本文为西班牙卡塔赫纳理工大学（作者：Josena LopezHerrera）的博士论文，共231页。

本文描述了模糊归纳推理（FIR）方法中加入的新元素，这些新元素允许预测时间序列的未来行为。在系统识别方面，使用这一方法的良好结果已在早些时候报道过。因此，决定在预测时间序列的背景下评估该方法，这是一项更为复杂的工作，因为无法运用通过输入生成这些时间序列的系统。

为了确定该方法是否可用于时间序列分析，对不同的方法进行了比较研究，包括连接方法以及线性和非线性预测方法。这项研究可以描述FIR对时间序列类型的预测效果良好。结果表明，FIR算法充分利用了时间序列中含有确定性元素的准静态训练数据中的所有信息。

由于方法论的定性性质，最初得到的预测是模棱两可的。为了克服这些困难，引入了新的预测元素。修改了用于计算五个最近邻相对距离和绝对权重的公式，并将新的置信测度（基于相似度和接近度）并入，允许在不必知道序列真值的情况下估计预测误差。接近度测量基于距离函数，而相似性度量基于模糊集之间的相似性。本文对经典等价函数作了一个推广，它是基于模糊集理论的基数与差分定义，最早由Dubois和Prade提出。

利用这些置信度发展了两种新的预测技术，这些方法允许在每个时刻选择最佳的定性预测模型，新技术允许改进准静态时间序列的预测。通过动态地改变定性模型，可以大大降低多区域非平稳时间序列的预测误差。

以定量的方式评估了累积置信测度的劣化程度与信号可预测范围之间的关系。结果表明，相似性测度比邻近测度对预测误差更敏感。

本文还介绍了将该方法应用于智能传感器和预测控制器设计问题时所获得的初步结果。

本文分为八章和两个附录。第一章介绍了本次研究的主要内容及其前因。

在第二章中，我们建立了能够对本研究所分析时间序列进行分类的参数。本章还简要回顾了时间序列分析中使用的方法。

第三章介绍了模糊归纳推理方法的研究现状。

第四章比较了FIR和最著名的时间序列预测方法的性能。在FIR方法中引入了两种新的预测质量度量方法，研究结果见第五章。描述了这些措施的理论基础，并展示了它们在不同类型时间序列中的应用。

第六章介绍了在非平稳时间序列情况下，将前一章介绍的预测质量测度应用于提高FIR预测能力问题的结果。

为了评估一个预测在哪一点上是可靠的，第7章介绍了可用于估计准平稳时间序列的可预测范围的累积预测质量的度量。

第八章总结了本文在FIR算法方面的研究成果，其作为智能传感器和预测控制器设计方法的应用在附录A和附录B中。

In this dissertation, new elements aredescribed that have been added to the methodology of Fuzzy Inductive Reasoning(FIR), elements that allow the prediction of the future behavior of timeseries. In the identification of systems, very good results of using thismethodology had been reported earlier. Therefore, it was decided to evaluatethe methodology also in the context of predicting time series, a more complexundertaking, because of the impossibility of exerting the systems that generatethese time series through their inputs.

In order to determine whether themethodology could be used in the analysis of time series, a comparative studyof different methodologies was made, including connectionist methods, as wellas linear and nonlinear predictors. This study allowed to characterize thetypes of time series that FIR predicts well. It turns out that FIR exploits allthe information that is contained in the available training data of time seriesthat are quasistationary with deterministic elements.

Due to the qualitative nature of themethodology, predictions were initially obtained that were ambiguous. In orderto overcome these difficulties, new elements of prediction were introduced. Theformula used for calculating the relative distances and the absolute weights ofthe five nearest neighbors was modified, and new confidence measures (based onsimilarity and proximity) were incorporated, measures that allow to estimatethe prediction error without necessity of knowing the true value of the series.The proximity measure is based on a distance function, whereas the similaritymeasure is based on the similarity between fuzzy sets. A generalization of theclassical equivalence function is used that is based on definitions ofcardinality and difference of the theory of fuzzy sets, originally proposed byDubois and Prade.

Two new techniques of prediction weredeveloped that make use of these confidence measures. These methods allow toselect, at every time instant, the best qualitative prediction model.These newtechniques allow to improve the prediction of a quasistationary time series. Bydynamically changing the qualitative model, the prediction error can be reducedconsiderably in non{stationary time series that operate in multiple regimes.

The relation between the degree ofdeterioration of the accumulated confidence measure and the horizon ofpredictability of a signal was evaluated in a quantitative fashion. It wasshown that the similarity measure is more sensitive to the prediction errorthan the proximity measure.

Also presented are first results obtainedwhen applying the methodology to the problems of the design of intelligent sensorsand predictive controllers.

This thesis is structured into eightchapters and two appendices. In Chapter 1, the principal focus of theinvestigation is described as well as its antecedents.

In Chapter 2, the parameters areestablished that allow to classify the time series that are analyzed in thisinvestigation. The chapter also offers a brief review of the methodologies thatare being used in time series analysis.

In Chapter 3, the state of the art of theFuzzy Inductive Reasoning methodology is presented.

A study comparing the performance of FIRwith that of the best known time series prediction methods is presented inChapter 4.

Two new measures of the prediction qualityare introduced in the FIR methodology. The results of this investigation are presentedin Chapter 5. The theoretical foundations of these measures are described, andtheir application to different types of time series is shown.

In Chapter 6, the results of applying theprediction quality measures, introduced in the previous chapter, to the problemof improving the prediction capability of FIR in the case of nonstationary timeseries are presented.

In order to evaluate up to which point aprediction is reliable, Chapter 7 introduces measures of accumulated predictionquality that can be used to estimate the horizon of predictability inquasi{stationary time series.

In Chapter 8, the contributions obtained inthis dissertation related to the FIR methodology are summarized. Itsapplications as a methodology for designing intelligent sensors and predictivecontrollers are presented in Appendices A and B.

1. 引言、研究动机与回顾

2. 时间序列建模与仿真

3. 时间序列预测的模糊归纳推理

4. 时间序列预测方法的比较

5. 模糊归纳推理中预测的收敛性度量

6. 利用动态掩码分配提高模糊归纳推理的预测能力

7. 可预测范围的估计

8. 结论

附录A 使用具有前瞻功能的智能传感器进行预警

附录B 信号预测控制

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