ENTROPY OF FUZZY DYNAMICAL-SYSTEMS

Entropy of a finite fuzzy partition had been defined (Dumitrescu, 1983, 1993) using an additive fuzzy measure (Butnariu, 1983). In this paper we define the independence of fuzzy partitions with respect to a fuzzy measure. Some properties concerning the entropy of independent fuzzy partitions are proved. This concept of independence is also relevant for the study of the entropy of a fuzzy process (Dumitrescu, 1993). We prove some new results concerning the entropy of a fuzzy process. The fuzzy measure-preserving transformations (Dumitrescu, 1993) may be related with the fuzzy ergodic theory. The main problem in ergodic theory is to build the isomorphism invariants. Kolmogorov's (1958) transformation entropy is such an invariant. In this paper we define the entropy of a fuzzy dynamical system. We prove that this entropy is an isomorphism invariant.