Properties of Lanthanides Considered in This Study

We compared fuzzy principal component analysis (FPCA) to classical PCA methods to characterize lanthanum, the 14 lanthanides, and the other 

The 18 selected properties were atomic mass (A), density (d), atomic radius (r), first (II), second (12) and third (13) ionization energy, Pauling electronegativity (X), melting point (MP), boiling point (BP), enthalpy of fusion (HF), vaporization (ITV), atomization (HA), standard entropy (S), specific heat capacity (SHC), surface tension (ST) at the melting point, electrical resistivity (ER), heat conductivity (HC), and the formation free energy of the chloride Ends per mol of Cl (FFE)—as a characteristic of chemical reactivity. 

The electron configurations of the elements studied and of their tripositive ions are the following  

Therefore, Eu and Yb have relatively stable electron configurations for the ions, Gd and Lu should be the most stable, as well as Ce , Tb , Eu, Yb. The elements La, Gd, and Lu have configurations analogous to those of Sc and Y. 

In the case of classical PCA, the first principal component explains only 34.21% of the total variance and the second one 27.40% a two component model, for example, thus accounts for only 61.62% of the total variance see Table 5. 

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