A comparative view of interpolation methods between sparse fuzzy rules

Several approaches have been proposed in the last few years for interpolating between sparse fuzzy rules. These proposed methods yield very different results in some cases. This is due to different views on the basic principles underlying the interpolation process. In particular, the problem can be viewed as the one of completing a partially-known mapping associating fuzzy sets with other fuzzy sets, or the one of extending the interpolation mechanism that is applicable to classical functions to fuzzily-specified ones. This paper clarifies the differences between the various methods.

[1]  László T. Kóczy,et al.  Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases , 1993, Inf. Sci..

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

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

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

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

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

[7]  C. Marsala,et al.  Several forms of fuzzy analogical reasoning , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[8]  Shyi-Ming Chen,et al.  A new interpolative reasoning method in sparse rule-based systems , 1998, Fuzzy Sets Syst..

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

[10]  B. Bouchon-Meunier,et al.  Analogy and Fuzzy Interpolation in the case of Sparse Rules , 1999 .

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

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

[13]  Henri Prade,et al.  Fuzzy interpolation by convex completion of sparse rule bases , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[14]  L.T. Koczy,et al.  /spl alpha/-cut interpolation technique in the space of regular conclusion , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).