Fuzzy-valued Markov processes and their properties

If F denotes a set-valued random variable, we establish the relations among a-algebras induced by F. By the set-valued Markov process, we define the fuzzy-valued Markov process, and give its Castaing representation. Finally, we obtain a few of equivalent conditions of set-valued Markov processes and fuzzy-valued Markov processes, which are similar to classical ones of Markov processes. (C) 1997 Elsevier Science B.V.