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Scheme 2 | Journal of Cheminformatics

Scheme 2

From: Choquet integral-based fuzzy molecular characterizations: when global definitions are computed from the dependency among atom/bond contributions (LOVIs/LOEIs)

Scheme 2

Workflow for the calculation of a specific fuzzy two-linear descriptor based on the linear algebraic form, Euclidean metric, simple-stochastic matrix, electronegativity as property, and the Choquet integral as aggregation operator. (1) Computation of the simple-stochastic matrix for \(k = 1\) \(\left( {{}_{ss}^{{}} {\mathbb{G}}^{1} } \right)\) from the 3D coordinates matrix, by using the Euclidean metric; (2) Computation of the property vector using the electronegativity property, \(\bar{X}_{e}\); (3) Split the \({}_{ss}^{{}} {\mathbb{G}}^{1}\) matrix into “n” (number of atoms) atom-level matrices, \({}_{ss}^{{}} {\mathbb{G}}^{a,1}\), where “a” represent a specific atom; (4) Computation of the atom-level descriptors, by multiplying each \({}_{ss}^{{}} {\mathbb{G}}^{a,1}\) matrix by the \(\bar{X}_{e}\) vector, and then a linear combination is performed on each vector obtained (linear algebraic form); and (5–6) Apply the Choquet integral on the entries of the vector \(\bar{L}\), considering the L-parameter of the L-measure equal to − 0.5 (subadditivity) and 0.5 (superadditivity), respectively

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