Toward quantitative definition of explanation ability of fuzzy rule-based classifiers

Explanation ability of a fuzzy rule-based classifier is its ability to explain why an input pattern is classified as a particular class in a convincing way. This ability is important especially when fuzzy rule-based classifiers are used as support systems for human users. This is because human users often want to know why the current input pattern is classified as a particular class. The explanation ability looks similar to the interpretability. They are, however, clearly different concepts. Whereas the explanation ability is directly related to the classification of each pattern, the interpretability is usually independent of classification results. The interpretability has been taken into account in multiobjective design of fuzzy rule-based classifiers. However, the explanation ability has not been used for fuzzy rule-based classifier design. This is because its quantitative definition is very difficult. In this paper, we discuss various factors that are related to quantitative definition of the explanation ability of fuzzy rule-based classifiers. Using simple numerical examples, we explain that the complexity minimization of fuzzy rule-based classifiers does not always lead to the explanation ability maximization. We also explain that the accuracy of fuzzy rules is related to the explanation ability.

[1]  Hisao Ishibuchi,et al.  Designing fuzzy rule-based classifiers that can visually explain their classification results to human users , 2008, 2008 3rd International Workshop on Genetic and Evolving Systems.

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

[3]  Hisao Ishibuchi,et al.  Design of Linguistically Interpretable Fuzzy Rule-Based Classifiers: A Short Review and Open Questions , 2011, J. Multiple Valued Log. Soft Comput..

[4]  Francisco Herrera,et al.  Multiobjective genetic fuzzy rule selection of single granularity-based fuzzy classification rules and its interaction with the lateral tuning of membership functions , 2011, Soft Comput..

[5]  Robert P. W. Duin,et al.  On the nonlinearity of pattern classifiers , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[6]  Núria Macià,et al.  In search of targeted-complexity problems , 2010, GECCO '10.

[7]  José Ramón Cano,et al.  Diagnose Effective Evolutionary Prototype Selection Using an Overlapping Measure , 2009, Int. J. Pattern Recognit. Artif. Intell..

[8]  Hisao Ishibuchi,et al.  Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining , 2004, Fuzzy Sets Syst..

[9]  Hisao Ishibuchi,et al.  Appropriate granularity specification for fuzzy classifier design by data complexity measures , 2010, 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC).

[10]  José Martínez Sotoca,et al.  An analysis of how training data complexity affects the nearest neighbor classifiers , 2007, Pattern Analysis and Applications.

[11]  H. Ishibuchi,et al.  A visual explanation system for explaining fuzzy reasoning results by fuzzy rule-based classifiers , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[12]  Magne Setnes,et al.  GA-fuzzy modeling and classification: complexity and performance , 2000, IEEE Trans. Fuzzy Syst..

[13]  Hisao Ishibuchi,et al.  Voting in fuzzy rule-based systems for pattern classification problems , 1999, Fuzzy Sets Syst..

[14]  Sameer Singh,et al.  Multiresolution Estimates of Classification Complexity , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Alessio Botta,et al.  Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index , 2008, Soft Comput..

[16]  Hisao Ishibuchi,et al.  Selecting fuzzy if-then rules for classification problems using genetic algorithms , 1995, IEEE Trans. Fuzzy Syst..

[17]  Hisao Ishibuchi,et al.  Adaptive fuzzy rule-based classification systems , 1996, IEEE Trans. Fuzzy Syst..

[18]  José Martínez Sotoca,et al.  Data Characterization for Effective Prototype Selection , 2005, IbPRIA.

[19]  Francisco Herrera,et al.  Domains of competence of fuzzy rule based classification systems with data complexity measures: A case of study using a fuzzy hybrid genetic based machine learning method , 2010, Fuzzy Sets Syst..

[20]  Jesús Alcalá-Fdez,et al.  A Proposal for the Genetic Lateral Tuning of Linguistic Fuzzy Systems and Its Interaction With Rule Selection , 2007, IEEE Transactions on Fuzzy Systems.

[21]  Hannu Koivisto,et al.  Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms , 2008, Int. J. Approx. Reason..

[22]  Yong Zhang,et al.  On generating interpretable and precise fuzzy systems based on Pareto multi-objective cooperative co-evolutionary algorithm , 2011, Appl. Soft Comput..

[23]  Francisco Herrera,et al.  Genetic fuzzy systems: taxonomy, current research trends and prospects , 2008, Evol. Intell..

[24]  Tzung-Pei Hong,et al.  Fuzzy data mining for interesting generalized association rules , 2003, Fuzzy Sets Syst..

[25]  Hisao Ishibuchi,et al.  Complexity, interpretability and explanation capability of fuzzy rule-based classifiers , 2009, 2009 IEEE International Conference on Fuzzy Systems.

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

[27]  Hisao Ishibuchi,et al.  Three-objective genetics-based machine learning for linguistic rule extraction , 2001, Inf. Sci..

[28]  Ralf Mikut,et al.  Interpretability issues in data-based learning of fuzzy systems , 2005, Fuzzy Sets Syst..

[29]  Keith E. Mathias,et al.  Crossover Operator Biases: Exploiting the Population Distribution , 1997, ICGA.

[30]  John C. Platt,et al.  Fast training of support vector machines using sequential minimal optimization, advances in kernel methods , 1999 .

[31]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[32]  Francisco Herrera,et al.  Generating single granularity-based fuzzy classification rules for multiobjective genetic fuzzy rule selection , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[33]  Tin Kam Ho,et al.  Measures of Geometrical Complexity in Classification Problems , 2006 .

[34]  Serge Guillaume,et al.  Designing fuzzy inference systems from data: An interpretability-oriented review , 2001, IEEE Trans. Fuzzy Syst..

[35]  Hisao Ishibuchi,et al.  Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems , 1997, Fuzzy Sets Syst..

[36]  Tzung-Pei Hong,et al.  Trade-off Between Computation Time and Number of Rules for Fuzzy Mining from Quantitative Data , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[37]  Ferenc Szeifert,et al.  Data-driven generation of compact, accurate, and linguistically sound fuzzy classifiers based on a decision-tree initialization , 2003, Int. J. Approx. Reason..

[38]  John Q. Gan,et al.  Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling , 2008, Fuzzy Sets Syst..

[39]  Anna Maria Fanelli,et al.  Interpretability constraints for fuzzy information granulation , 2008, Inf. Sci..

[40]  Beatrice Lazzerini,et al.  Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets , 2010, Soft Comput..

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

[42]  José M. Alonso,et al.  Looking for a good fuzzy system interpretability index: An experimental approach , 2009, Int. J. Approx. Reason..

[43]  Hisao Ishibuchi,et al.  Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning , 2007, Int. J. Approx. Reason..

[44]  Anna Maria Fanelli,et al.  Interpretability assessment of fuzzy knowledge bases: A cointension based approach , 2011, Int. J. Approx. Reason..

[45]  Tin Kam Ho,et al.  Complexity Measures of Supervised Classification Problems , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[46]  Hisao Ishibuchi,et al.  Fuzzy data mining: effect of fuzzy discretization , 2001, Proceedings 2001 IEEE International Conference on Data Mining.

[47]  Hisao Ishibuchi,et al.  Discussions on Interpretability of Fuzzy Systems using Simple Examples , 2009, IFSA/EUSFLAT Conf..

[48]  Antonio González Muñoz,et al.  Including a simplicity criterion in the selection of the best rule in a genetic fuzzy learning algorithm , 2001, Fuzzy Sets Syst..

[49]  Albert Orriols-Puig,et al.  Fuzzy knowledge representation study for incremental learning in data streams and classification problems , 2011, Soft Comput..