A principled approach to fuzzy rule base interpolation using similarity relations

In this work we consider a very general principle for fuzzy rule interpolation methods based on an interpretation of the generalized modus ponens rule in terms of closeness relations. Then we present two particular instances of the general principle when the closeness relations are defined from parametric families of similarity fuzzy relations on the input and output spaces. The case of multiple input variables is also considered.

[1]  László T. Kóczy,et al.  Approximate reasoning by linear rule interpolation and general approximation , 1993, Int. J. Approx. Reason..

[2]  Jonathan Lawry,et al.  FUZZ-IEEE 2000 , 2000 .

[3]  Yan Shi,et al.  An improvement to Kóczy and Hirota's interpolative reasoning in sparse fuzzy rule bases , 1996, Int. J. Approx. Reason..

[4]  Bernadette Bouchon-Meunier,et al.  Similarity-based fuzzy interpolation method , 2004 .

[5]  Dionís Boixader,et al.  Extensionality based approximate reasoning , 1998, Int. J. Approx. Reason..

[6]  C. Marsala,et al.  Interpolative reasoning based on graduality , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[7]  Enrique H. Ruspini,et al.  On the semantics of fuzzy logic , 1991, Int. J. Approx. Reason..

[8]  Lluís Godo,et al.  Dealing with covering problems in fuzzy rule systems by similarity-based extrapolation , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[9]  H. Prade,et al.  A comparative view of interpolation methods between sparse fuzzy rules , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[10]  Lluis Godo,et al.  Restoring Consistency in Systems of Fuzzy Gradual Rules Using Similarity Relations , 2002, SBIA.

[11]  D. Dubois,et al.  ON FUZZY INTERPOLATION , 1999 .

[12]  Masaharu Mizumoto,et al.  Reasoning conditions on Kóczy's interpolative reasoning method in sparse fuzzy rule bases , 1995, Fuzzy Sets Syst..

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