Sequential fuzzy system identification

The problem of deriving the structure of a non-deterministic system from its behavior is a difficult one even when that behavior is itself well-defined. When the behavior can be described only in fuzzy terms structural inference may appear virtually impossible. However, a rigorous formulation and solution of the problem for stochastic automata has recently been given [1] and, in this paper, the results are extended to fuzzy stochastic automata and grammars. The results obtained are of interest on a number of counts, (1) They are a further step towards an integrated ´theory of uncertainty´; (2) They give new insights into problems of inductive reasoning and processes of ´precisiation´; (3) They are algorithmic and have been embodied in a computer program that can be applied to the modelling of sequential fuzzy data.