Fuzzy Probability Spaces, Fuzzy Dynamical Systems, and Entropy Dagmar Markechova

When planning experiments it is very important to know the amount of information that we obtain from their realization. It is known that a measure of information is entropy. A usual mathematical model of experiment in the classical information theory is a measurable partition. Partitions are standardly defined in the context of classical sets. It has appeared however, that for a solution of real problems are partitions defined by means of the concept of fuzzy sets more appropriate. The book contains a review of results of author related to the study of entropy in the fuzzy case. These results represent fuzzy generalizations of some concepts from the classical probability theory. The entropy of fuzzy partition can be considered as a measure of information of experiment, the results of which are fuzzy events. The concept of entropy of a fuzzy partition is exploited to define the entropy of fuzzy dynamical systems. Subsequently an ergodic theory for these systems is proposed. Presented... Это и многое другое вы найдете в книге Fuzzy Probability Spaces, Fuzzy Dynamical Systems, and Entropy (Dagmar Markechova)