Sequential fuzzy system identification

Abstract The problem of deriving the structure of a non-deterministic system from its behaviour is a difficult one even when that behaviour is itself well-defined. When the behaviour 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; (4) They demonstrate that sequential fuzzy data may be modelled naturally in terms of ‘possibility’ vectors.

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