概率粗糙直觉模糊集的不确定性度量方法研究

Research on the Uncertainty Measurement Method of Probabilistic Rough Intuitionistic Fuzzy Sets

Pawlak粗糙集模型忽视了信息的不确定性和模糊性,等价类完全包含于目标概念才能被划分到下近似,在处理数据时显得过于苛刻。针对这个问题,本文结合概率粗糙集与直觉模糊集,对概率粗糙直觉模糊集模型进行研究,其模型具有一定的容错能力,能够较为有效的处理含有噪声和模糊的数据。首先,在概率近似空间中,定义模糊事件的条件概率,构建概率粗糙直觉模糊集模型,并讨论了一些性质。在此基础上构建2种概率粗糙直觉模糊集模型,0.5-概率粗糙直觉模糊集和变精度概率粗糙直觉模糊集。其次,由于传统的概率粗糙直觉模糊集的粗糙度具有一定的局限性,无法准确表示因为边界域的存在而引起的不确定性问题,针对这个问题,定义了基于概率粗糙直觉模糊集模型的近似质量和粗糙度,引入粗糙熵的概念,将粗糙熵与粗糙度结合,提出了一种新的基于概率粗糙直觉模糊集模型的不确定性度量方法。最后,通过实例验证了所提基于概率粗糙直觉模糊集模型的不确定性度量方法的有效性,并在UCI数据集上进行了对比分析。

The Pawlak rough set model ignores the uncertainty and ambiguity of information, and the equivalence class is completely included in the target concept to be classified into the lower approximation, which is too harsh when processing data. In response to this problem, this paper combines probabilistic rough sets and intuitionistic fuzzy sets to study the probabilistic rough intuitionistic fuzzy set models. The model has certain fault tolerance and can effectively deal with noise and fuzzy data. Firstly, in the probability approximation space, the conditional probability of fuzzy events is defined, the probabilistic rough-intuitive fuzzy set model is constructed, and some properties are discussed. On this basis, two probabilistic rough intuitionistic fuzzy set models are constructed, 0.5-probability rough intuitionistic fuzzy set and variable precision probabilistic rough intuitionistic fuzzy set. Secondly, because the roughness of the traditional probabilistic rough intuitionistic fuzzy set has certain limitations, it cannot accurately represent the uncertainty problem caused by the existence of the boundary domain. For this problem, an approximation based on the probabilistic rough intuitionistic fuzzy set model is defined. Quality and roughness, the concept of rough entropy is introduced, and rough entropy is combined with roughness, and a new uncertainty measurement method based on probabilistic rough intuitionistic fuzzy set model is proposed. Finally, the effectiveness of the proposed uncertainty measurement method based on the probabilistic rough intuitionistic fuzzy set model is verified by an example, and compared and analyzed on the UCI data set.