On the Properties of Prototype-Based Fuzzy Classifiers

The use of natural language rules that are able to handle vague and, possibly, even contradicting knowledge in order to model formal dependences is an intriguing idea. Fuzzy if-then rules have been proposed as classification methods that can easily be defined and interpreted by humans or built automatically by learning algorithms. This paper gives an intuitive insight into the properties and the behavior of prototype-based fuzzy classifiers, using formal descriptions and visualization methods. This can help to avoid some common peculiarities and pitfalls in the manual or automated design of fuzzy classifiers.

[1]  Aljoscha Klose,et al.  Applying Boolean Transformations to Fuzzy Rule Bases , 1999 .

[2]  Frank Klawonn,et al.  Mathematical Analysis of Fuzzy Classifiers , 1997, IDA.

[3]  F. Klawonn,et al.  Construction of fuzzy classification systems with the Lukasiewicz-t-norm , 2000, PeachFuzz 2000. 19th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.00TH8500).

[4]  J. Casillas Interpretability issues in fuzzy modeling , 2003 .

[5]  Jeen-Shing Wang,et al.  Self-adaptive neuro-fuzzy inference systems for classification applications , 2002, IEEE Trans. Fuzzy Syst..

[6]  W Pedrycz,et al.  Solvability of fuzzy relational equations and manipulation of fuzzy data , 1986 .

[7]  Q. Shen,et al.  Regaining Comprehensibility of Approximative Fuzzy Models via the Use of Linguistic Hedges , 2003 .

[8]  Detlef Nauck,et al.  Foundations Of Neuro-Fuzzy Systems , 1997 .

[9]  A. Nurnberger,et al.  Improving naive Bayes classifiers using neuro-fuzzy learning , 1999, ICONIP'99. ANZIIS'99 & ANNES'99 & ACNN'99. 6th International Conference on Neural Information Processing. Proceedings (Cat. No.99EX378).

[10]  Julie A. Dickerson,et al.  Visualizing membership in multiple clusters after fuzzy c-means clustering , 2001, IS&T/SPIE Electronic Imaging.

[11]  E. H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Man Mach. Stud..

[12]  Siegfried Gottwald Characterizations of the Solvability of Fuzzy Equations , 1986, J. Inf. Process. Cybern..

[13]  Ludmila I. Kuncheva,et al.  Fuzzy Classifier Design , 2000, Studies in Fuzziness and Soft Computing.

[14]  Hisao Ishibuchi,et al.  Effect of rule weights in fuzzy rule-based classification systems , 2001, IEEE Trans. Fuzzy Syst..

[15]  B. Jiang Visualisation of Fuzzy Boundaries of Geographic Objects , 1998 .

[16]  Julie A. Dickerson,et al.  Creating metabolic and regulatory network models using fuzzy cognitive maps , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[17]  Hisao Ishibuchi,et al.  Rule weight specification in fuzzy rule-based classification systems , 2005, IEEE Transactions on Fuzzy Systems.

[18]  Hisao Ishibuchi,et al.  Classification and modeling with linguistic information granules - advanced approaches to linguistic data mining , 2004, Advanced information processing.

[19]  Uzay Kaymak,et al.  Fuzzy classification using probability-based rule weighting , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[20]  Frank Klawonn,et al.  Equality Relations as a Basis for Fuzzy Control , 1993 .

[21]  Rudolf Kruse,et al.  Data mining with neuro-fuzzy models , 2001 .

[22]  F. Herrera,et al.  A proposal on reasoning methods in fuzzy rule-based classification systems , 1999 .

[23]  Rudolf Kruse,et al.  A New Approach to Semantic Aspects of Possibilistic Reasoning , 1993, ECSQARU.

[24]  Ross Brown,et al.  Analysis of visualisation requirements for fuzzy systems , 2003, GRAPHITE '03.

[25]  S. Gottwald,et al.  Fuzzy control and fuzzy relation equations. A unified view as interpolation problem , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

[26]  A. Nurnberger,et al.  Discussing cluster shapes of fuzzy classifiers , 1999, 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397).

[27]  Michael R. Berthold,et al.  Visualizing high dimensional fuzzy rules , 2000, PeachFuzz 2000. 19th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.00TH8500).

[28]  Rudolf Kruse,et al.  How the learning of rule weights affects the interpretability of fuzzy systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[29]  A. Nurnberger,et al.  Analyzing borders between partially contradicting fuzzy classification rules , 2000, PeachFuzz 2000. 19th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.00TH8500).

[30]  Lawrence O. Hall,et al.  Visualizing fuzzy points in parallel coordinates , 2003, IEEE Trans. Fuzzy Syst..

[31]  H. Ishibuchi Genetic fuzzy systems: evolutionary tuning and learning of fuzzy knowledge bases , 2004 .

[32]  Detlef D. Nauck,et al.  Adaptive Rule Weights in Neuro-Fuzzy Systems , 2000, Neural Computing & Applications.

[33]  Frank Klawonn,et al.  Fuzzy Max-Min Classifiers Decide locally on the Basis of Two Attributes , 1999 .

[34]  Frank Klawonn,et al.  Foundations of fuzzy systems , 1994 .

[35]  Ludmila I. Kuncheva,et al.  How good are fuzzy If-Then classifiers? , 2000, IEEE Trans. Syst. Man Cybern. Part B.

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

[37]  Ron Kohavi,et al.  Supervised and Unsupervised Discretization of Continuous Features , 1995, ICML.

[38]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.