A practical inference method with several implicative gradual rules and a fuzzy input: one and two dimensions

A general approach to practical inference with gradual implicative rules and fuzzy inputs is presented. Gradual rules represent constraints restricting outputs of a fuzzy system for each input. They are tailored for interpolative reasoning. Our approach to inference relies on the use of inferential independence. It is based on fuzzy output computation under an interval-valued input. A double decomposition of fuzzy inputs is done in terms of alpha-cuts and in terms of a partitioning of these cuts according to areas where only a few rules apply. The case of one and two dimensional inputs is considered.

[1]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[2]  Roger Martin-Clouaire,et al.  Semantics and computation of the generalized modus ponens: The long paper , 1989, Int. J. Approx. Reason..

[3]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[4]  E. H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Man Mach. Stud..

[5]  Michel Grabisch,et al.  Gradual rules and the approximation of control laws , 1995 .

[6]  Henri Prade,et al.  What are fuzzy rules and how to use them , 1996, Fuzzy Sets Syst..

[7]  D. Dubois,et al.  Efficient inference procedures with fuzzy inputs , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[8]  Didier Dubois,et al.  Checking the coherence and redundancy of fuzzy knowledge bases , 1997, IEEE Trans. Fuzzy Syst..

[9]  Laurent Ughetto.  Inferential Independence of Fuzzy Rules , 1998, ECAI.

[10]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[11]  Didier Dubois,et al.  Implicative and conjunctive fuzzy rules - A tool for reasoning from knowledge and examples , 1999, AAAI/IAAI.

[12]  Aly A. Fahmy,et al.  On generalized modus ponens with multiple rules and a residuated implication , 2002, Fuzzy Sets Syst..

[13]  Didier Dubois,et al.  Imprecise specification of ill-known functions using gradual rules , 2004, Int. J. Approx. Reason..

[14]  Nehad N. Morsi,et al.  A small set of axioms for residuated logic , 2005, Inf. Sci..

[15]  Didier Dubois,et al.  Practical use of fuzzy implicative gradual rules in knowledge representation and comparison with Mamdani rules , 2005, EUSFLAT Conf..