Fuzzy Hierarchical Cross-Classification of Chemical Elements Based on Ten Physical Properties

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

The hierarchical cross-clustering using the same 10 physical properties, but with data normalization, gave a very similar partition as that obtained with the 10 normalized physical characteristics. Also, the membership degrees of the elements in the fuzzy sets of the fuzzy partition were similar. 

The first partitioning in classes 1 and 2 is the same as in the nonnorma-lized classification on the basis of 10 physical, chemical, and structural characteristics, except for aluminum, which is classified with the main group elements Tm and Cu are near the boundary between classes. All the characteristics, except the boiling point, are assigned to this class only the melting point has a lower MD, being at the limit of the class. 

The next partitioning of class 1 exhibits, only small differences from the previous one Na passes to class 1.2, with the other alkaline metals, and Cd also moves to class 1.2, while A1 belongs to class 1.1. The element Tm is at the boundary between these classes. The characteristics attributed to class 1.1 are the density, the covalent radius, the chloride formation free energy, and the index of negative oxidation states. The melting point is included in class 1.2, but near the classes boundary. 

Class 1.2.1 is divided by the separation of the most electronegative elements (O and F), forming class 1.2.1.1 Ne, Ar, and Hg also have significant MDs for this class. Their characteristics are the ionization energy and the number of s, p, d, and f electrons in the outer shells, both with relatively small MDs. Among the metals of class 1.2.1.1, Cd and Hg are at the border between the two classes. 

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