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Logic-based fuzzy networks: a study in system modeling with triangular norms and uninorms. (English) Zbl 1185.68546

Summary: The ultimate challenges of system modeling concern designing accurate yet highly transparent and user-centric models. We have witnessed a plethora of neurofuzzy architectures which are aimed at addressing these two highly conflicting requirements. This study is concerned with the design and the development of transparent logic networks realized with the aid of fuzzy neurons and fuzzy unineurons. The construction of networks of this form requires a formation of efficient interfaces that constitute a conceptually appealing bridge between the model and the real-world experimental environment in which the model is to be used.
In general, the interfaces are constructed by invoking some form of granulation of information; and binary (Boolean) discretization, in particular. We introduce a new discretization environment that is realized by means of particle swarm optimization (PSO) and data clustering implemented by the K-Means algorithm. The underlying structure of the network is optimized by invoking a combination of the PSO and the mechanisms of conventional gradient-based learning. We discuss various optimization strategies by considering Boolean as well as fuzzy data coming as the result of discretization of original experimental data and then involving several learning strategies. We elaborate on the interpretation aspects of the network and show how those could be strengthened through efficient pruning. We also show how the interpreted network leads to a simpler and more accurate logic description of the experimental data. A number of experimental studies are included.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
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[1] Akella, P., Structure of n-uninorms, Fuzzy Sets and Systems, 158, 15, 1631-1651 (2007) · Zbl 1122.03044
[2] Alcalá, R.; Alcalá-Fdez, J.; Casillas, J.; Cordón, O.; Herrera, F., Hybrid learning models to get the interpretability-accuracy trade-off in fuzzy modeling, Soft Computing, 10, 9, 717-734 (2006)
[3] Bargiela, A.; Pedrycz, W., Granular Computing: An Introduction (2002), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht
[4] Broekhoven, E. V.; Adriaenssens, V.; Baets, B. D., Interpretability-preserving genetic optimization of linguistic terms in fuzzy models for fuzzy ordered classification: an ecological case study, International Journal of Approximate Reasoning, 44, 1, 65-90 (2007) · Zbl 1107.68450
[5] Calvo, T.; Mesiar, R., Continuous generated associative aggregation operators, Fuzzy Sets and Systems, 126, 191-197 (2002) · Zbl 0996.03034
[6] Castellano, G.; Fanelli, A. M.; Mencar, C., A neuro-fuzzy network to generate human-understandable knowledge from data, Cognitive Systems Research, 3, 2, 125-144 (2002)
[7] J. Catlett, On changing continuous attributes into ordered discrete attributes, in: Proc. 5th European Working Session on Learning, 1991, pp. 164-177.; J. Catlett, On changing continuous attributes into ordered discrete attributes, in: Proc. 5th European Working Session on Learning, 1991, pp. 164-177.
[8] Chmielewski, M. R.; Grzymala-Busse, J. W., Global discretization of continuous attributes as preprocessing for machine learning, International Journal of Approximate Reasoning, 15, 319-331 (1996) · Zbl 0949.68560
[9] Chung, F. L.; Duan, J. C., On multistage fuzzy neural network modeling, IEEE Transactions on Fuzzy Systems, 8, 125-142 (2000)
[10] Ciaramella, A.; Tagliaferri, R.; Pedrycz, W., The genetic development of ordinal sums, Fuzzy Sets and Systems, 151, 303-325 (2005) · Zbl 1065.68082
[11] Cordón, O.; Herrera, F.; Zwir, I., A hierarchical knowledge-based environment for linguistic modeling: models and iterative methodology, Fuzzy Sets and Systems, 138, 2, 307-341 (2003)
[12] Duan, J. C.; Chung, F. L., Multilevel fuzzy relational systems: structure and identification, Soft Computing, 6, 73-86 (2002) · Zbl 1001.68101
[13] Eftekhari, M.; Katebi, S. D.; Karimi, M.; Jahanmiri, A. H., Eliciting transparent fuzzy model using differential evolution, Applied Soft Computing, 8, 1, 466-476 (2008)
[14] Evsukoff, A. G.; Galichet, S.; de Lima, B. S.L. P.; Ebecken, N. F.F., Design of interpretable fuzzy rule-based classifiers using spectral analysis with structure and parameters optimization, Fuzzy Sets and Systems, 160, 7, 857-881 (2009) · Zbl 1186.68409
[15] U.M. Fayyad, K.B. Irani, Multi-interval discretization of continuous-valued attributes for classification learning, in: Proc. of the 13th Internat. Joint Conf. on Artificial Intelligence, 1993, pp. 1022-1027.; U.M. Fayyad, K.B. Irani, Multi-interval discretization of continuous-valued attributes for classification learning, in: Proc. of the 13th Internat. Joint Conf. on Artificial Intelligence, 1993, pp. 1022-1027.
[16] Gobi, A. F.; Pedrycz, W., Fuzzy modeling through logic optimization, International Journal of Approximate. Reasoning, 45, 3, 488-510 (2007) · Zbl 1120.93032
[17] Gobi, A. F.; Pedrycz, W., The potential of fuzzy neural networks in the realization of approximate reasoning engines, Fuzzy Sets and Systems, 157, 22, 2954-2973 (2006) · Zbl 1107.68440
[18] González, J.; Rojas, I.; Pomares, H.; Herrera, L. J.; Guillén, A.; Palomares, J. M.; Rojas, F., Improving the accuracy while preserving the interpretability of fuzzy function approximators by means of multi-objective evolutionary algorithms, International Journal of Approximate Reasoning, 44, 1, 32-44 (2007) · Zbl 1109.68090
[19] Herrera, L. J.; Pomares, H.; Rojas, I.; Guillén, A.; González, J.; Awad, M.; Herrera, A., Multigrid-based fuzzy systems for time series prediction: CATS competition, Neurocomputing, 70, 13-15, 2410-2425 (2007)
[20] Herrera, L. J.; Pomares, H.; Rojas, I.; Valenzuela, O.; Prieto, A., TaSe, a Taylor series-based fuzzy system model that combines interpretability and accuracy, Fuzzy Sets and Systems, 153, 3, 403-427 (2005) · Zbl 1068.93008
[21] Ho, S. Y.; Hsieh, C.-H.; Chen, H.-M.; Huang, H.-L., Interpretable gene expression classifier with an accurate and compact fuzzy rule base for microarray data analysis, Biosystems, 85, 3, 165-176 (2006)
[22] H. Ishibuchi, T. Yamamoto, T. Nakashima, Fuzzy data mining: effect of fuzzy discretization, in: The 2001 IEEE Internat. Conf. on Data Mining, 2001, pp. 241-248.; H. Ishibuchi, T. Yamamoto, T. Nakashima, Fuzzy data mining: effect of fuzzy discretization, in: The 2001 IEEE Internat. Conf. on Data Mining, 2001, pp. 241-248.
[23] Jin, Y., Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement, IEEE Transactions on Fuzzy Systems, 8, 2, 212-221 (2000)
[24] J. Kennedy, R.C. Eberhart, Particle swarm optimization, in: Proc. 1995 IEEE Internat. Conf. on Neural Networks, Piscataway, NJ, 1995, pp. 1942-1948.; J. Kennedy, R.C. Eberhart, Particle swarm optimization, in: Proc. 1995 IEEE Internat. Conf. on Neural Networks, Piscataway, NJ, 1995, pp. 1942-1948.
[25] R. Kerber, Chimerge: discretization for numeric attributes, in: Proc. 10th National Conf. on Artificial Intelligence, San Jose, CA 1992, pp. 123-128.; R. Kerber, Chimerge: discretization for numeric attributes, in: Proc. 10th National Conf. on Artificial Intelligence, San Jose, CA 1992, pp. 123-128.
[26] Klawonn, F., Reducing the number of parameters of a fuzzy system using scaling functions, Soft Computing, 10, 9, 749-756 (2006)
[27] Kurgan, L. A.; Cios, K. J., CAIM discretization algorithm, IEEE Transactions on Knowledge and Data Engineering, 16, 2, 145-153 (2004)
[28] W. Kwedlo, M. Kretowski, An evolutionary algorithm using multivariate discretization for decision rule induction, in: Principles of Data Mining and Knowledge Discovery, Lecture Notes in Artificial Intelligence, Vol. 1704, 1999, pp. 392-397.; W. Kwedlo, M. Kretowski, An evolutionary algorithm using multivariate discretization for decision rule induction, in: Principles of Data Mining and Knowledge Discovery, Lecture Notes in Artificial Intelligence, Vol. 1704, 1999, pp. 392-397.
[29] Liang, X.; Pedrycz, W., Fuzzy logic-based networks: a study in logic data interpretation, International Journal of Intelligent Systems, 21, 12, 1249-1267 (2006) · Zbl 1109.68092
[30] Liu, H.; Hussain, F.; Tan, C. L.; Dash, M., Discretization: an enabling technique, Journal of Data Mining and Knowledge Discovery, 6, 4, 393-423 (2002)
[31] J.B. MacQueen, Some methods for classification and analysis of multivariate observations, in: Proc. 5th Berkeley Symp. on Mathematical Statistics and Probability, Vol. 1, 1967, pp. 281-297.; J.B. MacQueen, Some methods for classification and analysis of multivariate observations, in: Proc. 5th Berkeley Symp. on Mathematical Statistics and Probability, Vol. 1, 1967, pp. 281-297. · Zbl 0214.46201
[32] Mencar, C.; Fanelli, A. M., Interpretability constraints for fuzzy information granulation, Information Sciences, 178, 24, 4585-4618 (2008)
[33] Monserrat, M.; Torrens, J., On the reversibility of uninorms and t-operators, Fuzzy Sets and Systems, 131, 3, 303-314 (2002) · Zbl 1012.03034
[34] Paiva, R. P.; Dourado, A., Interpretability and learning in neuro-fuzzy systems, Fuzzy Sets and Systems, 147, 1, 17-38 (2004) · Zbl 1068.68125
[35] Paterlini, S.; Krink, T., Differential evolution and particle swarm optimization in partitional clustering, Computational Statistics Data Analysis, 50, 1, 1220-1247 (2006) · Zbl 1431.62268
[36] Pedrycz, W., Logic-based fuzzy neurocomputing with unineurons, IEEE Transactions on Fuzzy Systems, 14, 6, 860-873 (2006)
[37] Pedrycz, W., Heterogeneous fuzzy logic networks: fundamentals and development studies, IEEE Transactions on Neural Networks, 15, 1466-1481 (2004)
[38] Pedrycz, W., Fuzzy neural networks and neurocomputations, Fuzzy Sets and Systems, 56, 1-28 (1993)
[39] Pedrycz, W., A fuzzy cognitive structure for pattern recognition, Pattern Recognition Letters, 9, 305-313 (1989) · Zbl 0800.68750
[40] Pedrycz, W., Selected issues of frame of knowledge representation realized by means of linguistic labels, International Journal of Intelligent Systems, 7, 155-169 (1992)
[41] Pedrycz, W., Interfaces of fuzzy models: a study in fuzzy information processing, Information Sciences, 90, 231-280 (1996)
[42] Pedrycz, W.; Gomide, F., An Introduction to Fuzzy Sets: Analysis and Design (1998), MIT Press: MIT Press Boston · Zbl 0938.03078
[43] Pedrycz, W.; Hirota, K., Uninorm-based logic neurons as adaptive and interpretable processing constructs, Soft Computing, 11, 1, 41-52 (2007) · Zbl 1114.68477
[44] Pedrycz, W.; Reformat, M.; Han, C. W., Cascade architectures of fuzzy neural networks, Fuzzy Optimization and Decision Making, 3, 1, 5-37 (2004) · Zbl 1062.68104
[45] Pedrycz, W.; Reformat, M.; Li, K., OR/AND neurons and the development of interpretable logic models, IEEE Transactions on Neural Networks, 17, 3, 636-658 (2006)
[46] Raju, G. V.S.; Zhou, J.; Kisner, R. A., Hierarchical fuzzy control, International Journal of Control, 54, 5, 1201-1216 (1991) · Zbl 0741.93001
[47] Salgado, P., Rule generation for hierarchical collaborative fuzzy system, Applied Mathematical Modelling, 32, 7, 1159-1178 (2008) · Zbl 1179.93118
[48] Souza, F. J.; Vellasco, M. M.R.; Pacheco, M. A.C., Hierarchical neuro-fuzzy quadtree models, Fuzzy Sets and Systems, 130, 2, 189-205 (2002) · Zbl 1035.93007
[49] Tay, E. H.; Shen, L., A modified chi2 algorithm for discretization, IEEE Transactions on Knowledge and Data Engineering, 14, 3, 666-670 (2002)
[50] Tsipouras, M. G.; Exarchos, T. P.; Fotiadis, D. I., A methodology for automated fuzzy model generation, Fuzzy Sets and Systems, 159, 3201-3220 (2008) · Zbl 1182.90106
[51] Wang, L. X., Analysis and design of hierarchical fuzzy systems, IEEE Transactions on Fuzzy Systems, 7, 5, 617-624 (1999)
[52] Yager, R. R., Uninorms in fuzzy systems modeling, Fuzzy Sets and Systems, 122, 167-175 (2001) · Zbl 0978.93007
[53] Yager, R. R., Defending against strategic manipulation in uninorm-based multi-agent decision making, European Journal of Operational Research, 141, 217-232 (2002) · Zbl 0998.90046
[54] Yager, R. R.; Rybalov, A., Uninorm aggregation operators, Fuzzy Sets and Systems, 80, 111-122 (1996) · Zbl 0871.04007
[55] Yang, Y.; Webb, G. I.; Wu, X., Discretization methods, (Data Mining and Knowledge Discovery Handbook (2005), Springer: Springer Berlin), 113-130
[56] Zhou, S.-M.; Gan, J. Q., Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling, Fuzzy Sets and Systems, 159, 23, 3091-3131 (2008)
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