Multi-objective evolutionary design of fuzzy rule-based systems

This paper clearly demonstrates advantages of our evolutionary multiobjective optimization approach to the design of fuzzy rule-based classification systems over single-objective methods. The main advantage of our approach is that a large number of tradeoff (i.e., nondominated) fuzzy rule-based systems can be obtained by its single run with respect to conflicting objectives: accuracy maximization and complexity minimization. By analyzing the obtained fuzzy rule-based systems, the decision maker can understand the tradeoff between these two objectives. Such understanding is of great help when the decision maker chooses a final compromise fuzzy rule-based system. In the case of single-objective methods, only a single fuzzy rule-based system is obtained based on the pre-specified preference of the decision maker. We compare four formulations of genetic algorithm-based rule selection through computational experiments on well-known benchmark data sets. The four formulations have two objectives, their weighted sum, three objectives, and their weighted sum, respectively.

[1]  Magne Setnes,et al.  Rule-based modeling: precision and transparency , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[2]  Alberto Maria Segre,et al.  Programs for Machine Learning , 1994 .

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

[4]  F. Herrera,et al.  Accuracy Improvements in Linguistic Fuzzy Modeling , 2003 .

[5]  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..

[6]  Hisao Ishibuchi,et al.  Evolutionary Multiobjective Optimization for Generating an Ensemble of Fuzzy Rule-Based Classifiers , 2003, GECCO.

[7]  Magne Setnes,et al.  Compact and transparent fuzzy models and classifiers through iterative complexity reduction , 2001, IEEE Trans. Fuzzy Syst..

[8]  Yaochu Jin,et al.  Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement , 2000, IEEE Trans. Fuzzy Syst..

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

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

[11]  Antonio González Muñoz,et al.  SLAVE: a genetic learning system based on an iterative approach , 1999, IEEE Trans. Fuzzy Syst..

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

[13]  Heikki Mannila,et al.  Fast Discovery of Association Rules , 1996, Advances in Knowledge Discovery and Data Mining.

[14]  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..

[15]  Rudolf Kruse,et al.  A neuro-fuzzy method to learn fuzzy classification rules from data , 1997, Fuzzy Sets Syst..

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

[17]  Heikki Mannila,et al.  Verkamo: Fast Discovery of Association Rules , 1996, KDD 1996.

[18]  C. L. Karr,et al.  Fuzzy control of pH using genetic algorithms , 1993, IEEE Trans. Fuzzy Syst..

[19]  Hisao Ishibuchi,et al.  Effects of Three-Objective Genetic Rule Selection on the Generalization Ability of Fuzzy Rule-Based Systems , 2003, EMO.

[20]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[21]  Gregory Piatetsky-Shapiro,et al.  Advances in Knowledge Discovery and Data Mining , 2004, Lecture Notes in Computer Science.

[22]  Bernhard Sendhoff,et al.  On generating FC3 fuzzy rule systems from data using evolution strategies , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[23]  Shigeo Abe,et al.  Tuning of a fuzzy classifier derived from data , 1996, Int. J. Approx. Reason..

[24]  Shigeo Abe,et al.  A neural-network-based fuzzy classifier , 1995, IEEE Trans. Syst. Man Cybern..

[25]  Tapio Elomaa,et al.  General and Efficient Multisplitting of Numerical Attributes , 1999, Machine Learning.

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