Taxonomic evidence and robustness of the classification applying intelligent data mining.

Numerical Taxonomy aims to group in families, using so-called structure analysis of operational taxonomic units (OTUs or taxons or taxa). Clusters that constitute families with a new criterion, is the purpose of this series of papers. Structural analysis, based on phenotypic characteristics, exhibits the relationships, in terms of degrees of similarity, through the computation of the Matrix of Similarity, applying the technique of integration dynamic of independent domains, of the semantics of the Dynamic Relational Database Model. The main contribution is to introduce the concept of spectrum of the OTUs, based in the states of their characters. The concept of families' spectra emerges, if the principles of superposition and interference, and the Invariants (centroid, variance and radius) determined by the maximum of the Bienayme-Tchebycheff relation, are applied to the spectra of the OTUs. Using in successive form an updated database through the increase of the cardinal of the tuples, and as the resulting families are the same, we ascertain the robustness of the method. Through Intelligent Data Mining, we focused our interest on the Quinlan algorithms, applied in classification problems with the Gain of Entropy, we contrast the Computational Taxonomy, obtaining a new criterion of the robustness of the method.