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Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling
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Zadeh, L. A. (1965) · Information and Control · doi:10.1016/s0019-9958(65)90241-x · Cited by 67,855
Cortes, C., & Vapnik, V. (1995) · Machine Learning · doi:10.1007/bf00994018 · Cited by 59,421
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
Estimating the Dimension of a Model
Schwarz, G. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344136 · Cited by 47,033
Zadeh, L. A. (1996) · Cited by 46,844
The Nature of Statistical Learning Theory
Vapnik, V. N. (1995) · doi:10.1007/978-1-4757-2440-0 · Cited by 39,138
Wu, Y. (1999) · Technometrics · doi:10.1080/00401706.1999.10485951 · Cited by 27,221
Quinlan, J. R. (1986) · Machine Learning · doi:10.1007/bf00116251 · Cited by 21,439
Fuzzy identification of systems and its applications to modeling and control
Takagi, T., & Sugeno, M. (1985) · IEEE Transactions on Systems, Man, and Cybernetics · doi:10.1109/tsmc.1985.6313399 · Cited by 19,592
Research works printed but not linked: 77
- Alcala, 2006, Hybrid learning models to get the interpretability-accuracy trade-off in fuzzy modelling, Soft Comput., 10, 717, 10.1007/s00500-005-0002-1 · doi:10.1007/s00500-005-0002-1
- Alcala, 2007, A multi-objective genetic algorithm for tuning and rule selection to Obtain accurate and compact linguistic fuzzy rule-based systems, Internat. J. Uncertainty Fuzziness Knowledge-Based Systems, 15, 539, 10.1142/S0218488507004868 · doi:10.1142/s0218488507004868
- Alcalá, 2001, Building fuzzy graphs: features and taxonomy of learning non-grid-oriented fuzzy rule-based systems, Internat. J. Intelligent Fuzzy Systems, 11, 99
- T. G. Amaral, V. F. Pires, and M. M. Crisostomo, An approach to improve the interpretability of neuro-fuzzy systems, in: Proc. IEEE International Conf. on Fuzzy Systems (FUZZ-IEEE), 16–21 July, Vancouver, BC, Canada, 2006, pp. 8502–8509. · doi:10.1109/fuzzy.2006.1681956
- H. C. Anderson, The controller output error method, Ph.D. Dissertation, University of Queensland, Australia, 1998.
- Berthold, 1999, Constructing fuzzy graphs from examples, Intelligent Data Anal., 3, 37, 10.1016/S1088-467X(99)00004-9 · doi:10.1016/s1088-467x(99)00004-9
- Bezdek, 1985, An application of the c-varieties clustering algorithm to polygonal curve fitting, IEEE Trans. Systems Man Cybernet., 15, 637, 10.1109/TSMC.1985.6313440 · doi:10.1109/tsmc.1985.6313440
- Bezdek, 1995, Two soft relative of learning vector quantization, Neural Networks, 8, 729, 10.1016/0893-6080(95)00024-T · doi:10.1016/0893-6080(95)00024-t
- Bikdash, 1999, A highly interpretable form of Sugeno inference systems, IEEE Trans. Fuzzy Systems, 7, 686, 10.1109/91.811237 · doi:10.1109/91.811237
- K. M. Bossley, Neurofuzzy modelling approaches in system identification, Ph.D. Dissertation, University of Southampton, UK, 1997. · doi:10.1049/ic:19970788
- Casillas, 2005, Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction, IEEE Trans. Fuzzy Systems, 13, 13, 10.1109/TFUZZ.2004.839670 · doi:10.1109/tfuzz.2004.839670
- Castellano, 2002, Generation of interpretable fuzzy granules by a double-clustering technique, Arch. Control Sci. Special Issue Granular Comput., 12, 397
- S. Chiu, J.J. Cheng, Automatic rule generation of fuzzy rule base for robot arm posture selection, in: Proc. of NAFIPS Conf., San Antonio, TX, December 1994, pp. 436–440. · doi:10.1109/ijcf.1994.375071
- Cococcioni, 2007, A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems, Soft Comput., 11, 1013, 10.1007/s00500-007-0150-6 · doi:10.1007/s00500-007-0150-6
- Cordón, 2003, Author's reply (to comments on the benchmarks in ‘a proposal for improving the accuracy of linguistic modelling’ and related articles), IEEE Trans. Fuzzy Systems, 11, 866
- de Oliveira, 1995, A design methodology for fuzzy system interfaces, IEEE Trans. Fuzzy Systems, 3, 404, 10.1109/91.481949 · doi:10.1109/91.481949
- Destercke, 2007, Building an interpretable fuzzy rule base from data using orthogonal least squares-application to a depollution problem, Fuzzy Sets and Systems, 158, 2078, 10.1016/j.fss.2007.04.026 · doi:10.1016/j.fss.2007.04.026
- Dubois, 1997, Checking the coherence and redundancy of fuzzy knowledge bases, IEEE Trans. Fuzzy Systems, 5, 398, 10.1109/91.618276 · doi:10.1109/91.618276
- Espinosa, 2000, Constructing fuzzy models with linguistic integrity from numerical data-AFRELI algorithm, IEEE Trans. Fuzzy Systems, 8, 591, 10.1109/91.873582 · doi:10.1109/91.873582
- B. Fritzke, Incremental neuro-fuzzy systems, in: Proc. of Application of Soft Computing, SPIE Internat. Symp. on Optical Science, Engineering and Instrumentation, San Diego, USA, 1997, pp. 86–97. · doi:10.1117/12.284208
- T. Furuhashi and T. Suzuki, On interpretability of fuzzy models based on conciseness measure, in: Proc. Tenth IEEE Internat. Conf. on Fuzzy Sets (FUZZ-IEEE’01), Melbourne Australia, December, 2001, pp. 284–287. · doi:10.1109/fuzz.2001.1007304
- Gan, 1999, Fuzzy local linearization and local basis function expansion in nonlinear system modelling, IEEE Trans. Systems Man Cybernet.—Part B, 29, 559, 10.1109/3477.775275 · doi:10.1109/3477.775275
- Gan, 2001, A hybrid learning scheme combining EM and MASMOD algorithms for fuzzy local linearization modelling, IEEE Trans. Neural Networks, 12, 43, 10.1109/72.896795 · doi:10.1109/72.896795
- S. Gottwald and U. Petri, An algorithmic approach toward consistency checking systems of fuzzy control rules, in: Proc. Third European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, 1995, pp. 682–687.
- Hefny, 2007, Comments on ‘Distinguishability quantification of fuzzy sets’, Inform. Sci., 177, 4832, 10.1016/j.ins.2007.02.027 · doi:10.1016/j.ins.2007.02.027
- Hoeppner, 1997, Fuzzy shell clustering algorithms in image processing: fuzzy c-rectangular and 2-rectangular shells, IEEE Trans. Fuzzy Systems, 5, 599, 10.1109/91.649912 · doi:10.1109/91.649912
- Hong, 2000, Generalized neurofuzzy network modelling algorithms using Bézier–Bernstein polynomial functions and additive decomposition, IEEE Trans. Neural Networks, 11, 889, 10.1109/72.857770 · doi:10.1109/72.857770
- F. Hoppner, F. Klawonn, Obtaining interpretable fuzzy models from fuzzy clustering and fuzzy regression, in: Proc. Fourth Internat. Conf. on Knowledge-based Intelligent Engineering Systems and Allied Tech (KES), Brighton, UK, 2000, pp. 162–165. · doi:10.1109/kes.2000.885783
- Ishibuchi, 2001, Three-objective genetics-based machine learning for linguistic rule extraction, Inform. Sci., 136, 109, 10.1016/S0020-0255(01)00144-X · doi:10.1016/s0020-0255(01)00144-x
- J. Jakel, L. Groll and R. Mikut, Tree-oriented hypothesis generation for interpretable fuzzy rules, in: Proc. Seventh European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, 1999, pp. 279–280.
- Jang, 1993, Functional equivalence between radial basis function networks and fuzzy inference systems, IEEE Trans. Neural Networks, 4, 156, 10.1109/72.182710 · doi:10.1109/72.182710
- C. Jerome, B. Noel, H. Michel, A new fuzzy clustering technique based on PDF estimation, in: Proc. Information Processing and Managing of Uncertainty (IPMU’2002), 2002, pp. 225–232.
- F. Jimenez, G. Sanchez, A.F. Gomez-Skarmeta, H. Roubos, R. Babuska, Fuzzy modelling with multi-objective neuro-evolutionary algorithms, in: Proc. of IEEE Internat. Conf. on Systems, Man and Cybernetics (IEEE SMC’02), Yasmine Hammamet, Tunisia, 2002, pp. 253–258.
- Jin, 1999, On generating FC3 fuzzy rule systems from data using evolution strategies, IEEE Trans. Systems Man Cybernet. Part B, 29, 829, 10.1109/3477.809036 · doi:10.1109/3477.809036
- Johansen, 2000, On the interpretation and identification of dynamic Takagi–Sugeno fuzzy models, IEEE Trans. Fuzzy Systems, 8, 297, 10.1109/91.855918 · doi:10.1109/91.855918
- Kanjilal, 1995, On the application of orthogonal transformation for the design and analysis of feedforward networks, IEEE Trans. Neural Networks, 6, 1061, 10.1109/72.410351 · doi:10.1109/72.410351
- Kim, 1998, A transformed input-domain approach to fuzzy modelling, IEEE Trans. Fuzzy Systems, 596
- Kim, 2005, On utilizing search methods to select subspace dimensions for kernel-based nonlinear subspace classifiers, IEEE Trans. Pattern Anal. Mach. Intell., 27, 136, 10.1109/TPAMI.2005.15 · doi:10.1109/tpami.2005.15
- A. Klose, A. Nürnberger, Applying Boolean transformations to fuzzy rule bases, in: Proc. Seventh European Congress on Intelligent Techniques and Soft Computing (EUFIT’99), Verlag Mainz, Aachen, Germany, 1999, p. 6.
- A. Klose, A. Nürnberger, D. Nauck, Some approaches to improve the interpretability of neuro-fuzzy classifiers, in: Proc. Sixth European Congress on Intelligent Techniques and Soft Computing (EUFIT’98), Verlag und Druck Mainz GmbH, Aachen, 1998, pp. 629–633.
- A. Klose, A. Nürnberger, D. Nauck, Improved NEFCLASS pruning techniques applied to a real world domain, in: G. Krell, B. Michaelis, D. Nauck, R. Kruse (Eds.), Proceedings of Neural Networks in Applications (NN’99), Logisch GmbH, Magdeburg, Germany, 1999, pp. 47–52.
- Kumar, 2006, A robust design criterion for interpretable fuzzy models with uncertain data, IEEE Trans. Fuzzy Systems, 14, 314, 10.1109/TFUZZ.2005.861614 · doi:10.1109/tfuzz.2005.861614
- Laha, 2001, Some novel classifiers designed using prototypes extracted by a new scheme based on self-organizing feature map, IEEE Trans. Systems Man Cybernet. and Cybernet. B, 31, 881, 10.1109/3477.969492 · doi:10.1109/3477.969492
- Lotfi, 1996, Interpretation preservation of adaptive fuzzy inference systems, Internat. J. Approx. Reason., 15, 379, 10.1016/S0888-613X(96)00070-9 · doi:10.1016/s0888-613x(96)00070-9
- Mamdani, 1974, Applications of fuzzy algorithm for control a simple dynamic plant, Proc. IEEE, 121, 1585
- Mamdani, 1976, Advances in the linguistic synthesis of fuzzy controllers, Internat. J. Man Mach. Stud., 8, 669, 10.1016/S0020-7373(76)80028-4 · doi:10.1016/s0020-7373(76)80028-4
- Mastorocostas, 2001, A constrained orthogonal least-squares method for generating TSK fuzzy models: application to short-term load forecasting, Fuzzy Sets and Systems, 118, 215, 10.1016/S0165-0114(98)00344-3 · doi:10.1016/s0165-0114(98)00344-3
- Mencar, 2007, Distinguishability quantification of fuzzy sets, Inform. Sci., 177, 130, 10.1016/j.ins.2006.04.008 · doi:10.1016/j.ins.2006.04.008
- C. Mencar, G. Castellano, A.M. Fanelli, A. Bargiela, Similarity vs. possibility in measuring fuzzy sets distinguishability, in: Proc. Fifth Internat. Conf. on Recent Advances in Soft Computing (RASC), Nottingham, UK, 2004, pp. 354–359.
- D. Nauck, R. Kruse, A neuro-fuzzy approach to obtain interpretable fuzzy systems for function approximation, in: Proc. IEEE Internat. Conf. on Fuzzy Systems (FUZZ-IEEE), Anchorage, AK, May 4–9, 1998, pp. 1106–1111. · doi:10.1109/fuzzy.1998.686273
- O. Nelles, Nonlinear system identification with local linear neuro-fuzzy models, Ph.D. Thesis, Darmstadt University, Darmstadt, Germany, 1999.
- Nelles, 2000, Comparison of two construction algorithms for Takagi-Sugeo fuzzy models, Internat. J. Appl. Math. Comput. Sci., 10, 835
- O. Nelles, R. Isermann, Basis function networks for interpolation of local linear models, in: Proc. IEEE Conf. on Decision and Control (CDC), Kobe, Japan, 1996, pp. 470–475. · doi:10.1109/cdc.1996.574356
- Pal, 2001, Fuzzy rule extraction from ID3-type decision trees for real data, IEEE Trans. Systems Man Cybernet. Part B, 31, 745, 10.1109/3477.956036 · doi:10.1109/3477.956036
- Pedrycz, 1996, Optimization of fuzzy models, IEEE Trans. Systems Man Cybernet. Part B, 26, 627, 10.1109/3477.517038 · doi:10.1109/3477.517038
- A. Riid, Transparent fuzzy systems: modelling and control, Ph.D. Dissertation, Department of Computer Control, Tallinn Technical University, Estonia, 2002.
- A. Riid, R. Isotamm, E. Rustern, Transparent analysis of first-order Takagi–Sugeno systems, in: Proc. 10th Internat. Symp. on System-Modelling-Control, Zakopane, Poland, 2001, pp. 165–170.
- A. Riid, E. Rustern, Transparent fuzzy systems and modelling with transparency protection, in: Proc. IFAC Symp. on Artificial Intelligence in Real Time Control, Budapest, 2000, pp. 229–234.
- Rojas, 2000, Self-organized fuzzy system generation from training examples, IEEE Trans. Fuzzy Systems, 8, 23, 10.1109/91.824763 · doi:10.1109/91.824763
- Roubos, 2001, Compact and transparent fuzzy models and classifiers through iterative complexity reduction, IEEE Trans. Fuzzy Systems, 9, 516, 10.1109/91.940965 · doi:10.1109/91.940965
- Roubos, 2003, Comments on the benchmarks in ‘a proposal for improving the accuracy of linguistic modelling’ and related articles, IEEE Trans. Fuzzy Systems, 11, 861, 10.1109/TFUZZ.2003.819822 · doi:10.1109/tfuzz.2003.819822
- Roubos, 2003, Learning fuzzy classification rules from labeled data, Inform. Sci., 150, 77, 10.1016/S0020-0255(02)00369-9 · doi:10.1016/s0020-0255(02)00369-9
- Setnes, 2001, Rule base reduction: some comments on the use of orthogonal transforms, IEEE Trans. Systems Man Cybernet. Part C, 31, 199, 10.1109/5326.941843 · doi:10.1109/5326.941843
- Setnes, 1998, Similarity measures in fuzzy rule base simplification, IEEE Trans. Systems Man Cybernet. Part B, 28, 376, 10.1109/3477.678632 · doi:10.1109/3477.678632
- M. Setnes, H. Hellendoorn, Orthogonal transforms for ordering and reduction of fuzzy rules, Proc. Ninth IEEE Internat. Conf. on Fuzzy Systems, San Antonio, USA, 2000, pp. 700–705. · doi:10.1109/fuzzy.2000.839117
- Q. Shen, J.G. Marin-Blazquez, Microtuning of membership functions: accuracy vs. interpretability, in: Proc. IEEE Internat. Conf. on Fuzzy Systems (FUZZ-IEEE’02), Honolulu, Hawai, USA, 2002, pp. 168–173.
- Silipo, 2000, Input features’ impact on fuzzy decision processes, IEEE Trans. Systems Man Cybernet. Part B, 30, 821, 10.1109/3477.891144 · doi:10.1109/3477.891144
- Taniguchi, 1980, On the selection of the order of the spectral density of a stationary process, Ann. Instit. Statist. Math., 32, 401, 10.1007/BF02480345 · doi:10.1007/bf02480345
- Van Broekhoven, 2007, Interpretability-preserving genetic optimization of linguistic terms in fuzzy models for fuzzy ordered classification: an ecological case study, Internat. J. Approx. Reason., 44, 65, 10.1016/j.ijar.2006.03.003 · doi:10.1016/j.ijar.2006.03.003
- Wang, 2005, Agent-based evolutionary approach to interpretable rule-based knowledge extraction, IEEE Trans. Systems Man Cybernet. Part C, 29, 143, 10.1109/TSMCC.2004.841910 · doi:10.1109/tsmcc.2004.841910
- Wang, 1995, Building Sugeno-type models using fuzzy discretization and orthogonal parameter estimation techniques, IEEE Trans. Fuzzy Systems, 3, 454, 10.1109/91.481954 · doi:10.1109/91.481954
- Yen, 1998, Application of statistical information criteria for optimal fuzzy model construction, IEEE Trans. Fuzzy Systems, 6, 362, 10.1109/91.705503 · doi:10.1109/91.705503
- Yen, 1998, Improving the interpretability of TSK fuzzy models by combining global learning and local learning, IEEE Trans. Fuzzy Systems, 6, 530, 10.1109/91.728447 · doi:10.1109/91.728447
- Zadeh, 1996, Fuzzy logic and the calculi of fuzzy rules and fuzzy graphs: a précis, Internat. J. Multiple-Valued Logic, 1, 1
- Zhou, 2004, An unsupervised kernel based fuzzy c-means clustering algorithm with kernel normalization, Internat. J. Comput. Intell. Appl., 4, 355, 10.1142/S1469026804001379 · doi:10.1142/s1469026804001379
- Zhou, 2006, Constructing accurate and parsimonious fuzzy models with distinguishable fuzzy sets based on an entropy measure, Fuzzy Sets and Systems, 157, 1057, 10.1016/j.fss.2005.08.004 · doi:10.1016/j.fss.2005.08.004
- Zhou, 2007, Constructing parsimonious fuzzy classifiers based on L2-SVM in high-dimensional space with automatic model selection and fuzzy rule ranking, IEEE Trans. on Fuzzy Systems, 15, 398, 10.1109/TFUZZ.2006.882464 · doi:10.1109/tfuzz.2006.882464
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Metadata
- Authors
- Zhou, S.-M., & Gan, J. Q.
- Venue
- Fuzzy Sets and Systems
- Publisher
- Elsevier BV
- Published
- 2008-12
- Volume
- 159
- Issue
- 23
- Pages
- 3091-3131
- ISSN
- 0165-0114 (ISSN-L)
- OpenAlex
- W2016563381
- Cited by
- 269
- References
- 125
- FWCI
- 30.74
- Type
- journal article
- Language
- en
- Open access
- green
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
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