逆P-集合的边界特征与系统状态监测

Boundary Characteristics of Inverse P-sets and System Condition Monitoring

逆P-集合是具有动态特性的集合模型,逆P-集合的动态特性来自集合内元素(属性)的动态迁移:元素迁入使得集合的边界向外扩展,元素迁出使得集合的边界向内收缩,从而产生扰动的边界和稳定的核。基于上述事实,在逆P-集合的基础上,提出逆P-集合的边界、核的概念和特征,给出逆P-集合与有限普通元素集合之间的关系、边界和核的扰动定理及逆P-集合、边界和核在系统状态监测中的应用。

Inverse P-sets are set models which have dynamic characteristics, and their dynamic characteristics come from element （or attribute） dynamic transferring. Elements transferring into the set makes the boundary of the set expand, and elements moving out from the set makes the boundary of the set contract, generating perturbation boundary and sta- ble core. Based on the fact above and the inverse P-set theory, the concepts of boundary and core of inverse P-sets were proposed, their characteristics were given, and the relationships between inverse P-sets and finite ordinary element set were discussed. Then based on the aforementioned results, the perturbation theorems of the boundaries and the pertur- bation theorems of core were presented. Finally the application of inverse P-set, the boundary and the core in system condition monitoring was given.