Learning Fuzzy Cognitive Maps using Structure Optimization Genetic Algorithm
Fuzzy cognitive map (FCM) is a soft computing methodology that allows to describe the analyzed problem as a set of nodes (concepts) and connections (links) between them. In this paper a new Structure Optimization Genetic Algorithm (SOGA) for FCMs learning is presented for modeling complex decision support systems. The proposed approach allows to automatic construct and optimize the FCM model on the basis of historical multivariate time series. The SOGA defines a new learning error function with an additional penalty for highly complexity of FCM understood as a large number of concepts and a large number of connections between them. The aim of this study is the analysis of usefulness of the Structure Optimization Genetic Algorithm for fuzzy cognitive maps learning. Comparative analysis of the SOGA with other well-known FCM learning algorithms (RealCoded Genetic Algorithm and Multi-Step Gradient Method) was performed on the example of prediction of rented bikes count. Simulations were done with the ISEMK (Intelligent Expert System based on Cognitive Maps) software tool. The obtained results show that the use of SOGA allows to significantly reduce the structure of the FCM model by selecting the most important concepts and connections between them. (original abstract)
- S. Ahmadi, N. Forouzideh, S. Alizadeh, and E. Papageorgiou, "Learning Fuzzy Cognitive Maps using Imperialist Competitive Algorithm," Neural Computing and Applications, in press, http://dx.doi.org/10.1007/s00521- 014-1797-4.
- M. Amer, A. J. Jetter, and T. U. Daim, "Scenario planning for the national wind energy sector through Fuzzy Cognitive Maps," Proceedings of PICMET'13, 2013, pp. 2153-2162.
- J. Arabas, Lectures on genetic algorithms, WNT, Warsaw, 2001.
- A. Buruzs, M. F. Hatwágner, A. Torma, and L. T. Kóczy, "Expert Based System Design for Integrated Waste Management," International Scholarly and Scientific Research & Innovation, vol. 8, no. 12, 2014, pp. 685-693.
- J. P. Carvalho, "On the semantics and the use of fuzzy cognitive maps and dynamic cognitive maps in social sciences," Fuzzy Sets and Systems, vol. 214, 2013, pp. 6-19, http://dx.doi.org/10.1016/j.fss.2011.12.009.
- H. Fanaee-T and J. Gama, "Event labeling combining ensemble detectors and background knowledge," Progress in Artificial Intelligence, Springer Berlin Heidelberg 2013, pp. 1-15, http://dx.doi.org/10.1007/s13748-013- 0040-3.
- W. Froelich, E.I. Papageorgiou, M. Samarinasc, and K. Skriapasc, "Application of evolutionary fuzzy cognitive maps to the long-term prediction of prostate cancer," Applied Soft Computing, vol. 12, 2012, pp. 3810-3817, http://dx.doi.org/10.1016/j.asoc.2012.02.005.
- W. Froelich and J. Salmeron, "Evolutionary learning of fuzzy grey cognitive maps for the forecasting of multivariate, interval-valued time series," International Journal of Approximate Reasoning, vol. 55, 2014, pp. 1319-1335, http://dx.doi.org/10.1016/j.ijar.2014.02.006.
- D. B. Fogel, Evolutionary Computation. Toward a new philosophy of machine inteligence 3rd edition, John Wiley & Sons, Inc., Hoboken, New Jersey, 2006.
- ] L. Grad, "An example of feed forward neural network structure optimisation with genetic algorithm," BIULETYN INSTYTUTU AUTOMATYKI I ROBOTYKI, no. 23, 2006, pp. 31-41.
- F. Herrera, M. Lozano, and J. L. Verdegay, "Tackling Real-Coded Genetic Algorithms: Operators and Tools for Behavioural Analysis," Artificial Intelligence Review, vol. 12, 1998, pp. 265-319, http://dx.doi.org/10.1023/A:1006504901164.
- W. Homenda, A. Jastrzebska, and W. Pedrycz, "Nodes Selection Criteria for Fuzzy Cognitive Maps Designed to Model Time Series," Advances in Intelligent Systems and Computing, vol. 323, 2015, pp. 859-870, http://dx.doi.org/10.1007/978-3-319-11310-4_75.
- W. Homenda, A. Jastrzebska, and W. Pedrycz, "Time Series Modeling with Fuzzy Cognitive Maps: Simplification Strategies. The Case of a Posteriori Removal of Nodes and Weights," Lecture Notes in Computer Science LNCS, vol. 8838, 2014, pp. 409-420, http://dx.doi.org/10.1007/978-3-662-45237-0_38.
- A. Jastriebow and K. Piotrowska, "Simulation analysis of multistep algorithms of relational cognitive maps learning," in: A. Yastrebov, B. Kuźminska-Sołśnia and M. Raczyńska (Eds.) ´ Computer Technologies in Science, Technology and Education, Institute for Sustainable Technologies - National Research Institute, Radom, 2012, pp. 126-137.
- A. Jastriebow and K. Poczęta, "Analysis of multi-step algorithms for cognitive maps learning," BULLETIN of the POLISH ACADEMY of SCIENCES TECHNICAL SCIENCES, vol. 62, Issue 4, 2014, pp. 735- 741, http://dx.doi.org/10.2478/bpasts-2014-0079.
- B. Kosko, "Fuzzy cognitive maps," International Journal of Man-Machine Studies, vol. 24, no.1, 1986, pp. 65-75, http://dx.doi.org/10.1016/S0020-7373(86)80040-2.
- W. Lu, W. Pedrycz, X. Liu, J. Yang, and P. Li, "The modeling of time series based on fuzzy information granules," Expert Systems with Applications, vol. 41, 2014, pp. 3799-3808, http://dx.doi.org/10.1016/j.eswa.2013.12.005.
- E. I. Papageorgiou , "Fuzzy Cognitive Maps for Applied Sciences and Engineering From Fundamentals to Extensions and Learning Algorithms," Intelligent Systems Reference Library, vol. 54, Springer Verlag, 2014.
- E. I. Papageorgiou and W. Froelich, "Multi-step prediction of pulmonary infection with the use of evolutionary fuzzy cognitive maps," Neurocomputing, vol. 92, 2012, pp. 28-35, http://dx.doi.org/10.1016/j.neucom.2011.08.034.
- E. I. Papageorgiou, K. E. Parsopoulos, C. D. Stylios, P. P. Groumpos, and M. N. Vrahtis, "Fuzzy Cognitive Maps Learning Using Particle Swarm Optimization," Journal of Intelligent Information Systems, 25:1, 2005, pp. 95-121, http://dx.doi.org/10.1007/s10844-005-0864-9.
- E. I. Papageorgiou, K. Poczęta and C. Laspidou, "Application of Fuzzy Cognitive Maps to Water Demand Prediction," 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Istanbul, Turkey, in press.
- E. I. Papageorgiou and J. L. Salmeron, "A Review of Fuzzy Cognitive Maps Research during the last decade," IEEE Transactions on Fuzzy Systems, vol.21 , Issue: 1, 2013, pp. 66-79, http://dx.doi.org/10.1109/TFUZZ.2012.2201727.
- G. A. Papakostas, D. E. Koulouriotis, A. S. Polydoros, and V. D. Tourassis, "Towards Hebbian learning of Fuzzy Cognitive Maps in pattern classification problems," Expert Systems with Applications, vol. 39, 2012, pp. 10620-10629, http://dx.doi.org/10.1016/j.eswa.2012.02.148.
- K. Piotrowska, "Intelligent expert system based on cognitive maps," STUDIA INFORMATICA, vol. 33, no 2A (105), 2012, pp. 605-616.
- K. Poczęta and A. Yastrebov, "Analysis of Fuzzy Cognitive Maps with Multi-Step Learning Algorithms in Valuation of OwnerOccupied Homes," 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Beijing, China, 2014, pp.1029-1035, http://dx.doi.org/10.1109/FUZZ-IEEE.2014.6891587.
- J. L. Salmeron, "Fuzzy cognitive maps for artificial emotions forecasting," Applied Soft Computing, vol. 12, 2012, pp. 3704-3710, http://dx.doi.org/10.1016/j.asoc.2012.01.015.
- G. Słon, "Application of Models of Relational Fuzzy Cognitive Maps ´ for Prediction of Work of Complex Systems," Lecture Notes in Artificial Intelligence LNAI, vol. 8467, Springer Verlag, 2014, pp. 307-318, http://dx.doi.org/10.1007/978-3-319-07173-2_27.
- W. Stach, L. Kurgan, W. Pedrycz, and M. Reformat, "Genetic learning of fuzzy cognitive maps," Fuzzy Sets and Systems, vol. 153, no. 3, 2005, pp. 371-401, http://dx.doi.org/10.1016/j.fss.2005.01.009.