Studies on Parameter Identification Using Fuzzy Random Data

本文从模糊感知随机现象的一致性观点出发，引入了一类模糊随机向量及其统计矩，并从理论上研究了模糊随机向量及其二阶统计矩的一些性质。所提出的模糊随机向量的特点如下：1.由于模糊随机向量与模糊随机向量之间的运算是可行的，所以模糊集的集合表示被完全采用。通过采用紧凸对应族作为FRVCS的集合表示，我们得到了FRVCS的期望的合理定义，它与Kwakernak提出的(标量)模糊随机变量基本兼容，而不是从它们的简单扩展中得到的。作为随机向量模糊感知的FRVCs概念在某种意义上可能是两种主要类型的FlizzyMndoin变量之间的桥梁。此外，未来还需要研究以下事项：1.FRVCs的高统计矩的定义及其估计。更温和条件下FRVCS的统计特性3.将该方法应用于对AR、MA、ARMA等模型描述的时间序列的输出过程进行模糊感知所得到的模糊随机数据。利用模糊随机数据对上述时间序列模型的系统参数进行辨识。

In this research, a class of fuzzy random vectors(FRVCs) and their statistical moments have been introduced from the consistent viewpoint of vague perceptions of random phenomena, and some properties of FRVCs and their statistical moments up to second ones have been examined theoretically.The features of proposed FRVCs are as follows :1. Set representations of fuzzy sets are thoroughly adopted because of ilie feasibility for describing operations between FRVCs.2. By adopting the family of compact convex correspondences as the set representation of a FRVCS, we have been able to introduce the reasonable definition of expectations of FRVCs, which is basically compatible with (scalar) fuzzy random variables proposed by Kwakernaak and is never obtained from their simple extensions.3. The proposed concept of FRVCs as vague perceptions of random vectors may be, in some sense, a bridge between two major types of flizzy mndoin variables.Furthermore, the following items should be investigated in the future :1. Definitions of higher statistical moments of FRVCs and their estimators.2. Statistical properties of FRVCS under more moderate conditions3. Applications of the proposed approach to fuzzy random data obtained by vague perceptions of output processes of time series described by AR, MA and ARMA models and so on.4. Identification of system parameters of time series models as mentioned above bv using fuzzy random data.