Abstract
A new type of a fuzzy model is proposed in this paper. It uses a reduced number of fuzzy rules with respective radial basis activation functions. The optimal number of the rules is defined experimentally and their locations are obtained by clustering or by PSO optimization procedure. All other parameters are also optimized in order to produce the best model. The obtained model is able to work with sparse data in the multidimensional experimental space. As a proof a synthetic example, as well as a real example of a 5-dimensional sparse data have been used. The results obtained show that the PSO optimization of the fuzzy rule locations is a better approach than the clustering algorithm, which utilizes the distribution of the available experimental data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cannon, R.L., Dave, J.V., Bezdek, J.C.: Efficient Implementation of the Fuzzy c-Means Clustering Algorithms. IEEE Trans. on Pattern Analysis and Machine Intelligence 8(2) (1986)
Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 224–227 (1979)
Eberhart, R., Kennedy, J.: A New Optimizer Using Particle Swarm Theory. In: Proc. of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39–43. IEEE Service Center, Piscataway (1995)
Fogel, L., Owens, A.J., Walsh, M.J.: Artificial Intelligence through Simulated Evolution. Wiley, New York (1996)
Guo, P., Chen, C.L., Lyu, M.R.: Cluster Number Selection for a Small Set of Samples Using the Bayesian Ying-Yang Model. IEEE Trans. Neural Networks. 13(3), 757–763 (2002)
Ismail, M.A., Selim, S.Z.: Fuzzy c-means: Optimality of solutions and effective termination of the algorithm. Pattern Recognition 19, 481–485 (1986)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948. IEEE Press, Piscataway (1995)
Orr, M.J.L.: Regularisation in the Selection of Radial Basis Function Centres. Neural Computation 7(3), 606–623 (1995)
Pal, N.R., Bezdek, J.C.: On Cluster Validity for the Fuzzy C-Means Model. IEEE Trans. Fuzzy Systems 3(3), 370–379 (1995)
Pedrycz, W., Waletzky, J.: Fuzzy clustering with partial supervision. IEEE Trans. Syst. Man Cybern. Part B Cybern. 27, 787–795 (1997)
Kacprzyk, J., Fedrizzi, M.: Developing a fuzzy logic controller in case of sparse testimonies. Int. Journal of Approximate Reasoning 12(3/4), 221–236 (1995)
Chorukova, E., Simeonov, I.: Monitoring System of Pilot Scale Bioreactor for Anaerobic Digestion of Organic Wastes. In: Proc. of the Int. Symposium on Control of Industrial and Energy Systems, Bankja, Bulgaria, November 7-8 (2013) (in Bulgarian)
Powell, M.J.D.: Radial basis functions for multivariable interpolation: a review. In: Algorithms for Approximation, pp. 143–167. Clarendon Press, Oxford (1987)
Roger Jang, J.S., Sun, C.T.: Functional equivalence between radial basis function networks and fuzzy inference systems. IEEE Transactions on Neural Networks 4(1), 156–159 (1993)
Schilling, R.J., Carroll, J.J.: Approximation of Nonlinear Systems with Radial Basis Function Neural Networks. IEEE Trans. on Neural Networks 12(1) (2001)
Das, S., Abraham, A.: Automatic Clustering Using An Improved Differential Evolution Algorithm. IEEE Transactions on Systems, Man, And Cybernetics—Part A: Systems And Humans 38(1), 218–237 (2008)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst., Man, Cybern. 15, 116–132 (1985)
Wang, X., Wang, Y., Wang, L.: Improving fuzzy c-means clustering based on feature-weight learning. Pattern Recognit. Lett. 25, 1123–1132 (2004)
Webb, A., Shannon, S.: Shape-adaptive radial basis functions. IEEE Trans. Neural Networks 9 (1998)
Xie, X.L., Beni, G.A.: Validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 3, 841–846 (1991)
Xu, C., Shin, Y.C.: Intelligent Systems Modeling, Optimization, and Control (Automation and Control Engineering Series) Summary. CRC Press (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Vachkov, G., Christova, N., Valova, M. (2015). Multi-dimensional Fuzzy Modeling with Incomplete Fuzzy Rule Base and Radial Basis Activation Functions. In: Angelov, P., et al. Intelligent Systems'2014. Advances in Intelligent Systems and Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-11313-5_63
Download citation
DOI: https://doi.org/10.1007/978-3-319-11313-5_63
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11312-8
Online ISBN: 978-3-319-11313-5
eBook Packages: EngineeringEngineering (R0)