قارن الطرق

	تباعد كولباك-لايبلر	مسافة هيلينجر
المجال	اتخاذ القرار	اتخاذ القرار
العائلة	MCDM	MCDM
سنة النشأة	1951	1909
صاحب الطريقة	Solomon Kullback and Richard Leibler	Ernst Hellinger
النوع	Asymmetric probability distribution dissimilarity	Symmetric metric for probability distributions
المصدر التأسيسي	Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22(1), 79-86.	Hellinger, E. (1909). Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Journal für die Reine und Angewandte Mathematik, 136, 210-271.
الأسماء البديلة	KL divergence, relative entropy, information divergence	Bhattacharyya distance, Hellinger metric
ذات صلة	2	2
الملخص	Kullback-Leibler divergence, also called relative entropy or information divergence, measures the asymmetric difference between two probability distributions. Introduced by Solomon Kullback and Richard Leibler in 1951, this information-theoretic measure quantifies how one probability distribution diverges from a reference distribution, ranging from 0 (identical distributions) to infinity. It is foundational in information theory, machine learning, and decision-making with probabilistic frameworks.	Hellinger distance is a symmetric, bounded metric that measures the difference between two probability distributions. Rooted in the work of Ernst Hellinger (1909) and later formalized in statistical divergence by Anil Bhattacharyya (1946), this distance ranges from 0 (identical distributions) to 1. It is a true metric satisfying all mathematical distance properties and is particularly well-suited for comparing probability distributions in a symmetric, numerically stable manner.