Several types of entropy of fuzzy variables or fuzzy sets have been given in the literature in order to measure the degree of uncertainty. In order to measure the degree of uncertainty of fuzzy vectors, a new definition of entropy of fuzzy vectors is proposed. Some properties are then investigated and the relations between the entropy of fuzzy variables and fuzzy vectors are discussed.

Set-valued information systems are generalized models of single-valued information systems. In this paper, we propose two new relations for set-valued information systems. Based on these two relations, the concepts of knowledge information entropy, knowledge rough entropy, knowledge granulation and knowledge granularity measure are defined in set-valued information systems, and some properties ...

In this paper we present a new entropy measure to grow decision trees. This measure has the characteristic to be asymmetric, allowing the user to grow trees which better correspond to his expectation in terms of recall and precision on each class. Then we propose decision rules adapted to such trees. Experiments have been realized on real medical data from breast cancer screening units.

A new measure for assessing camera focusing via recorded image is presented in this paper. The proposed measure bases on calculating entropy in image frequency domain, and we call it frequency domain entropy or FDE. First an intuitive explanation of measure is presented, and next tests for some classical properties that such measure should meet are conducted and commented.

We prove that for a certain class of Z shifts of nite type with positive topological entropy there is always an invariant measure with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.