No Access

FUZZY OPERATOR TREES FOR MODELING RATING FUNCTIONS

YU YI

Philipps-Universität Marburg, Mathematics and Computer Science Department, 35032 Marburg, Germany

Search for more papers by this author

THOMAS FOBER

Philipps-Universität Marburg, Mathematics and Computer Science Department, 35032 Marburg, Germany

Search for more papers by this author

, and

EYKE HÜLLERMEIER

Philipps-Universität Marburg, Mathematics and Computer Science Department, 35032 Marburg, Germany

Search for more papers by this author

https://doi.org/10.1142/S1469026809002679Cited by:20 (Source: Crossref)

Abstract

We introduce a new method for modeling rating (utility) functions which employs techniques from fuzzy set theory. The main idea is to build a hierarchical model, called a fuzzy operator tree (FOT), by recursively decomposing a rating criterion into sub-criteria, and to combine the evaluations of these sub-criteria by means of suitable aggregation operators. Apart from the model conception itself, we propose an evolutionary method for model calibration that fits the parameters of an FOT to exemplary ratings. The possibility to adapt an FOT to a given set of data makes the approach also interesting from a machine learning point of view. The performance of the approach is evaluated by means of a suitable experimental study.

Keywords:

Remember to check out the Most Cited Articles!
Check out these titles in artificial intelligence!

References

T. Bartz-Beielstein , Experimental Research in Evolutionary Computation — The New Experimentalism , Natural Computing Series ( Springer Verlag , Heidelberg, Berlin , 2006 ) . Google Scholar
H. G. Beyer and H. P. Schwefel, J. Natural Computing 1, (2002). Google Scholar
M. Bohanec and V. Rajkovic, Knowledge acquisition and explanation for multi-attribute decision making, 8th Int. Workshop Expert Systems and their Applications1 (1988) pp. 59–78. Google Scholar
E. U. Choo and W. C. Wedley, J. Oper. Res. Soc. 36, 983 (1985), DOI: 10.1057/jors.1985.177. Crossref, Google Scholar
W. W. Cohen, Fast effective rule induction, Proc. 12th Int. Conf. Machine Learning (1995) pp. 115–123. Google Scholar
J. S. Dyer, Manag. Sci. 36, 249 (1990), DOI: 10.1287/mnsc.36.3.249. Crossref, Google Scholar
D. P. Filev and R. R. Yager, Fuzzy Sets Syst. 94, 157 (1998), DOI: 10.1016/S0165-0114(96)00254-0. Crossref, Google Scholar
J. Fodor and M. Roubens , Fuzzy Preference Modelling and Multicriteria Decision Support ( Kluwer Academic Publishers , Dordrecht, The Netherlands , 1994 ) . Crossref, Google Scholar
J. Fodor and R. R. Yager, Fundamentals of Fuzzy Sets, eds. D. Dubois and H. Prade (Kluwer Academic Publishers, Boston/London/Dordrecht, 2002) pp. 125–194. Google Scholar
R. Fuller and P. Majlender, Fuzzy Sets Syst. 124, 53 (2001), DOI: 10.1016/S0165-0114(01)00007-0. Crossref, Google Scholar
R. Fuller and P. Majlender, Fuzzy Sets Syst. 136, 203 (2003), DOI: 10.1016/S0165-0114(02)00267-1. Crossref, Google Scholar
J. Fürnkranz and M. Kubat (eds.) , Machines That Learn to Play Games , Advances in Computation: Theory and Practice ( Nova Biomedical , 2002 ) . Google Scholar
P. Gärdenfors and N. E. Sahlin (eds.) , Decision, Probability, and Utility ( Cambridge University Press , Cambridge , 1988 ) . Crossref, Google Scholar
K. Ishii and M. Sugeno, Int. J. Man Mach. Stud. 22, 19 (1985), DOI: 10.1016/S0020-7373(85)80075-4. Crossref, Google Scholar
J. S. R. Jang, IEEE Trans. Syst. Man Cybern. 23, 665 (1993), DOI: 10.1109/21.256541. Crossref, Google Scholar
E. P. Klement , R. Mesiar and E. Pap , Triangular Norms ( Kluwer Academic Publishers , 2002 ) . Google Scholar
G. Lakoff, J. Phil. Logic 2, 458 (1973), DOI: 10.1007/BF00262952. Google Scholar
J. L. Marichal and M. Roubens, Eur. J. Oper. Res. 124, 641 (2000), DOI: 10.1016/S0377-2217(99)00182-4. Crossref, Google Scholar
P. Meyer and M. Roubens, Multiple Criteria Decision Analysis: State of the Art Surveys, eds. J. Figueira, S. Greco and M. Ehrgott (Springer-Verlag, 2005) pp. 471–506. Crossref, Google Scholar
D. Nauck , F. Klawonn and R. Kruse , Foundations of Neuro-Fuzzy Systems ( Chichester, UK , 1997 ) . Google Scholar
J. Von Neumann and O. Morgenstern , Theory of Games and Economic Behavior ( John Wiley and Sons , USA , 1953 ) . Google Scholar
J. R. Quinlan , C4.5: Programs for Machine Learning ( Morgan Kaufmann , San Mateo, CA , 1993 ) . Google Scholar
J. D. M. Rennie and N. Srebro , Loss functions for preference levels: Regression with discrete ordered labels , Proc. IJCAI Multidisciplinary Workshop on Advances in Preference Handling ( 2005 ) . Google Scholar
P. Resnik and H. R. Varian, Comm. ACM 40, (1997). Google Scholar
T. L. Saaty , The Analytic Hierarchy Process ( McGraw-Hill , New York , 1980 ) . Google Scholar
B. Schweizer and A. Sklar , Probabilistic Metric Spaces ( North-Holland , New York , 1983 ) . Google Scholar
D. Sklansky , Hold'em Poker: A Complete Guide to Playing the Game ( Two Plus Two , 1996 ) . Google Scholar
D. Sklansky and M. Malmuth , Hold 'em Poker for Advanced Players , 3rd edn. ( Non Basic Stock Line , 1999 ) . Google Scholar
V. Torra, Mathware and Soft Computing 6, 249 (1999). Google Scholar
V. Torra, IEEE Trans. Fuzzy Syst. 12, 652 (2004), DOI: 10.1109/TFUZZ.2004.834814. Crossref, Google Scholar
Z. Wanget al., Int. J. Approximate Reasoning 25, 71 (2000), DOI: 10.1016/S0888-613X(00)00048-7. Crossref, Google Scholar
I. H. Witten and E. Frank , Data Mining: Practical Machine Learning Tools and Techniques , 2nd edn. ( Morgan Kaufmann , San Francisco , 2005 ) . Google Scholar
R. R. Yager, IEEE Trans. Syst. Man Cybern. 18, 183 (1988), DOI: 10.1109/21.87068. Crossref, Google Scholar
L. A. Zadeh, J. Cybern. 2, 4 (1972), DOI: 10.1080/01969727208542910. Crossref, Google Scholar