Dynamic Fuzzy Pattern Recognition with Applications to by Larisa Angstenberger

By Larisa Angstenberger

Dynamic Fuzzy trend popularity with functions to Finance andEngineering specializes in fuzzy clustering equipment that have confirmed to be very robust in development attractiveness and considers the whole technique of dynamic development acceptance. This publication units a normal framework for Dynamic trend attractiveness, describing intimately the tracking approach utilizing fuzzy instruments and the variation technique within which the classifiers must be tailored, utilizing the observations of the dynamic technique. It then specializes in the matter of a altering cluster constitution (new clusters, merging of clusters, splitting of clusters and the detection of slow alterations within the cluster structure). ultimately, the publication integrates those elements right into a whole set of rules for dynamic fuzzy classifier layout and classification.

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However, there is a number of applications, in particular diagnosis problems, in which gradual transitions from one state to another are observed over time. In order to follow such slow changes of a system's state and to be able to anticipate the occurrence of new states, it is important to consider explicitly the temporal development of a system. In general, there can be two possibilities to deal with dynamic objects in pattern recognition: 1. To pre-process trajectories of dynamic objects by extracting some characteristic values (temporal features, trends) that can represent components of conventional feature vectors.

Clustering of dynamic objects can also be applied in The Problem ofDynamic Pattern Recognition 29 scenario analysis for complexity reduction. In order to find typical scenarios of the future development of economic characteristics for strategic planning it is reasonable to consider the characteristics' temporal behaviour instead of their final values only. Figure 8 shows three typical scenarios found after clustering 150 different scenarios [Hofmeister, 2000, p. 280-287]. Thus, due to the clustering of trajectories (scenarios) it is possible to reduce a large set of raw scenarios to a few typical scenarios, which can be used to make strategic decisions and to avoid an important loss of information in the case of considering the final values of scenarios.

On the other side, considering any point of the state space there is exactly one trajectory containing this point [Follinger, Franke, 1982]. Considering dynamic systems in control theory, great attention is dedicated to adaptive controL The primary reason for introducing this 22 General Framework ofDynamic Pattern Recognition research area was to obtain controllers that could adapt their parameters to changes in process dynamics and disturbance characteristics. [Astrom, Wittenmark, 1995] propose the following definition: 'An adaptive controller is a controller with adjustable parameters and a mechanism for adjusting the parameters' .

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