逆P-集合的扰动定理与数据的扰动挖掘

逆P-集合是把动态特征引入到有限普通元素集合内提出的,逆P-集合具有动态特征。逆P-集合的动态特征来自集合的元素(属性)迁移,元素迁入使得集合的边界发生扩展扰动,元素迁出使得集合的边界发生收缩扰动。本文基于逆P-集合的概念与结构,提出内逆P-集合的F-扰动度、外逆P-集合的(-overF)-扰动度与逆P-集合的(F,(-overF))-扰动度概念,给出它们的度量,并给出F-扰动定理、(-overF)-扰动定理与(F,(-overF))-扰动定理,以及在扰动存在的条件下,逆P-集合、逆P-集合族与有限普通元素集合X的关系。利用这些结果,提出数据的F-扰动挖掘定理、(-overF)-扰动挖掘定理与(F,(-overF))-扰动挖掘定理。最后给出基于扰动度的数据挖掘应用。

Perturbation theorems of inverse P-sets and perturbation-based data mining

Inverse P-sets were proposed by introducing dynamic characteristics into finite ordinary element set; inverse P-sets have dynamic characteristics, which characteristics come from element(attribute)transferring. Elements transferred into set make the boundary of the set expanding, while elements transferred from the set makes the boundary of the set contracting. Based on inverse P-sets, this paper proposes F-perturbation degree of internal inverse P-set, (-overF)-perturbation degree of outer inverse P-set and(F,(-overF))-perturbation degree of inverse P-set, and gives their measurements. Then this paper gives F-perturbation theorem, (-overF)-perturbation theorem and (F,(-overF))-perturbation theorem, and shows the relationships anong inverse P-sets, inverse P-sets faminly and finite ordinary element set under perturbations. By using the aforementioned results, F-perturbation based data mining theorem, (-overF)-perturbation based data mining theorem and (F,(-overF))-perturbation based data mining theorem are presented. Finally an application of data mining based on perturbation degree is shown.