Entropy of discrete fuzzy measures
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on measures and aggregation: formal aspects and applications to clustering and decision
On the entropy of fuzzy measures
IEEE Transactions on Fuzzy Systems
An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
Information Sciences—Informatics and Computer Science: An International Journal
An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
Information Sciences: an International Journal
Entropy of capacities on lattices and set systems
Information Sciences: an International Journal
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The concept of entropy is an important part of the theory of additive measures. In this paper, a definition of entropy is introduced for general (not necessarily additive) measures as the infinum of the Shannon entropies of "subordinate" additive measures. Several properties of the general entropy are discussed and proved. Some of the properties require that the measure belongs to the class of so-called "equientropic" general measures introduced and studied in this paper. The definition of general entropy is extended to the countable case for which a sufficient condition of convergence is proved. We introduce a method of "conditional combination" of general measures and prove that in that case the general entropy possesses the "subset independence" property.