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.

[1]  B. Gaines.  Approximate identification of automata , 1975 .

[2]  Joseph A. Goguen,et al.  Concept Representation in Natural and Artificial Languages: Axioms, Extensions and Applications for Fuzzy Sets , 1974, Int. J. Man Mach. Stud..

[3]  H. Jeffreys.  Logical Foundations of Probability , 1952, Nature.

[4]  Jerome A. Feldman,et al.  Some Decidability Results on Grammatical Inference and Complexity , 1972, Inf. Control..

[5]  Brian R. Gaines,et al.  Linear and Nonlinear Models of the Human Controller , 1969 .

[6]  Brian R. Gaines,et al.  The Fuzzy Decade: A Bibliography of Fuzzy Systems and Closely Related Topics , 1977, Int. J. Man Mach. Stud..

[7]  Brian R. Gaines,et al.  On the Complexity of Causal Models , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  The Confirmation Machine , 1970 .

[9]  J. Pfanzagl,et al.  Remarks on the measurement of subjective probability and information , 1967 .

[10]  Manuel Blum,et al.  A Machine-Independent Theory of the Complexity of Recursive Functions , 1967, JACM.

[11]  G. Gregory,et al.  Probability, Induction and Statistics , 1974 .

[12]  A. Nerode,et al.  Linear automaton transformations , 1958 .

[13]  B. R. Gainfs.  Foundations of fuzzy reasoning , 1976 .

[14]  Bruno de Finetti,et al.  Probability, induction and statistics , 1972 .

[15]  Judea Pearl,et al.  An economic basis for certain methods of evaluating probabilistic forecasts , 1978 .

[16]  Robert Moll,et al.  An Operator Embedding Theorem for Complexity Classes of Recursive Functions , 1976, Theor. Comput. Sci..

[17]  A. Church.  Edward F. Moore. Gedanken-experiments on sequential machines. Automata studies , edited by C. E. Shannon and J. McCarthy, Annals of Mathematics studies no. 34, litho-printed, Princeton University Press, Princeton1956, pp. 129–153. , 1958, Journal of Symbolic Logic.

[18]  B. Gaines,et al.  THE LOGIC OF AUTOMATA , 1975 .

[19]  James Jay Horning,et al.  A study of grammatical inference , 1969 .

[20]  L. J. Savage.  Elicitation of Personal Probabilities and Expectations , 1971 .

[21]  Fred Joseph Maryanski.  Inference of probabilistic grammars. , 1974 .

[22]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part II , 1964, Inf. Control..

[23]  B. Gaines.  SYSTEM IDENTIFICATION, APPROXIMATION AND COMPLEXITY , 1977 .

[24]  P. J. B. Slater,et al.  Describing Sequences of Behavior , 1973 .

[25]  Taylor L. Booth,et al.  Grammatical Inference: Introduction and Survey - Part I , 1975, IEEE Trans. Syst. Man Cybern..

[26]  B. Zeigler.  SIMULATION BASED STRUCTURAL COMPLEXITY OF MODELS , 1975 .

[27]  Ray J. Solomonoff,et al.  A new method for discovering the grammars of phrase structure languages , 1959, IFIP Congress.

[28]  R. M. Wharton.  Approximate Language Identification , 1974, Inf. Control..

[29]  Edward F. Moore,et al.  Gedanken-Experiments on Sequential Machines , 1956 .

[30]  R. M. Wharton.  Grammar Enumeration and Inference , 1977, Inf. Control..

[31]  Namio Honda,et al.  RECOGNITION OF FUZZY LANGUAGES , 1975 .

[32]  Brian R. Gaines,et al.  Behaviour/structure transformations under uncertainty , 1976 .

[33]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[34]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part I , 1964, Inf. Control..