A definition for the entropy of fuzzy measures defined on set systems is proposed. The underlying set is not necessarily the whole power set, but satisfy a condition of regularity. This definition encompasses the classical definition of Shannon for probability measures, as well as the definition of Marichal et al.
Abstract: Fuzzy measures provides a structure for modeling the knowledge available about variables whose values are unknown and uncertain.
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In this work, we introduce a quantification of the amount of uncertainty associated with a fuzzy measure in the spirit of the Shannon entropy [4]. With this ...
In this work, we provide a measure of entropy that can be used to calculate the amount of uncertainty associated with a fuzzy measure.
A function g from 3 to [0, l] is said to be a fuzzy measure [7], if and only if the following conditions hold: (i) s(0) = 0, ,9(X) = 1,. (ii) if A, BE 2 ...
Using fuzzy measures and fuzzy integrals, a theorem is presented, which gives a sufficient condition for the existence of entropy measures under a list of ...
On the entropy of λ-additive fuzzy measures - ScienceDirect.com
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7. M Sugeno. Theory of fuzzy integrals and its applications. Thesis, Tokyo Institute of Technology (1974).
Oct 22, 2024 · In this paper we deal with the entropy of fuzzy sets. We first review several defined entropies of fuzzy sets and then propose a new one.
Feb 7, 2022 · This paper defines the fuzzy entropy that satisfies the properties based on the axiomatized definition of fuzzy entropy.
Entropy measures of a fuzzy set defined on a denumerable support are studied. A necessary and sufficient condition for the convergence of the logarithmic ...