概率粗糙集Ⅲ型与Ⅳ型之研究

Research of Probabilistic Rough Set Mode Ⅲ and Ⅳ

经典粗糙集理论在解决系统不确定性知识时有明显的不足,对于不协调的决策表的规则提取存在很大的局限性.因此许多学者从不同的角度如变精度、概率论、模糊集来拓展其研究领域.概率粗糙集是从概率论出发,充分利用近似边界区域提供的统计信息,能提取带有确定因子的决策规则.概率粗糙集Ⅲ型与Ⅳ型是其后两种形式.论文推导了概率Ⅲ型与Ⅳ型的若干定理及重要性质,并予以证明;把最小风险Bayes决策转化为概率Ⅲ型与Ⅳ型下的问题来解决,最后用一个实例说明了其有效性.

Classical rough set theory is not good enough in solving problems with system uncertainty,and it also has critical limitations in extracting rules of the inconsistent decision table.From different perspectives,such as variable precision,probability,and fuzzy sets,many scholars have extended their research fields.The probabilistic rough set proceeds from probability theory and makes full use of the statistical information provided from approximate border area to extract the decision rules with determining factor,based on which Probabilistic rough set model Ⅲ and Ⅳ are two forms.This paper deduced and proved some theorems and important properties of probabilistic rough set model Ⅲ and Ⅳ.Besides,in the paper minimum risk Bayes decision was transformed into problem of model Ⅲ and Ⅳ and was solved.Finally,an example was used to illustrate the effectiveness.