Hierarchical Fuzzy Classification of Chemical Elements Based on Ten Physical Properties

HIERARCHICAL FUZZY CLASSIFICATION OF CHEMICAL ELEMENTS BASED ON TEN PHYSICAL PROPERTIES 

In order to use the methods presented above to classify the chemical elements, the problem we are first faced with is to decide the characteristics this classification is built upon. We started with 10 physical properties relative atomic mass, A (1), density, p (2), melting point, Tf (3), boiling point, T, (4), Pauling electronegativity, x (5), enthalpy of vaporization, AH (6) and fusion, AHf (7), specific heat capacity, Cs (8), first ionization energy, E (9), and covalent radius, r (10). 

The last subdivision distinguishes a class (1.2.1.1) containing the alkali metals (membership degrees—MDs—of 0.60) and Se and Cd. The last one has a smaller MD (0.43), only a little more than its MD for the class 1.1.2. 

Class 1.1.2 includes, among others, Zn, which has a MD of 0.22 for the class 1.2.1. The elements of the class 1.2.1.1 are similar mostly with respect to their boiling points ( 700-750°C), while the elements of class 1.2.1.2 have lower T],. Class 1.2.1.2 includes solid nonmetals (P, S, I) and Hg, elements with very similar ionization energies (240-250 kcal/mol). Nonmembers of this class. As and Br, have MDs of 0.15-0.16 for it. It is interesting that grouped together here are mercury and sulfur, elements that the alchemists thought to be at the source of all matter. 

The other class (1.1.1) includes elements from group 13 (IIIA) (Ga, In), group 14 (IVA) (Sn, Pb), silver, and the lanthanides Sm and Tm. It is a rather heterogeneous class, its elements having quite different properties and relatively small MDs, from 0.54 (Ga) to 0.26 (Tm). Also, related to this class are Ba, Bi, and Mn. 

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