基于不完备信息系统的三角模糊数决策粗糙集

Triangular fuzzy number decision-theoretic rough sets under incomplete information systems

在不完备信息系统中,针对用区间值表示一个未知参量时,整个区间内取值机会被认为是均等的,得到的结果可能会产生过大误差的问题,将三角模糊数引入到决策粗糙集中,提出了一种基于不完备信息系统的三角模糊数决策粗糙集。首先,定义了一种描述不完备信息的相似关系;然后,针对不完备信息系统中的缺失值,利用三角模糊数来获取损失函数,构建了三角模糊数决策粗糙集模型;实例表明,本文提出的方法不仅能够弥补用区间数表示的不足,而且可以突出可能性最大的主值,从而减少分类误差。

Aiming at the problems that when using an interval value to represent an unknown parameter in an incompleteinformation system, the opportunity to obtain the value over the whole interval is considered to be equal, butthe result may cause an over-large error. In order to solve this problem, a triangular fuzzy number was introducedinto decision-theoretic rough sets, and a triangular fuzzy decision-theoretic rough set under incomplete informationsystems is proposed. Firstly, a new similarity relation was defined to describe incomplete information systems.Then, in view of the missing values, a model of triangular fuzzy number decision-theoretic rough sets was constructedto obtain the loss function. Finally, examples show that the proposed method not only makes up for deficiency inrepresentation of the interval value, but also highlights the main value most likely to reduce the classification error.