Benchmark Based Comparison of Two Fuzzy Rule Base Optimization Methods

Parameter optimization is a key step during the creation of a fuzzy rule based system. It also has a determining effect on the resulting system’s performance. In this chapter, we examine the performance of several fuzzy systems obtained by applying two different optimization methods. In each case we start from an initial rule base that is created using fuzzy c-means clustering of a sample data set. The first examined optimization approach is the cross-entropy method while the second one is a hill-climbing based technique. We compare them in case of four benchmarking problems.

[1]  Weina Wang,et al.  On fuzzy cluster validity indices , 2007, Fuzzy Sets Syst..

[2]  Igor Skrjanc,et al.  Identification of dynamical systems with a robust interval fuzzy model , 2005, Autom..

[3]  Z.C. Johanyak,et al.  Sparse Fuzzy Model Identification Matlab Toolox - RuleMaker Toolbox , 2008, 2008 IEEE International Conference on Computational Cybernetics.

[4]  Shyi-Ming Chen,et al.  Fuzzy Interpolative Reasoning for Sparse Fuzzy Rule-Based Systems Based on ${\bm \alpha}$-Cuts and Transformations Techniques , 2008, IEEE Transactions on Fuzzy Systems.

[5]  Zsolt Csaba Johanyák,et al.  Fuzzy Rule Interpolation based on Subsethood Values , 2010, 2010 IEEE International Conference on Systems, Man and Cybernetics.

[6]  Shie Mannor,et al.  Basis Function Adaptation in Temporal Difference Reinforcement Learning , 2005, Ann. Oper. Res..

[7]  L. Kovacs Rule approximation in metric spaces , 2010, 2010 IEEE 8th International Symposium on Applied Machine Intelligence and Informatics (SAMI).

[8]  Szilveszter Kovács,et al.  Extending the Fuzzy Rule Interpolation "FIVE" by Fuzzy Observation , 2006 .

[9]  D. Hladek,et al.  Hierarchical fuzzy inference system for robotic pursuit evasion task , 2008, 2008 6th International Symposium on Applied Machine Intelligence and Informatics.

[10]  José Carlos M. Pires,et al.  Prediction of Ground-level Ozone Concentrations through Statistical Models , 2016, IJCCI.

[11]  Dirk P. Kroese,et al.  Sequence alignment by rare event simulation , 2002, Proceedings of the Winter Simulation Conference.

[12]  S. Kovács,et al.  Fuzzy Rule Interpolation by the Least Squares Method , 2006 .

[13]  Zhiheng Huang,et al.  Fuzzy interpolation with generalized representative values , 2004 .

[14]  Bjarne E. Helvik,et al.  Using the Cross-Entropy Method to Guide/Govern Mobile Agent's Path Finding in Networks , 2001, MATA.

[15]  Dirk P. Kroese,et al.  Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment , 2005, Ann. Oper. Res..

[16]  E. Horlait Mobile Agents for Telecommunication Applications , 2003, Lecture Notes in Computer Science.

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

[18]  Stefan Preitl,et al.  Stability analysis and development of a class of fuzzy control systems , 2000 .

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

[20]  Szilveszter Kovács,et al.  Incremental Rule Base Creation with Fuzzy Rule Interpolation-Based Q-Learning , 2010 .

[21]  Avraham Shtub,et al.  Managing Stochastic, Finite Capacity, Multi-Project Systems through the Cross-Entropy Methodology , 2005, Ann. Oper. Res..

[22]  Olga Papp,et al.  Comparative analysis of two fuzzy rule base optimization methods , 2011, 2011 6th IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI).

[23]  R. Rubinstein The Cross-Entropy Method for Combinatorial and Continuous Optimization , 1999 .

[24]  Z.C. Johanyak,et al.  Sparse Fuzzy System Generation by Rule Base Extension , 2007, 2007 11th International Conference on Intelligent Engineering Systems.

[25]  Kok Wai Wong,et al.  Petrophysical properties prediction using self-generating fuzzy rules inference system with modified alpha-cut based fuzzy interpolation , 2000 .

[26]  József K. Tar,et al.  Fuzzy Control System Performance Enhancement by Iterative Learning Control , 2008, IEEE Transactions on Industrial Electronics.

[27]  Pieter Tjerk de Boer,et al.  Analysis and efficient simulation of queueing models of telecommunications systems , 2000 .

[28]  Reuven Y. Rubinstein,et al.  Estimation of rare event probabilities using cross-entropy , 2002, Proceedings of the Winter Simulation Conference.

[29]  László T. Kóczy,et al.  Application of interpolation-based fuzzy logic reasoning in behaviour-based control structures , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[30]  D. Shepard A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[31]  Dirk P. Kroese,et al.  A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks , 2004, Manag. Sci..

[32]  A. M. Ádámné,et al.  Effect of multiwall nanotube on the properties of polypropylenes , 2008 .

[33]  Kevin Kok Wai Wong,et al.  Fuzzy Rule Interpolation Matlab Toolbox - FRI Toolbox , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[34]  László T. Kóczy,et al.  Extracting Trapezoidal Membership Functions of a Fuzzy Rule System by Bacterial Algorithm , 2001, Fuzzy Days.