Stochastic Fuzzy Discrete Event Systems and Their Model Identification
提出一类新的随机模糊离散事件系统，由多个随机出现的模糊自动机构成，并开发了一种无需先验知识即可辨识其结构和参数的技术。
We introduce a new class of fuzzy discrete event systems (FDESs) called stochastic FDESs (SFDESs), which is significantly different from the probabilistic FDESs (PFDESs) in the literature. It offers an effective modeling framework for applications that are unsuitable for the PFDES framework. An SFDES is comprised of multiple fuzzy automata that occur randomly one at time with different occurrence probabilities. It uses either the max-product fuzzy inference or the max–min fuzzy inference. This article focuses on single-event SFDES—each of the fuzzy automata of such an SFDES has one event. Assuming nothing is known about an SFDES, we develop an innovative technique capable of determining number of fuzzy automata and their event transition matrices as well as estimating their occurrence probabilities. The technique, called prerequired-pre-event-state-based technique, creates and uses merely <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> particular pre-event state vectors of dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> to identify event transition matrices of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> fuzzy automata, involving a total of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$MN^{2}$ </tex-math></inline-formula> unknown parameters. One necessary and sufficient condition and three sufficient conditions are established for the identification of SFDES with different settings. The technique does not have any adjustable parameter or hyperparameter to set. A numerical example is provided to concretely illustrate the technique.