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In order to determine whether the methodology could be used in the analysis of time series, a comparative study of different methodologies was made, including connectionist methods, as well as linear and non-linear predictors. This study allowed to characterize the types of time series that FIR predicts well. It turns out that FIR exploits all the information that is contained in the available training data of time series that are quasi-stationary with deterministic elements.
Due to the qualitative nature of the methodology, predictions were initially obtained that were ambiguous. In order to overcome these difficulties, new elements of prediction were introduced. The formula used for calculating the relative distances and the absolute weights of the five nearest neighbors was modified, and new confidence measures (based on similarity and proximity) were incorporated, measures that allow to estimate the prediction error without necessity of knowing the true value of the series. The proximity measure is based on a distance function, whereas the similarity measure is based on the similarity between fuzzy sets. A generalization of the classical equivalence function is used that is based on definitions of cardinality and difference of the theory of fuzzy sets, originally proposed by Dubois and Pradé.
Two new techniques of prediction were developed that make use of these confidence measures. These methods allow to select, at every time instant, the best qualitative prediction model. These new techniques allow to improve the prediction of a quasi-stationary time series. By dynamically changing the qualitative model, the prediction error can be reduced considerably in non-stationary time series that operate in multiple regimes.
The relation between the degree of deterioration of the accumulated confidence measure and the horizon of predictability of a signal was evaluated in a quantitative fashion. It was shown that the similarity measure is more sensitive to the prediction error than the proximity measure.
Also presented are first results obtained when applying the methodology to the problems of the design of intelligent sensors and predictive controllers.
This thesis is structured into eight chapters and two appendices.
In Chapter 1, the principal focus of the investigation is described as well as its antecedents.
In Chapter 2, the parameters are established that allow to classify the time series that are analyzed in this investigation. The chapter also offers a brief review of the methodologies that are being used in time series analysis.
In Chapter 3, the state of the art of the Fuzzy Inductive Reasoning methodology is presented.
A study comparing the performance of FIR with that of the best known time-series prediction methods is presented in Chapter 4.
Two new measures of the prediction quality are introduced in the FIR methodology. The results of this investigation are presented in Chapter 5. The theoretical foundations of these measures are described, and their application to different types of time series is shown.
In Chapter 6, the results of applying the prediction quality measures, introduced in the previous chapter, to the problem of improving the prediction capability of FIR in the case of non-stationary time series are presented.
In order to evaluate up to which point a prediction is reliable, Chapter 7 introduces measures of accumulated prediction quality that can be used to estimate the horizon of predictability in quasi-stationary time series.
In Chapter 8, the contributions obtained in this dissertation related to the FIR methodology are summarized.
Its applications as a methodology for designing intelligent sensors and predictive controllers are presented in Appendices A and B.
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