ENTROPY AND MUTUAL INFORMATION OF EXPERIMENTS IN THE FUZZY CASE

In my previous papers ([181, [19]) the entropy of fuzzy partitions had been defined. The concept of the entropy of a fuzzy partition was used to define the entropy of a fuzzy dynamical system and to propose an ergodic theory for fuzzy dynamical systems ([19], [201). In this paper, using my previous results related to the entropy of fuzzy partitions, a measure of average mutual information of fuzzy partitions is defined. Some properties concerning this measure are proved. It is shown that the entropy of fuzzy partitions can be considered as a special case of their mutual information. We obtain that subadditivity and additivity of entropy of fuzzy partitions are simple consequences of these properties. The suggested measures can be applied whenever it is need to know the amount of information that we obtain by realization of experiments, the results of which are fuzzy events.