辨识-恢复