Ensembles of the Mamdani Fuzzy Systems
This chapter describes a family of fuzzy systems that use neural network like approach for learning and visualizing the system.Models in this chapter have their antecedents and consequents of rules connected by a t-norm. Such systems are called the Mamdani type neuro-fuzzy systems and they are the most common neuro-fuzzy systems. As it is emphasized in the previous chapter, the most important problem in case of creating ensembles from fuzzy systems as base hypothesis is that each rule base has different overall activation level. Thus we cannot treat them as one large fuzzy rule base. This possible “inequality” comes from different activation level during training. To overcome this problem, we apply the method proposed in the previous chapter to normalize all rule bases during learning. The normalization is achieved by adding the second output to the Mamdani system and keeping all rule bases at the same level.
KeywordsFuzzy System Fuzzy Rule Rule Base Previous Chapter AdaBoost Algorithm
Unable to display preview. Download preview PDF.
- 1.Breiman, L.: Bias, variance, and arcing classifiers. Tech. Rep. Technical Report 460, Statistics Department, University of California (1997)Google Scholar
- 2.Frank, A., Asuncion, A.: UCI machine learning repository (2010), http://archive.ics.uci.edu/ml
- 3.Korytkowski, M., Rutkowski, L., Scherer, R.: From Ensemble of Fuzzy Classifiers to Single Fuzzy Rule Base Classifier. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 265–272. Springer, Heidelberg (2008), http://www.springerlink.com/content/p2813172x2w414t2/ CrossRefGoogle Scholar
- 4.Korytkowski, M., Scherer, R.: Negative Correlation Learning of Neuro-fuzzy System Ensembles. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010. LNCS (LNAI), vol. 6113, pp. 114–119. Springer, Heidelberg (2010), http://www.springerlink.com/content/n4732566203326q1/ CrossRefGoogle Scholar
- 8.Schapire, R.E.: A brief introduction to boosting. In: Conference on Artificial Intelligence, pp. 1401–1406 (1999)Google Scholar
- 9.Wang, L.X.: Adaptive Fuzzy Systems and Control. PTR Prentice-Hall, Englewood Cliffs (1994)Google Scholar