Weighted additive information measures.
Weighted entropies
We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.
When Lagrangean and quasi-arithmetic means coincide.
Why Means in Two Arguments are Special.
Why -additive (fuzzy) measures?
The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that -additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity.