Fuzzy rule interpolation for multidimensional input spaces with applications: a case study

Fuzzy rule based systems have been very popular in many engineering applications. However, when generating fuzzy rules from the available information, this may result in a sparse fuzzy rule base. Fuzzy rule interpolation techniques have been established to solve the problems encountered in processing sparse fuzzy rule bases. In most engineering applications, the use of more than one input variable is common, however, the majority of the fuzzy rule interpolation techniques only present detailed analysis to one input variable case. This paper investigates characteristics of two selected fuzzy rule interpolation techniques for multidimensional input spaces and proposes an improved fuzzy rule interpolation technique to handle multidimensional input spaces. The three methods are compared by means of application examples in the field of petroleum engineering and mineral processing. The results show that the proposed fuzzy rule interpolation technique for multidimensional input spaces can be used in engineering applications.

[1]  László T. Kóczy,et al.  Fuzzy rule base interpolation based on semantic revision , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

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

[3]  George Asquith,et al.  Basic Well Log Analysis for Geologists , 1982 .

[4]  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).

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

[6]  I. Burhan Türksen,et al.  An approximate analogical reasoning approach based on similarity measures , 1988, IEEE Trans. Syst. Man Cybern..

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

[8]  Sándor Jenei,et al.  Interpolation and extrapolation of fuzzy quantities revisited – an axiomatic approach , 2001, Soft Comput..

[9]  K. Hirota,et al.  Ordering, distance and closeness of fuzzy sets , 1993 .

[10]  Yan Shi,et al.  Reasoning conditions on Kóczy's interpolative reasoning method in sparse fuzzy rule bases. Part II , 1997, Fuzzy Sets Syst..

[11]  Crain,et al.  Log analysis handbook , 1986 .

[12]  D. Tikk,et al.  Stability of a new interpolation method , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[13]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  Yan Shi,et al.  A note on reasoning conditions of Kóczy's interpolative reasoning method , 1998, Fuzzy Sets Syst..

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

[16]  Sándor Jenei,et al.  Interpolation and extrapolation of fuzzy quantities – the multiple-dimensional case , 2002, Soft Comput..

[17]  Didier Dubois,et al.  Gradual inference rules in approximate reasoning , 1992, Inf. Sci..

[18]  László T. Kóczy,et al.  Fuzzy Rule Interpolation by the Conservation of Relative Fuzziness , 2000, J. Adv. Comput. Intell. Intell. Informatics.

[19]  Liya Ding,et al.  METHODS OF REVISION PRINCIPLE FOR APPROXIMATE REASONING , 1999 .

[20]  M. Mukaidono,et al.  Fuzzy resolution principle , 1988, [1988] Proceedings. The Eighteenth International Symposium on Multiple-Valued Logic.

[21]  László T. Kóczy,et al.  A generalized concept for fuzzy rule interpolation , 2004, IEEE Transactions on Fuzzy Systems.

[22]  Piero P. Bonissone,et al.  Automated fuzzy knowledge base generation and tuning , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[23]  Peter Baranyi,et al.  Generalisation of a Rule Interpolation Method Resulting Always in Acceptable Conclusion , 2000 .

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

[25]  M. Rider,et al.  The Geological Interpretation of Well Logs , 1986 .

[26]  Kok Wai Wong,et al.  A self-generating fuzzy rules inference system for petrophysical properties prediction , 1997, 1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335).