Fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on the ranking values of fuzzy sets

Fuzzy interpolative reasoning is an important research topic of sparse fuzzy rule-based systems. In recent years, some methods have been presented for dealing with fuzzy interpolative reasoning. However, the involving fuzzy sets appearing in the antecedents of fuzzy rules of the existing fuzzy interpolative reasoning methods must be normal and non-overlapping. Moreover, the reasoning conclusions of the existing fuzzy interpolative reasoning methods sometimes become abnormal fuzzy sets. In this paper, in order to overcome the drawbacks of the existing fuzzy interpolative reasoning methods, we present a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on the ranking values of fuzzy sets. The proposed fuzzy interpolative reasoning method can handle the situation of non-normal and overlapping fuzzy sets appearing in the antecedents of fuzzy rules. It can overcome the drawbacks of the existing fuzzy interpolative reasoning methods in sparse fuzzy rule-based systems.

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

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

[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]  Y. Yam,et al.  Cartesian representation for fuzzy interpolation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[5]  Yan Shi,et al.  Some considerations on Koczy's fuzzy interpolative reasoning method , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[6]  L. Kóczy,et al.  A general interpolation technique in fuzzy rule bases with arbitrary membership functions , 1996, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929).

[7]  Péter Baranyi,et al.  Comprehensive analysis of a new fuzzy rule interpolation method , 2000, IEEE Trans. Fuzzy Syst..

[8]  László T. Kóczy,et al.  Size reduction by interpolation in fuzzy rule bases , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Xia Li,et al.  A new sparse rule-based fuzzy reasoning method , 2004, Fourth International Conference on Hybrid Intelligent Systems (HIS'04).

[10]  László T. Kóczy,et al.  Representing membership functions as points in high-dimensional spaces for fuzzy interpolation and extrapolation , 2000, IEEE Trans. Fuzzy Syst..

[11]  Qiang Shen,et al.  A new fuzzy interpolative reasoning method based on center of gravity , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[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]  Qiang Shen,et al.  Scale and move transformation-based fuzzy interpolative reasoning: a revisit , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[14]  E.C.C. Tsang,et al.  Weighted fuzzy interpolative reasoning method , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[15]  D. Tikk,et al.  A new method for avoiding abnormal conclusion for /spl alpha/-cut based rule interpolation , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

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

[17]  B. Bouchon-Meunier,et al.  Interpolative reasoning with multi-variable rules , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[18]  D.S. Yeung,et al.  A fuzzy interpolative reasoning method , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

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

[20]  Qiang Shen,et al.  Fuzzy interpolative reasoning via scale and move transformations , 2006, IEEE Transactions on Fuzzy Systems.

[21]  Shyi-Ming Chen,et al.  A New Fuzzy Interpolative Reasoning Method for Sparse Fuzzy Rule-Based Systems , 2007, IEA/AIE.