Fuzzy hierarchical cross-classification

The fuzzy hierarchical cross-classification algorithm was used to classify eight mud samples. Each sample was characterized as a vector with 23 components representing chemical analysis. The fuzzy partition tree obtained by using simultaneous classification of muds and their characteristics is shown in Fig. 8. There are six final fuzzy classes in this hierarchy. The classical partition corresponding to the final fuzzy classes of the muds is 111 Krinides Lisbori Ai 2z> Argilla Solare A 2i> Pnkolimni ... 

FUZZY HIERARCHICAL CROSS-CLASSIFICATION OF CHEMICAL ELEMENTS BASED ON TEN PHYSICAL PROPERTIES... 

We are now able to state the hierarchical cross-classification procedure. The root node of the partition tree corresponds to the pair (X,Y). At the first level a fuzzy partition P = A, A2 of X is computed. Let Y = y, y, ...,y be the characteristics set induced by A and A2- We then have... 

The fuzzy cross-classification algorithm produces both a fuzzy partition and a fuzzy partition of characteristics compatible with the former. The advantages of this algorithm include the ability to observe not only the fuzzy classes obtained and their relationship, but also the characteristics corresponding to each final class of objects. Each object class may be well described using the corresponding characteristics. These are the characteristics that have contributed to the separation of the respective fuzzy class. Fuzzy divisive hierarchical cross-classification of therapeutic muds based on their physicochemical characteristics allowed an objective interpretation of their origin and maturation and helped in their classification. It also permitted quantitative and qualitative identification of the compo-... 

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