Abstract: 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.

Key words: perturbation-based data mining theorems, perturbation degrees, boundary, inverse P-sets, perturbation theorems