Hierarchical clustering to validate fuzzy clustering

Fuzzy clustering is now extensively used for identification of (fuzzy) systems. Starting from a set of examples (input-output pairs) of a certain system, fuzzy clustering permits to disclose fuzzy rules governing the given system and also to make direct inference from new observations of the input. Our proposal in this paper attempts to present an approach to the problem of validating fuzzy clustering processes. The cluster method before the fuzzy clustering, in order to select a suitable initial structure. With this objective, several consistence measures for crisp classifications are introduced. Using these measures on the hierarchy of classifications associated to an hierarchical cluster the most suitable level is obtained. From this classification the fuzzy clustering process is started