A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: Designing interpretable genetic fuzzy systems

International Journal of Approximate Reasoning

Volumn 52, Issue 6, 2011, Pages 894-913

  Cordón, Oscar ^a,b  

^a EUROPEAN CENTRE FOR SOFT COMPUTING   (Spain)

^b Dept Computer Science and Artificial Intelligence   (Spain)

Author keywords

Fuzzy system identification; Genetic fuzzy systems; Interpretability accuracy tradeoff; Mamdani type fuzzy rule based systems

Indexed keywords

BLACK-BOX MODEL; DESIGN TECHNIQUE; EVOLUTIONARY LEARNING; FUZZY MODELING; FUZZY MODELS; FUZZY RULE-BASED SYSTEMS; GENETIC FUZZY SYSTEMS; HISTORICAL REVIEW; INHERENT FLEXIBILITY; INTERPRETABILITY; INTERPRETABILITY AND ACCURACY; INTERPRETABILITY-ACCURACY TRADEOFF; LINGUISTIC FUZZY MODELS; MAMDANI; OPTIMIZATION CRITERIA; SCIENTIFIC COMMUNITY; SYSTEM IDENTIFICATIONS;

FUZZY NEURAL NETWORKS; FUZZY RULES; FUZZY SETS; FUZZY SYSTEMS; OPTIMIZATION; SOFT COMPUTING;

FUZZY LOGIC;

EID: 79955551124     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2011.03.004     Document Type: Review

References (170)

1. R. Alcalá, J. Alcalá-Fdez, J. Casillas, O. Cordón, and F. Herrera Hybrid learning models to get the interpretability-accuracy trade-off in fuzzy modelling Soft Computing 10 9 2006 717 734 (Pubitemid 43615677)
2. R. Alcalá, J. Alcalá-Fdez, M.J. Gacto, and F. Herrera Rule base reduction and genetic tuning of fuzzy systems based on the linguistic 3-tuples representation Soft Computing 11 5 2007 401 419 (Pubitemid 44964060)
3. R. Alcalá, J. Alcalá-Fdez, M.J. Gacto, and F. Herrera Improving fuzzy logic controllers obtained by experts: a case study in HVAC systems Applied Intelligence 31 1 2009 15 30
4. R. Alcalá, J. Alcalá-Fdez, and F. Herrera A proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection IEEE Transactions on Fuzzy Systems 15 4 2007 616 635 (Pubitemid 47321552)
5. R. Alcalá, J. Alcalá-Fdez, F. Herrera, and J. Otero Genetic learning of accurate and compact fuzzy rule based systems based on the 2-tuples linguistic representation International Journal of Approximate Reasoning 44 1 2007 45 64
6. R. Alcalá, J.R. Cano, O. Cordón, F. Herrera, and P. Villar Linguistic modeling with hierarchical systems of weighted linguistic rules International Journal of Approximate Reasoning 32 2-3 2003 187 215
7. R. Alcalá, J. Casillas, O. Cordón, A. González, and F. Herrera A genetic rule weighting and selection process for fuzzy control of heating, ventilating and air conditioning systems Engineering Applications of Artificial Intelligence 18 3 2005 279 296 (Pubitemid 40339978)
8. R. Alcalá, J. Casillas, O. Cordón, and F. Herrera Fuzzy graphs: features and taxonomy of learning methods for non-grid oriented fuzzy rule-based systems International Journal of Intelligent Fuzzy Systems 11 2001 99 119 (Pubitemid 33665383)
9. R. Alcalá, J. Casillas, O. Cordón, and F. Herrera Applying rule weight derivation to obtain cooperative rules J.M. Benítez, O. Cordón, F. Hoffmann, R. Roy, Advances in Soft Computing. Engineering Design and Manufacturing 2003 Springer 139 147
10. R. Alcalá, J. Casillas, O. Cordón, and F. Herrera Linguistic modeling with weighted double-consequent fuzzy rules based on cooperative coevolutionary learning Integrated Computer Aided Engineering 10 4 2003 343 355
11. R. Alcalá, P. Ducange, F. Herrera, B. Lazzerini, and F. Marcelloni A multi-objective evolutionary approach to concurrently learn rule and data bases of linguistic fuzzy rule-based systems IEEE Transactions on Fuzzy Systems 17 5 2009 1106 1122
12. R. Alcalá, M.J. Gacto, F. Herrera, A fast and scalable multi-objective genetic fuzzy system for linguistic fuzzy modeling in high-dimensional regression problems, IEEE Transactions on Fuzzy Systems, in press. doi:10.1109/TFUZZ.2011.2131657.
13. R. Alcalá, M.J. Gacto, F. Herrera, and J. Alcalá-Fdez A multi-objective genetic algorithm for tuning and rule selection to obtain accurate and compact linguistic fuzzy rule-based systems International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15 5 2007 45 64
14. J.M. Alonso, L. Magdalena, Combining userGs preferences and quality criteria into a new index for guiding the design of fuzzy systems with a good interpretability-accuracy trade-off, in: Proceedings of the 2010 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2010), Barcelona, Spain, 2010, pp. 961-968.
15. J.M. Alonso, L. Magdalena, O. Cordón, Embedding hilk into a three-objective evolutionary algorithm with the aim of modeling highly interpretable fuzzy rule-based classifiers, in: Proceedings of the Fourth International Workshop on Genetic and Evolutionary Fuzzy Systems (GEFS 2010), Mieres, Spain, 2010, pp. 15-20.
16. J.M. Alonso, L. Magdalena, and G. González-Rodríguez Looking for a good fuzzy system interpretability index: an experimental approach International Journal of Approximate Reasoning 51 1 2009 115 134
17. J.M. Alonso, L. Magdalena, and S. Guillaume HILK: a new methodology for designing highly interpretable linguistic knowledge bases using the fuzzy logic formalism International Journal of Intelligent Systems 23 7 2008 761 794
18. M. Antonelli, P. Ducange, B. Lazzerini, and F. Marcelloni Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework International Journal of Approximate Reasoning 50 7 2009 1066 1080
19. M. Antonelli, P. Ducange, B. Lazzerini, and F. Marcelloni Multi-objective evolutionary learning of granularity, membership function parameters and rules of Mamdani fuzzy systems Evolutionary Intelligence 2 1-2 2009 21 37
20. M. Antonelli, P. Ducange, B. Lazzerini, F. Marcelloni, Exploiting a three-objective evolutionary algorithm for generating Mamdani fuzzy rule-based systems, in: Proceedings of the 2010 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2010), Barcelona, Spain, 2010, pp. 1373-1380.
21. M. Antonelli, P. Ducange, F. Marcelloni, Exploiting a coevolutionary approach to concurrently select training instances and learn rule bases of Mamdani fuzzy systems, in: Proceedings of the 2010 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2010), Barcelona, Spain, 2010, pp. 1366-1372.
22. A. Bardossy, and L. Duckstein Fuzzy Rule-Based Modeling with Application to Geophysical, Biological and Engineering Systems 1995 CRC Press
23. A. Bastian How to handle the flexibility of linguistic variables with applications International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 3 4 1994 463 484
24. A. Ben-Tal, L.E. Ghaoui, and A. Nemirovski Special issue on robust optimization Mathematical Programming 107 1-2 2006
25. F.J. Berlanga, A.J. Rivera, M.J. del Jesus, and F. Herrera GP-COACH: genetic programming based learning of compact and accurate fuzzy rule based classification systems for high dimensional problems Information Sciences 180 8 2010 1183 1200
26. P.P. Bonissone Foreword J. Casillas, O. Cordón, F. Herrera, L. Magdalena, Accuracy Improvements in Linguistic Fuzzy Modeling 2003 Springer V VII
27. P.P. Bonissone, P.S. Khedkar, Y. Chen, Genetic algorithms for automated tuning of fuzzy controllers: a transportation application, in: Proceedings of the Fifth IEEE International Conference on Fuzzy Systems (FUZZ-IEEE'96), New Orleans, USA, 1996, pp. 674-680.
28. A. Botta, B. Lazzerini, and F. Marcelloni Context adaptation of Mamdani fuzzy rule based systems International Journal of Intelligent Systems 23 4 2008 397 418 (Pubitemid 351518421)
29. A. Botta, B. Lazzerini, F. Marcelloni, and D.C. Stefanescu Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index Soft Computing 13 5 2009 437 449
30. R. Cannone, J.M. Alonso, L. Magdalena, Multi-objective design of highly interpretable fuzzy rule-based classifiers with semantic cointension, in: Proceedings of the Fifth IEEE International Workshop on Genetic and Evolutionary Fuzzy Systems (GEFS 2011), Paris, France, in press.
31. J. Casillas, O. Cordón, M.J. del Jesus, and F. Herrera Genetic tuning of fuzzy rule deep structures preserving interpretability for linguistic modeling IEEE Transactions on Fuzzy Systems 13 1 2005 13 29 (Pubitemid 40319306)
32. J. Casillas, O. Cordón, F. Herrera, A cooperative coevolutionary algorithm for jointly learning fuzzy rule bases and membership functions, in: Proceedings of the Second International Conference in Fuzzy Logic and Technology (EUSFLAT 2001), Leicester, UK, 2001, pp. 118-121.
33. J. Casillas, O. Cordón, and F. Herrera COR: a methodology to improve ad hoc data-driven linguistic rule learning methods by inducing cooperation among rules IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 32 4 2002 526 537
34. J. Casillas, O. Cordón, F. Herrera, and L. Magdalena Accuracy Improvements in Linguistic Fuzzy Modeling 2003 Springer
35. J. Casillas, O. Cordón, F. Herrera, and L. Magdalena Accuracy improvements to find the balance interpretability-accuracy in linguistic fuzzy modeling: an overview J. Casillas, O. Cordón, F. Herrera, L. Magdalena, Accuracy Improvements in Linguistic Fuzzy Modeling 2003 Springer 3 24
36. J. Casillas, O. Cordón, F. Herrera, and L. Magdalena Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview J. Casillas, O. Cordón, F. Herrera, L. Magdalena, Interpretability Issues in Fuzzy Modeling 2003 Springer 3 22
37. J. Casillas, O. Cordón, F. Herrera, and L. Magdalena Interpretability Issues in Fuzzy Modeling 2003 Springer
38. J. Casillas, L. Sánchez, Knowledge extraction from fuzzy data for estimating consumer behavior models, in: Proceedings of the 2006 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2006), Vancouver, Canada, 2006, pp. 572-578.
39. L. Castillo, A. González, and R. Pérez Including a simplicity criterion in the selection of the best rule in a fuzzy genetic learning algorithm Fuzzy Sets and Systems 120 2 2001 309 321 (Pubitemid 32407905)
40. J.S. Cho, and D.J. Park Novel fuzzy logic control based on weighting of partially inconsistent rules using neural network International Journal of Intelligent and Fuzzy Systems 8 2 2000 99 110
41. M. Cococcioni, P. Ducange, B. Lazzerini, and F. Marcelloni A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems Soft Computing 11 11 2007 1013 1031 (Pubitemid 46865424)
42. C.C. Coello, G.B. Lamont, and D.A. Van Veldhuizen Evolutionary Algorithms for Solving Multi-objective Problems second ed. 2007 Springer
43. O. Cordón, M.J. del Jesus, and F. Herrera Genetic learning of fuzzy rule-based classification systems cooperating with fuzzy reasoning methods International Journal of Intelligent Systems 13 10-11 1998 1025 1053 (Pubitemid 128608590)
44. O. Cordón, M.J. del Jesus, and F. Herrera A proposal on reasoning methods in fuzzy rule-based classification systems International Journal of Approximate Reasoning 20 1999 21 45
45. O. Cordón, M.J. del Jesús, F. Herrera, and M. Lozano MOGUL: a methodology to obtain genetic fuzzy rule-based systems under the iterative rule learning approach International Journal of Intelligent Systems 14 11 1999 1123 1153 (Pubitemid 30547150)
46. O. Cordón, M.J. del Jesus, F. Herrera, P. Villar, A multiobjective genetic algorithm for feature selection and granularity learning in fuzzy-rule based classification systems, in: Proceedings of the Joint 9th IFSA World Congress and 20th NAFIPS International Conference (IFSA-NAFIPS 2001), vol. 3, Vancouver, Canada, pp. 1253-1258.
47. O. Cordón, M.J. del Jesus, F. Herrera, and P. Villar A multiobjective genetic learning process for joint feature selection and granularity and contexts learning in fuzzy rule-based classification systems J. Casillas, O. Cordón, F. Herrera, L. Magdalena, Interpretability Issues in Fuzzy Modeling 2003 Springer 79 99
48. O. Cordón, and F. Herrera A three-stage evolutionary process for learning descriptive and approximate fuzzy logic controller knowledge bases from examples International Journal of Approximate Reasoning 17 4 1997 369 407 (Pubitemid 127403031)
49. O. Cordón, and F. Herrera A proposal for improving the accuracy of linguistic modeling IEEE Transactions on Fuzzy Systems 8 3 2000 335 344
50. O. Cordón, F. Herrera, L. Magdalena, and P. Villar A genetic learning process for the scaling factors, granularity and contexts of the fuzzy rule-based system data base Information Sciences 136 1-4 2001 85 107 (Pubitemid 32621496)
51. O. Cordón, F. Herrera, and A. Peregrín Applicability of the fuzzy operators in the design of fuzzy logic controllers Fuzzy Sets and Systems 86 1997 15 41 (Pubitemid 127683597)
52. O. Cordón, F. Herrera, and P. Villar Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base IEEE Transactions on Fuzzy Systems 9 4 2001 667 674 (Pubitemid 32933051)
53. O. Cordón, F. Gomide, F. Herrera, F. Hoffmann, and L. Magdalena Ten years of genetic fuzzy systems: current framework and new trends Fuzzy Sets and Systems 141 1 2004 5 31
54. O. Cordón, F. Herrera, F. Hoffmann, and L. Magdalena Genetic fuzzy systems Evolutionary Tuning and Learning of Fuzzy Knowledge Bases 2001 World Scientific
55. O. Cordón, F. Herrera, and I. Zwir Linguistic modeling by hierarchical systems of linguistic rules IEEE Transactions on Fuzzy Systems 10 1 2002 2 20 (Pubitemid 34291665)
56. I. Couso, and L. Sánchez Higher order models for fuzzy random variables Fuzzy Sets and Systems 159 3 2008 237 258 (Pubitemid 350086691)
57. M.A. De Vega, J.M. Bardallo, F.A. Mrquez, A. Peregrín, Parallel distributed two-level evolutionary multiobjective methodology for granularity learning and membership functions tuning in linguistic fuzzy systems, in: Proceedings of the 9th International Conference on Intelligent Systems Design and Applications (ISDA2009), Pisa, Italy, 2009, pp. 134-139.
58. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan A fast and elitist multiobjective genetic algorithm: NSGA-II IEEE Transactions on Evolutionary Computation 6 2 2002 182 197 (Pubitemid 34555372)
59. K. DeJong Learning with genetic algorithms: an overview Machine Learning 3 3 1988 121 138
60. D. Driankov, and H. Hellendoorn Fuzzy Model Identification. Selected Approaches 1997 Springer-Verlag
61. D. Driankov, H. Hellendoorn, and M. Reinfrank An Introduction to Fuzzy Control 1993 Springer-Verlag
62. P. Ducange, B. Lazzerini, and F. Marcelloni Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets Soft Computing 14 7 2010 713 728
63. A.E. Eiben, and J.E. Smith Introduction to Evolutionary Computing 2003 Springer-Verlag
64. L. Eshelman The CHC adaptive search algorithm: how to safe search when engaging in non traditional genetic recombination G. Rawlins, Foundations of Genetic Algorithms 1991 Morgan Kaufmann 265 283
65. L. Eshelman, and J. Schaffer Real-coded genetic algorithms and interval-schemata L.D. Whitley, Foundations of Genetic Algorithms 2 1993 Morgan Kaufmann 187 202
66. J.J. Espinosa, and J. Vandewalle Constructing fuzzy models with linguistic integrity - AFRELI algorithm IEEE Transactions on Fuzzy Systems 8 5 1998 591 600
67. M. Fathi-Torbaghan, and L. Hildebrand Model-free optimization of fuzzy rule based systems using evolution strategies IEEE Transactions on Systems, Man and Cybernetics - Part B: Cybernetics 27 2 1997 270 277 (Pubitemid 127770660)
68. P. Fazendeiro, J. Valente de Oliveira, A working hypothesis on the semantics/accuracy synergy, in: Proceedings of the Joint Fourth Conference of the European Society for Fuzzy Logic and Technology and the Eleventh Rencontres Francophones sur la Logique Floue et ses Applications (EUSFLAT-LFA 2005), Barcelona, Spain, 2005, pp. 266-271.
69. A. Fernández, M.J. Gacto, and F. Herrera Hierarchical fuzzy rule based classification systems with genetic rule selection for imbalanced data-sets International Journal of Approximate Reasoning 50 3 2009 561 577
70. A. Fernández, F. Herrera, Linguistic fuzzy rules in data mining: follow-up Mamdani fuzzy modeling principle, in: E. Trillas, P.P. Bonissone, L. Magdalena, J. Kacprycz, (Eds.), Combining Experimentation and Theory. A Hommage to Abe Mamdani, Springer, in press.
71. C.M. Fonseca, P.J. Fleming, Genetic algorithms for multiobjective optimization: formulation, discussion and generalization, in: Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA'93), Urbana-Champaign, IL, USA, 1993, pp. 416-423.
72. M.J. Gacto, R. Alcalá, and F. Herrera Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems Soft Computing 13 5 2009 419 436
73. M.J. Gacto, R. Alcalá, and F. Herrera Integration of an index to preserve the semantic interpretability in the multi-objective evolutionary rule selection and tuning of linguistic fuzzy systems IEEE Transactions on Fuzzy Systems 18 3 2010 515 531
74. M.J. Gacto, R. Alcalá, F. Herrera, Interpretability of linguistic fuzzy rule-based systems: an overview of interpretability measures, Information Sciences, in press. doi:10.1016/j.ins.2011.02.021.
75. M.J. Gacto, R. Alcalá, F. Herrera, A multi-objective evolutionary algorithm for an effective tuning of fuzzy logic controllers in heating, ventilating and air conditioning systems, Applied Intelligence, in press. doi:10.1007/s10489-010-0264-x.
76. A. Geyer-Schulz Fuzzy Rule-Based Expert Systems and Genetic Machine Learning 1995 Physica-Verlag Heidelberg
77. P.Y. Glorennec Coordination between autonomous robots International Journal of Approximate Reasoning 17 4 1997 433 446
78. A. González, and R. Pérez a genetic learning system based on an iterative approach IEEE Transactions on Fuzzy Systems 7 2 1999 176 191
79. A. González, and R. Pérez A study about the inclusion of linguistic hedges in a fuzzy rule learning algorithm International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 7 3 1999 257 266 (Pubitemid 129628520)
80. R. Gudwin, F. Gomide, and W. Pedrycz Context adaptation in fuzzy processing and genetic algorithms International Journal of Intelligent Systems 13 10/11 1998 929 948 (Pubitemid 128608585)
81. S. Guillaume Designing fuzzy inference systems from data: an interpretability-oriented review IEEE Transactions on Fuzzy Systems 9 3 2001 426 443 (Pubitemid 32636660)
82. H.B. Gurocak A genetic-algorithm-based method for tuning fuzzy logic controllers Fuzzy Sets and Systems 108 1 1999 39 47 (Pubitemid 30498249)
83. Y. Hamada, Y. Nojima, and H. Ishibuchi Use of multi-objective genetic rule selection for examining the effectiveness of inter-vehicle communication in traffic simulations Artificial Life and Robotics 14 3 2009 410 413
84. U.D. Hanebeck, and G.K. Schmidt Genetic optimization of fuzzy networks Fuzzy Sets and Systems 79 1 1996 59 68 (Pubitemid 126667391)
85. F. Herrera Genetic fuzzy systems: taxonomy, current research trends and prospects Evolutionary Intelligence 1 1 2008 27 46
86. F. Herrera, and L. Martínez A 2-tuple fuzzy linguistic representation model for computing with words IEEE Transactions on Fuzzy Systems 8 6 2000 746 752
87. A. Homaifar, and E. Mccormick Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms IEEE Transactions on Fuzzy Systems 3 2 1995 129 139
88. H. Ishibuchi, Multiobjective genetic fuzzy systems: review and future research directions, in: Proceedings of the 2007 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2007), London, UK, 2007, pp. 1-6.
89. H. Ishibuchi, and T. Murata A genetic-algorithm-based fuzzy partition method for pattern classification problems F. Herrera, J.L. Verdegay, Genetic Algorithms and Soft Computing. No. 8 in Studies in Fuzziness and Soft Computing 1996 Physica-Verlag 555 578
90. H. Ishibuchi, T. Murata, and I.B. Türksen Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems Fuzzy Sets and Systems 89 2 1997 135 150 (Pubitemid 127683667)
91. H. Ishibuchi, T. Nakashima, T. Murata, A fuzzy classifier system that generates fuzzy if-then rules for pattern classification problems, in: Proceedings of the 1995 IEEE international Conference on Evolutionary Computation (CEC'95), Perth, Australia, 1995, pp. 759-764.
92. H. Ishibuchi, T. Nakashima, and T. Murata Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems IEEE Transactions on Systems, Man and Cybernetics - Part B: Cybernetics 29 5 1999 601 618
93. H. Ishibuchi, T. Nakashima, and T. Murata Three-objective genetics-based machine learning for linguistic rule extraction Information Sciences 136 1-4 2001 109 133 (Pubitemid 32621497)
94. H. Ishibuchi, T. Nakashima, and M. Nii Classification and Modeling with Linguistic Information Granules: Advanced Approaches to Linguistic Data Mining 2004 Springer-Verlag
95. H. Ishibuchi, and Y. Nojima Evolutionary multiobjective optimization for the design of fuzzy rule-based ensemble classifiers International Journal of Hybrid Intelligent Systems 3 3 2006 129 145
96. H. Ishibuchi, and Y. Nojima Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning International Journal of Approximate Reasoning 44 1 2007 4 31
97. H. Ishibuchi, K. Nozaki, N. Yamamoto, and H. Tanaka Selecting fuzzy if-then rules for classification problems using genetic algorithms IEEE Transactions on Fuzzy Systems 3 3 1995 260 270
98. H. Ishibuchi, T. Tsukamoto, Y. Nojima, Evolutionary many-objective optimization: a short review, in: Proceedings of the 2008 IEEE international Conference on Evolutionary Computation (CEC 2008), Hong Kong, China, 2008, pp. 2424-2431.
99. H. Ishibuchi, and T. Yamamoto Fuzzy rule selection by multiobjective genetic local search algorithms and rule evaluation measures in data mining Fuzzy Sets and Systems 141 1 2004 59 88
100. H. Ishibuchi, T. Yamamoto, and T. Nakashima Hybridization of fuzzy GBML approaches for pattern classification problems IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 35 2 2005 359 365 (Pubitemid 40535918)
101. Y. Jin Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement IEEE Transactions on Fuzzy Systems 8 2 2000 212 221
102. 3 fuzzy rule systems from data using evolutionary strategies IEEE Transactions on Systems, Man and Cybernetics - Part B: Cybernetics 29 6 1999 829 845 (Pubitemid 32211619)
103. C. Karr Genetic algorithms for fuzzy controllers AI Expert 6 2 1991 26 33
104. C. Karr, and E.J. Gentry Fuzzy control of pH using genetic algorithms IEEE Transactions on Fuzzy Systems 1 1 1993 46 53
105. J.D. Knowles, and D.W. Corne Approximating the non dominated front using the Pareto archived evolution strategy Evolutionary Computation 8 2 2000 149 172
106. M. Koeppen, K. Franke, B. Nickolay, Fuzzy-Pareto-dominance driven multi-objective genetic algorithm, in: Proceedings of the Tenth International Fuzzy Systems Association World Congress (IFSA 2003), Istanbul, Turkey, 2003, pp. 450-453.
107. L.I. Kuncheva Fuzzy Classifier Design No. 49 in Studies in Fuzziness and Soft Computing 2000 Physica-Verlag
108. P. Limbourg, Multi-objective optimization of problems with epistemic uncertainty, in: Proceedings of the Third International Conference on Evolutionary Multi-Criterion Optimization (EMO'05), Guanajuato, Mexico, 2005, pp. 413-427. (Pubitemid 41251780)
109. B.-D. Liu, C.-Y. Chen, and J.-Y. Tsao Design of adaptive fuzzy logic controller based on linguistic-hedge concepts and genetic algorithms IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 31 1 2001 32 53 (Pubitemid 32286790)
110. L. Magdalena Adapting the gain of an FLC with genetic algorithms International Journal of Approximate Reasoning 17 4 1997 327 349 (Pubitemid 127403029)
111. L. Magdalena, and F. Monasterio A fuzzy logic controller with learning through the evolution of its knowledge base International Journal of Approximate Reasoning 16 3/4 1997 335 358 (Pubitemid 127418357)
112. E.H. Mamdani Applications of fuzzy algorithm for control a simple dynamic plant Proceedings of the IEE 121 12 1974 1585 1588
113. E.H. Mamdani, and S. Assilian An experiment in linguistic synthesis with a fuzzy logic controller International Journal of Man-Machine Studies 7 1975 1 13
114. S. Medasani, J. Kim, and S. Krishnapuram An overview of membership function generation techniques for pattern recognition International Journal of Approximate Reasoning 19 3-4 1998 391 417 (Pubitemid 128426488)
115. C. Mencar, G. Castellano, and A.M. Fanelli Distinguishability quantification of fuzzy sets Information Sciences 177 1 2007 130 149 (Pubitemid 44556694)
116. C. Mencar, C. Castiello, R. Cannone, and A.M. Fanelli Interpretability assessment of fuzzy knowledge bases: a cointension based approach International Journal of Approximate Reasoning 52 4 2011 501 518
117. C. Mencar, and A.M. Fanelli Interpretability constraints for fuzzy information granulation Information Sciences 178 24 2008 4585 4618
118. R. Mikut, J. Jakel, and L. Groll Interpretability issues in data-based learning of fuzzy systems Fuzzy Sets and Systems 150 2005 179 197 (Pubitemid 40056017)
119. R. Muñoz-Salinas, E. Aguirre, O. Cordón, and M. García-Silvente Automatic tuning of a fuzzy visual system using evolutionary algorithms: single-objective vs. multiobjective approaches IEEE Transactions on Fuzzy Systems 16 2 2008 485 501 (Pubitemid 351586047)
120. D. Nauck, F. Klawoon, and R. Kruse Foundations of Neuro-Fuzzy Systems 1997 John Willey & Sons
121. D.D. Nauck, R. Kruse, How the learning of rule weights affects the interpretability of fuzzy systems, in: Proceedings of the 7th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE'98), IEEE Press, Anchorage, USA, 1998, pp. 1235-1240.
122. K.C. Ng, Y. Li, Design of sophisticated fuzzy logic controllers using genetic algorithms, in: Proceedings of the Third IEEE International Conference on Fuzzy Systems (FUZZ-IEEE'94), vol. 3, Orlando, FL, USA, 1994, pp. 1708-1712.
123. Y. Nojima, H. Ishibuchi, Effects of data reduction on the generalization ability of parallel distributed genetic fuzzy rule selection, in: Proceedings of the 9th International Conference on Intelligent Systems Design and Applications (ISDA2009), Pisa, Italy, 2009, pp. 96-101.
124. Y. Nojima, and H. Ishibuchi Incorporation of user preference into multi-objective genetic fuzzy rule selection for pattern classification problems Artificial Life and Robotics 14 3 2009 418 421
125. Y. Nojima, S. Mihara, H. Ishibuchi, Parallel distributed implementation of genetics-based machine learning for fuzzy classifier design, in: Proceedings of the 8th International Conference on Simulated Evolution and Learning (SEAL2010), Kanpur, India, 2010, pp. 309-318.
126. K. Nozaki, H. Ishibuchi, and H. Tanaka A simple but powerful heuristic method for generating fuzzy rules from numerical data Fuzzy Sets and Systems 86 1997 251 270 (Pubitemid 127683579)
127. N.R. Pal, and K. Pal Handling of inconsistent rules with an extended model of fuzzy reasoning Journal of Intelligent and Fuzzy Systems 7 1 1999 55 73
128. A.M. Palacios, L. Sánchez, and I. Couso Diagnosis of dyslexia with low quality data with genetic fuzzy systems International Journal on Approximate Reasoning 51 8 2010 993 1009
129. A.M. Palacios, L. Sánchez, and I. Couso Extending a simple cooperative-competitive learning fuzzy classifier to low quality datasets Evolutionary Intelligence 2 1-2 2010 73 84
130. A.M. Palacios, L. Sánchez, and I. Couso Future performance modelling in athletism with low quality data-based GFSs Journal of Multivalued Logic and Soft Computing 17 2-3 2011 207 228
131. D. Park, A. Kandel, and G. Langholz Genetic-based new fuzzy reasoning models with application to fuzzy control IEEE Transactions on Systems, Man, and Cybernetics 24 1 1994 39 47
132. W. Pedrycz Fuzzy Modelling: Paradigms and Practice 1996 Kluwer Academic Press
133. C.A. Peña-Reyes, and M. Sipper Fuzzy CoCo: a cooperative- coevolutionary approach to fuzzy modeling IEEE Transactions on Fuzzy Systems 9 5 2001 727 737 (Pubitemid 33106021)
134. M. Potter, and K.D. Jong Cooperative coevolution: an architecture for evolving coadapted subcomponents Evolutionary Computation 8 1 2000 1 29
135. P. Pulkkinen, J. Hytonen, and H. Koivisto Developing a bioaerosol detector using hybrid genetic fuzzy systems Engineering Applications of Artificial Intelligence 21 8 2008 1330 1346
136. P. Pulkkinen, and H. Koivisto Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms International Journal of Approximate Reasoning 48 2 2008 526 543 (Pubitemid 351602157)
137. R.C. Purshouse, and P.J. Fleming On the evolutionary optimisation of many conflicting objectives IEEE Transactions on Evolutionary Computation 11 6 2007 770 784 (Pubitemid 350187490)
138. I. Robles, R. Alcal, J.M. Benítez, and F. Herrera Evolutionary parallel and gradually distributed lateral tuning of fuzzy rule-based systems Evolutionary Intelligence 2 1-2 2009 5 19
139. E.H. Ruspini A new approach to clustering Information and Control 15 1 1969 22 32
140. T.L. Saaty How to make a decision: the analytic hierarchy process European Journal of Operational Research 48 1 1990 9 26
141. L. Sánchez, J. Casillas, O. Cordón, and M.J. del Jesus Some relationships between fuzzy and random classifiers and models International Journal of Approximate Reasoning 29 2 2002 175 213 (Pubitemid 34086637)
142. L. Sánchez, and I. Couso Advocating the use of imprecisely observed data in genetic fuzzy systems IEEE Transactions on Fuzzy Systems 15 4 2007 551 562 (Pubitemid 47316709)
143. L. Sánchez, I. Couso, Obtaining fuzzy rules from interval-censored data with genetic algorithms and a random sets-based semantic of the linguistic labels, Soft Computing, in press, doi:10.1007/s00500-010-0627-6.
144. L. Sánchez, I. Couso, J. Casillas, Modelling vague data with genetic fuzzy systems under a combination of crisp and imprecise criteria, in: Proceedings of the 2007 IEEE Symposium on Computational Intelligence in Multicriteria Decision Making (MCDM 2007), Honolulu, USA, 2007, pp. 30-37. (Pubitemid 47431757)
145. L. Sánchez, I. Couso, and J. Casillas Genetic learning of fuzzy rules based on low quality data Fuzzy Sets and Systems 160 17 2009 2524 2552
146. L. Sánchez, J. Otero, and I. Couso Obtaining linguistic fuzzy rule-based regression models from imprecise data with multiobjective genetic algorithms Soft Computing 13 3 2009 307 318
147. L. Sánchez, J. Otero, J.R. Villar, Boosting of fuzzy models for high-dimensional imprecise datasets, in: Proceedings of the Eleventh International Conference on Information Processing and Management (IPMU 2006), Paris, France, 2006, pp. 1965-1973.
148. M. Setnes, R. Babuska, and H.B. Verbruggen Rule-based modeling: precision and transparency IEEE Transactions on Systems, Man, and Cybernetics - Part C: Applications and Reviews 28 1 1998 165 169 (Pubitemid 128748617)
149. C. Setzkorn, and R.C. Paton On the use of multi-objective evolutionary algorithms for the induction of fuzzy classification rule systems BioSystems 81 2 2005 101 112 (Pubitemid 40966131)
150. T. Söderström, and P. Stoica System Identification 1989 Prentice Hall Englewood Cliffs, NJ, USA
151. M. Sugeno, and G.T. Kang Structure identification of fuzzy model Fuzzy Sets and Systems 28 1 1988 15 33
152. M. Sugeno, and T. Yasukawa A fuzzy-logic-based approach to qualitative modeling IEEE Transactions on Fuzzy Systems 1 1 1993 7 31
153. T. Takagi, and M. Sugeno Fuzzy identification of systems and its application to modeling and control IEEE Transactions on Systems, Man, and Cybernetics 15 1 1985 116 132
154. J. Teich, Pareto-front exploration with uncertain objectives, in: Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO'01), Zurich, Switzerland, 2001, pp. 314-328. (Pubitemid 33241396)
155. J. Valente de Oliveira Semantic constraints for membership functions optimization IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans 29 1999 128 138
156. M. Valenzuela-Rendón The fuzzy classifier system: motivations and first results H.P. Schwefel, R. Männer, Proceedings of the First International Conference on Parallel Problem Solving from Nature (PPSN I) 1991 Springer-Verlag Berlin 330 334
157. E. Van Broekhoven, V. Adriaenssens, and B. De Baets 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 2007 65 90 (Pubitemid 44802831)
158. J.R. Villar, A. Otero, J. Otero, and L. Sánchez Taximeter verification using imprecise data from GPS and multiobjective algorithms Engineering Applications of Applied Intelligence 22 2 2009 250 260
159. J.R. Villar, A. Otero, J. Otero, and L. Sánchez Taximeter verification with GPS and soft computing techniques Soft Computing 14 4 2009 405 418
160. A. Wald Statistical decision functions which minimize the maximum risk The Annals of Mathematics 46 2 1945 265 280
161. C.H. Wang, T.P. Hong, and S.S. Tseng Integrating fuzzy knowledge by genetic algorithms IEEE Transactions on Evolutionary Computation 2 4 1998 138 149
162. H. Wang, S. Kwong, Y. Jin, W. Wei, and K.F. Man Agent-based evolutionary approach for interpretable rule-based knowledge extraction IEEE Transactions on Systems, Man, and Cybernetics - Part C 35 2 2005 143 155 (Pubitemid 40654428)
163. L.X. Wang, and J.M. Mendel Generating fuzzy rules by learning from examples IEEE Transactions on Systems, Man, and Cybernetics 22 6 1992 1414 1427
164. R.R. Yager, and J. Kacprzyk The Ordered Weighted Averaging Operators: Theory and Applications 1997 Kluwer Academic Publishers
165. L.A. Zadeh A fuzzy-set-theoretic interpretation of linguistic hedges Journal of Cybernetics 2 1972 4 34
166. L.A. Zadeh Outline of a new approach to the analysis of complex systems and decision processes IEEE Transactions on Systems, Man, and Cybernetics 3 1973 28 44
167. L.A. Zadeh The concept of a linguistic variable and its applications to approximate reasoning - Parts I, II and III Information Sciences 1975 8 9 199-249, 301-357, 43-80
168. S.-M. Zhou, and J.Q. Gan Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling Fuzzy Sets and Systems 159 23 2008 3091 3131
169. E. Zitzler, M. Laumanns, L. Thiele, SPEA2: improving the strength Pareto evolutionary algorithm, in: Proceedings of the EUROGEN 2001 - Evolutionary Methods for Design, Optimisation and Control with Applications to Industrial Problems, 2001, pp. 19-26.
170. E. Zitzler, and L. Thiele Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach IEEE Transactions on Evolutionary Computation 3 4 1999 257 271 (Pubitemid 30544879)