A review of the application of multiobjective evolutionary fuzzy systems: Current status and further directions

IEEE Transactions on Fuzzy Systems

Volumn 21, Issue 1, 2013, Pages 45-65

  Fazzolari, Michela ^a   Alcala, Rafael ^a   Nojima, Yusuke ^b   Ishibuchi, Hisao ^b   Herrera, Francisco ^a  

^a UNIVERSITY OF GRANADA   (Spain)

^b Osaka City University   (Japan)

Author keywords

Accuracy interpretability tradeoff; fuzzy association rule mining; fuzzy control; fuzzy rule based systems (FRBSs); multiobjective evolutionary algorithms (EAs); multiobjective evolutionary fuzzy systems (MOEFSs)

Indexed keywords

EVOLUTIONARY FUZZY SYSTEMS; FUZZY ASSOCIATION RULE; FUZZY RULE-BASED SYSTEMS; INTERPRETABILITY; MULTI OBJECTIVE EVOLUTIONARY ALGORITHMS;

FUZZY CONTROL; GENETIC ALGORITHMS;

FUZZY SYSTEMS;

EID: 84864813509     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2012.2201338     Document Type: Article

References (136)

1. B. Kosko, "Fuzzy systems as universal approximators," IEEE Trans. Comput., vol. 43, no. 11, pp. 1329-1333, Nov. 1994.
2. D. Driankov, H. Hellendoorn, and M. Reinfrank, An Introduction to Fuzzy Control. London, U.K.: Springer-Verlag, 1993.
3. E. H. Mamdani and S. Assilian, "An experiment in linguistic synthesis with a fuzzy logic controller," Int. J. Man Mach. Stud., vol. 7, no. 1, pp. 1-13, 1975.
4. E. H. Mamdani, "Application of fuzzy algorithms for control of simple dynamic plant," Proc. IEEE, vol. 121, no. 12, pp. 1585-1588, Dec. 1974.
5. H. Ishibuchi, K. Nozaki, N. Yamamoto, and H. Tanaka, "Construction of fuzzy classification systems with rectangular fuzzy rules using genetic algorithms," Fuzzy Sets Syst., vol. 65, no. 2-3, pp. 237-253, 1994.
6. H. Ishibuchi, K. Nozaki, N. Yamamoto, and H. Tanaka, "Selecting fuzzy if-then rules for classification problems using genetic algorithms," IEEE Trans. Fuzzy Syst., vol. 3, no. 3, pp. 260-270, Aug. 1995.
7. H. Ishibuchi, T. Nakashima, and M. Nii, Classification and Modeling With Linguistic Information Granules: Advanced Approaches Advanced Approaches to Linguistic Data Mining. London, U.K.: Springer-Verlag, 2000.
8. L.Kuncheva, Fuzzy ClassifierDesign. London, U.K.: Springer-Verlag, 2000.
9. A. Bardossy and L. Duckstein, Fuzzy Rule-Based Modeling With Applications to Geophysical, Biological, and Engineering Systems. Boca Raton, FL: CRC, 1995.
10. O. Cord́on, F. Herrera, and P. Villar, "Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base," IEEE Trans. Fuzzy Syst., vol. 9, no. 4, pp. 667-674, Aug. 2001.
11. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst. Man Cybern., vol. SMC-15, no. 1, pp. 116-132, Feb. 1985.
12. R. Alcaĺa, J. Casillas, O. Cord́on, and F. Herrera, "Building fuzzy graphs: Features and taxonomy of learning for non-grid-oriented fuzzy rulebased systems," J. Intell. Fuzzy Syst., vol. 11, pp. 99-119, 2001.
13. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Boston, MA: Addison-Wesley, 1989.
14. J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. Cambridge, MA: MIT Press, 1992.
15. O. Cord́on, F. Herrera, F. Hoffmann, and L. Magdalena, Genetic Fuzzy Systems. Evolutionary Tuning and Learning of Fuzzy Knowledge Bases. Singapore: World Scientific, 2001.
16. F. Herrera, "Genetic fuzzy systems: Taxonomy, current research trends and prospects," Evol. Intell., vol. 1, pp. 27-46, 2008.
17. C. A. C. Coello, G. B. Lamont, and D. A. V. Veldhuizen, Evolutionary Algorithms for Solving Multi-Objective Problems. Secaucus, NJ: Springer-Verlag, 2007.
18. K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms. New York: Wiley, 2001.
19. H. Ishibuchi, T. Murata, and I. B. T̈urksen, "Single-objective and twoobjective genetic algorithms for selecting linguistic rules for pattern classification problems," Fuzzy Sets Syst., vol. 89, no. 2, pp. 135-150, 1997.
20. O. Cord'on, "A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: Designing interpretable genetic fuzzy systems," Int. J. Approx. Reason., vol. 52, no. 6, pp. 894-913, 2011.
21. S. Guillaume, "Designing fuzzy inference systems from data: An interpretability-oriented review," IEEE Trans. Fuzzy Syst., vol. 9, no. 3, pp. 426-443, Jun. 2001.
22. J. de Oliveira, "Semantic constraints for membership function optimization," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 29, no. 1, pp. 128-138, Jan. 1999.
23. M. Setnes, R. Babuska, and H. Verbruggen, "Rule-based modeling: Precision and transparency," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 28, no. 1, pp. 165-169, Feb. 1998.
24. C. Mencar, G. Castellano, and A. M. Fanelli, "Distinguishability quantification of fuzzy sets," Inf. Sci., vol. 177, no. 1, pp. 130-149, 2007.
25. 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 Syst., vol. 159, no. 23, pp. 3091-3131, 2008.
26. J. M. Alonso, L. Magdalena, and G. Gonźalez-Rodŕguez, "Looking for a good fuzzy system interpretability index: An experimental approach," Int. J. Approx. Reason., vol. 51, no. 1, pp. 115-134, 2009.
27. M. J. Gacto,R.Alcaĺa, and F.Herrera, "Interpretability of linguistic fuzzy rule-based systems: An overview of interpretability measures," Inf. Sci., vol. 181, no. 20, pp. 4340-4360, 2011.
28. M. Antonelli, P. Ducange, B. Lazzerini, and F. Marcelloni, "Learning concurrently data and rule bases of Mamdani fuzzy rule-based systems by exploiting a novel interpretability index," Soft Comput., vol. 15, pp. 1981-1998, 2011.
29. M. J. Gacto, R. Alcaĺa, and F. Herrera, "Integration of an index to preserve the semantic interpretability in the multiobjective evolutionary rule selection and tuning of linguistic fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 18, no. 3, pp. 515-531, Jun. 2010.
30. P. J. Fleming and R. C. Purshouse, "Evolutionary algorithms in control systems engineering: A survey," Control Eng. Pract., vol. 10, no. 11, pp. 1223-1241, 2002.
31. W. J. Frawley, G. Piatetsky-Shapiro, and C. J. Matheus, "Knowledge discovery in databases: An overview," in Knowledge Discovery in Databases. Cambridge, MA: AAAI/MIT Press, 1991, pp. 1-30.
32. U. Fayyad, G. Piatetsky-Shapiro, and P. Smyth, "From data mining to knowledge discovery in databases," AI Mag., vol. 17, pp. 37-54, 1996.
33. W. Kl̈osgen and J. M. Zytkow, "Subgroup discovery," in Handbook of Data Mining and Knowledge Discovery. New York: Addison-Wesley, 2005, pp. 354-367.
34. C. Zhang and S. Zhang, Association Rule Mining: Models and Algorithms. Berlin, Germany: Springer-Verlag, 2002.
35. M. Delgado, N. Marin, D. Sanchez, and M. A. Vila, "Fuzzy association rules:General model and applications," IEEE Trans. Fuzzy Syst., vol. 11, no. 2, pp. 214-225, Apr. 2003.
36. C. L. Karr and E. J. Gentry, "Fuzzy control of pH using genetic algorithms," IEEE Trans. Fuzzy Syst., vol. 1, no. 1, pp. 46-53, Feb. 1993.
37. F. Herrera, M. Lozano, and J. L. Verdegay, "Tuning fuzzy logic controllers by genetic algorithms," Int. J. Approx. Reason., vol. 12, no. 3-4, pp. 299-315, 1995.
38. O. Cord'on and F. Herrera, "A three-stage evolutionary process for learning descriptive and approximate fuzzy-logic-controller knowledge bases from examples," Int. J. Approx. Reason., vol. 17, no. 4, pp. 369-407, 1997.
39. R. Alcaĺa, J. Alcaĺa-Fdez, and F. Herrera, "A proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection," IEEE Trans. Fuzzy Syst., vol. 15, no. 4, pp. 616-635, Aug. 2007.
40. J. Alcaĺa-Fdez, F. Herrera, F. Ḿarquez, and A. Peregŕn, "Increasing fuzzy rules cooperation based on evolutionary adaptive inference systems: Research articles," Int. J. Intell. Syst., vol. 22, pp. 1035-1064, 2007.
41. R. Alcaĺa, M. J. Gacto, F. Herrera, and J. Alcaĺa-Fdez, "A multi-objective genetic algorithm for tuning and rule selection to obtain accurate and compact linguistic fuzzy rule-based systems," Int. J. Uncertainty Fuzz. Knowl. Based Syst., vol. 15, no. 5, pp. 539-557, 2007.
42. E. Zitzler,M. Laumanns, and L. Thiele, "SPEA2: Improving the strength Pareto evolutionary algorithm," Swiss Fed. Inst. Technol., Zurich, Switzerland, Tech. Rep. 103, 2001.
43. M. J. Gacto, R. Alcaĺa, and F. Herrera, "Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems," Soft Comput., vol. 13, no. 5, pp. 419-436, 2009.
44. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," IEEE Trans. Evol. Comput., vol. 6, no. 2, pp. 182-197, Apr. 2002.
45. P. Pulkkinen and H. Koivisto, "Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms," Int. J. Approx. Reason., vol. 48, no. 2, pp. 526-543, 2008.
46. K. Deb and R. B. Agrawal, "Simulated binary crossover for continuous search sSpace," Tech. Rep., Indian Inst. Technol., Kanpur, India, 1994.
47. P. Pulkkinen, J. Hytonen, and H. Kolvisto, "Developing a bioaerosol detector using hybrid genetic fuzzy systems," Eng. Appl. Artif. Intel., vol. 21, no. 8, pp. 1330-1346, 2008.
48. J. Kim, Y. Moon, and B. P. Zeigler, "Designing fuzzy net controllers using genetic algorithms," IEEE Control Syst. Mag., vol. 15, no. 3, pp. 66-72, Jun. 1995.
49. 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 Comput., vol. 13, no. 5, pp. 437-449, 2009.
50. A. A. Marquez, F. A. Marquez, andA. Peregrin, "Rule base and inference system cooperative learning of Mamdani fuzzy systems with multiobjective genetic algorithms," in Proc. Joint Int. Fuzzy Syst. Assoc. World Congr. 2009 Eur. Soc. Fuzzy Logic Technol. Conf., 2009, pp. 1045-1050.
51. A. A. Marquez, F. A. Marquez, and A. Peregrin, "A multi-objective evolutionary algorithm with an interpretability improvement mechanism for linguistic fuzzy systemswith adaptive defuzzification," in Proc. IEEE Int. Conf. Fuzzy Syst., Jul., 2010, pp. 1-7.
52. H. Ishibuchi, T. Murata, and M. Gen, "Performance evaluation of fuzzy rule-based classification systems obtained by multi-objective genetic algorithms," Comput. Ind. Eng., vol. 35, no. 3-4, pp. 575-578, 1998.
53. H. Ishibuchi and T. Yamamoto, "Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining," Fuzzy Sets Syst., vol. 141, no. 1, pp. 59-88, 2004.
54. H. Ishibuchi, T. Nakashima, and T. Murata, "Three-objective geneticsbased machine learning for linguistic rule extraction," Inf. Sci., vol. 136, no. 1-4, pp. 109-133, 2001.
55. L. Booker, "Intelligent behaviour as an adaption to the task environment," Ph.D. dissertation, Univ. Michigan, Ann Arbor, MI, 1982.
56. J. Holland and J. Reitman, "Cognitive systems based on adaptive algorithms," in Pattern Directed Inference Systems. New York: Academic, 1978, pp. 313-329.
57. S. Smith, "A learning system based on genetic adaptive algorithms," Ph.D. dissertation, Univ. Pittsburgh, Pittsburgh, PA, 1980.
58. H. Ishibuchi and Y. Nojima, "Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning," Int. J. Approx. Reason., vol. 44, no. 1, pp. 4-31, 2007.
59. H. Ishibuchi and Y. Nojima, "Evolutionary multiobjective optimization for the design of fuzzy rule-based ensemble classifiers," Int. J. Hybrid Intel. Syst., vol. 3, pp. 129-145, 2006.
60. C. Setzkorn and R. C. Paton, "On the use of multi-objective evolutionary algorithms for the induction of fuzzy classification rule systems," Biosyst., vol. 81, no. 2, pp. 101-112, 2005.
61. M. Cococcioni, P. Ducange, B. Lazzerini, and F. Marcelloni, "A Paretobased multi-objective evolutionary approach to the identification of Mamdani fuzzy systems," Soft Comput., vol. 11, no. 11, pp. 1013-1031, 2007.
62. J. D. Knowles and D.W. Corne, "Approximating the nondominated front using the Pareto Archived Evolution Strategy," Evol. Comput., vol. 8, no. 2, pp. 149-172, 2000.
63. P. Ducange, B. Lazzerini, and F. Marcelloni, "Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets," Soft Comput., vol. 14, no. 7, pp. 713-728, 2010.
64. O. Cord́on, M. J. del Jeśus, J. Casillas, F. Herrera, L. Magdalena, and P. Villar, "A multiobjective genetic learning process for joint feature selection and granularity and context learning in fuzzy rule-based classification systems," in Interpretability Issues in Fuzzy Modeling, J. Casillas, F. Herrera, O. Cord́on, and L. Magdalena, Eds. Secaucus NJ: Springer-Verlag, 2003, pp. 79-99.
65. R. Alcaĺa, P. Ducange, F. Herrera, B. Lazzerini, and F. Marcelloni, "A multiobjective evolutionary approach to concurrently learn rule and data bases of linguistic fuzzy-rule-based systems," IEEE Trans. Fuzzy Syst., vol. 17, no. 5, pp. 1106-1122, Oct. 2009.
66. F. Herrera and L. Martinez, "A 2-tuple fuzzy linguistic representation model for computing with words," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 746-752, Dec. 2000.
67. 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," Int. J. Approx. Reason., vol. 50, no. 7, pp. 1066-1080, 2009.
68. M. Antonelli, P. Ducange, B. Lazzerini, and F. Marcelloni, "Multiobjective evolutionary learning of granularity, membership function parameters and rules of Mamdani fuzzy systems," Evol. Intell., vol. 2, no. 1-2, pp. 21-37, 2009.
69. M. Antonelli, P. Ducange, B. Lazzerini, and F. Marcelloni, "Learning knowledge bases of multi-objective evolutionary fuzzy systems by simultaneously optimizing accuracy, complexity and partition integrity," Soft Comput., vol. 15, pp. 2335-2354, 2011.
70. J. Casillas, P. Martinez, and A. D. Benitez, "Learning consistent, complete and compact sets of fuzzy rules in conjunctive normal form for regression problems," Soft Comput., vol. 13, no. 5, pp. 451-465, 2009.
71. P. Pulkkinen and H. Koivisto, "A dynamically constrained multiobjective genetic fuzzy system for regression problems," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 161-177, Feb. 2010.
72. R. Alcaĺa, Y. Nojima, F. Herrera, and H. Ishibuchi, "Multiobjective genetic fuzzy rule selection of single granularity-based fuzzy classification rules and its interaction with the lateral tuning of membership functions," Soft Comput., vol. 15, no. 12, pp. 2303-2318, 2011.
73. R. Alcaĺa, M. J. Gacto, and F. Herrera, "A fast and scalable multiobjective genetic fuzzy system for linguistic fuzzy modeling in highdimensional regression problems," IEEE Trans. Fuzzy Syst., vol. 19, no. 4, pp. 666-681, Aug. 2011.
74. J. Alonso, L. Magdalena, and O. Cordon, "Embedding HILK in a threeobjective evolutionary algorithm with the aim of modeling highly interpretable fuzzy rule-based classifiers," in Proc. 4th IEEE Int. Workshop Genet. Evol. Fuzzy Syst., 2010, pp. 15-20.
75. J. M. Alonso, L. Magdalena, and G. Serge, "HILK: A new methodology for designing highly interpretable linguistic knowledge bases using the fuzzy logic formalism," Int. J. Intell. Syst., vol. 23, pp. 761-794, 2008.
76. P. Thrift, "Fuzzy logic synthesis with genetic algorithm," in Proc. 4th Int. Conf. Genet. Algorithms, 1991, pp. 509-513.
77. R. Cannone, J. Alonso, and L. Magdalena, "Multi-objective design of highly interpretable fuzzy rule-based classifiers with semantic cointension," in Proc. 5th IEEE Int. Workshop Genet. Evol. Fuzzy Syst., Apr., 2011, pp. 1-8.
78. R. Cannone, J.M. Alonso, and L.Magdalena, "An empirical study on interpretability indexes through multi-objective evolutionary algorithms," in Proc. Int. Conf. Fuzzy Logic. App., 2011, pp. 131-138.
79. H.Wang, S.Kwong,Y. Jin,W.Wei, andK. F.Man, "Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction," Fuzzy Sets Syst., vol. 149, no. 1, pp. 149-186, 2005.
80. M. R. Delgado, F. V. Zuben, and F. Gomide, "Hierarchical genetic fuzzy systems," Inf. Sci., vol. 136, no. 1-4, pp. 29-52, 2001.
81. C. M. Fonseca and P. J. Fleming, "Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization," in Proc. 5th Int. Conf. Genet. Algorithms, 1993, pp. 416-423.
82. Z.-Y. Xing, Y. Zhang, Y.-L. Hou, and L.-M. Jia, "On generating fuzzy systems based on Pareto multi-objective cooperative coevolutionary algorithm," Int. J. Control Autom. Syst., vol. 5, no. 4, pp. 444-455, 2007.
83. J. Paredis, "Coevolutionary computation," Artif. Life, vol. 2, no. 4, pp. 355-375, 1995.
84. J. Gonźalez, I. Rojas, H. Pomares, L. J. Herrera, A. Guilĺon, J. M. Palomares, and F. Rojas, "Improving the accuracy while preserving the interpretability of fuzzy function approximators by means of multi-objective evolutionary algorithms," Int. J. Approx. Reason., vol. 44, no. 1, pp. 32-44, 2007.
85. A. F. Ǵomez-Skarmeta, F. Jiḿenez, and G. Śanchez, "Improving interpretability in approximative fuzzy models via multiobjective evolutionary algorithms," Int. J. Intell. Syst., vol. 22, no. 9, pp. 943-969, 2007.
86. T. Chen and H. Chen, "Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks," IEEE Trans. Neural Networks, vol. 6, no. 4, pp. 904-910, Jul. 1995.
87. S. Elanayar V. T. and Y. Shin, "Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems," IEEE Trans. Neural Netw., vol. 5, no. 4, pp. 594-603, Jul. 1994.
88. O. Guenounou, A. Belmehdi, and B. Dahhou, "Multi-objective optimization of TSK fuzzy models," Expert Syst. Appl., vol. 36, no. 4, pp. 7416-7423, 2009.
89. M. Cococcioni, G. Corsini, B. Lazzerini, and F. Marcelloni, "Solving the ocean color inverse problem by using evolutionary multi-objective optimization of neuro-fuzzy systems," Int. J. Know. Based Intell. Eng. Syst., vol. 12, no. 5-6, pp. 339-355, 2008.
90. M. Cococcioni, B. Lazzerini, and F. Marcelloni, "On reducing computational overhead in multi-objective genetic Takagi-Sugeno fuzzy systems," Appl. Soft Comput., vol. 11, no. 1, pp. 675-688, 2011.
91. C. C. Lee, "Fuzzy logic in control systems: Fuzzy logic controller. I," IEEE Trans. Syst. Man Cybern., vol. 20, no. 2, pp. 404-418, Mar./Apr. 1990.
92. R. Alcaĺa, J. Alcaĺa-Fdez, M. J. Gacto, and F. Herrera, "Improving fuzzy logic controllers obtained by experts: A case study in HVAC systems," Appl. Intell., vol. 31, pp. 15-30, 2009.
93. M. J. Gacto, R. Alcaĺa, and F. Herrera, "A multi-objective evolutionary algorithm for an effective tuning of fuzzy logic controllers in heating, ventilating and air conditioning systems," Appl. Intell., vol. 36, no. 2, pp. 330-347, 2012.
94. F. Hoffmann, "Evolutionary algorithms for fuzzy control system design," Proc. IEEE, vol. 89, no. 9, pp. 1318-1333, Sep. 2001.
95. M. Jamshidi, R. A. Krohling, L. dos S. Coelho, and P. J. Fleming, Robust Control Systems with Genetic Algorithms. (Control Series). Boca Raton, FL: CRC, 2003.
96. A. S. Ahlawat and A. Ramaswamy, "Multiobjective optimal structural vibration control using fuzzy logic control system," J. Struct. Eng., vol. 127, no. 11, pp. 1330-1337, 2001.
97. A. S. Ahlawat and A. Ramaswamy, "Multi-objective optimal design of FLC driven hybrid mass damper for seismically excited structures," Earthquake Eng. Struct. Dyn., vol. 31, no. 7, pp. 1459-1479, 2002.
98. A. S. Ahlawat and A. Ramaswamy, "Multiobjective optimal FLC driven hybrid mass damper system for torsionally coupled, seismically excited structures," Earthquake Eng. Struct. Dyn., vol. 31, no. 12, pp. 2121-2139, 2002.
99. A. S. Ahlawat and A. Ramaswamy, "Multiobjective optimal fuzzy logic control system for response control of wind-excited tall buildings," J. Eng. Mech., vol. 130, no. 4, pp. 524-530, 2004.
100. A. S. Ahlawat and A. Ramaswamy, "Multiobjective optimal fuzzy logic controller driven active and hybrid control systems for seismically excited nonlinear buildings," J. Eng. Mech., vol. 130, no. 4, pp. 416-423, 2004.
101. A. J. Chipperfield, B. Bica, and P. J. Fleming, "Fuzzy scheduling control of a gas turbine aero-engine: A multiobjective approach," IEEE Trans. Ind. Electron., vol. 49, no. 3, pp. 536-548, Jun. 2002.
102. F. Jurado and M. Valverde, "Enhancing the electrical performance of a solid oxide fuel cell using multiobjective genetic algorithms," Renew. Energy, vol. 30, no. 6, pp. 881-902, 2005.
103. H.-S. Kim and P. N. Roschke, "Fuzzy control of base-isolation system using multi-objective genetic algorithm," Comput.-Aided Civ. Infrastruct. Eng., vol. 21, no. 6, pp. 436-449, 2006.
104. H.-S. Kim and P. N. Roschke, "GA-fuzzy control of smart base isolated benchmark building using supervisory control technique," Adv. Eng. Softw., vol. 38, no. 7, pp. 453-465, 2007.
105. D. A. Shook, P. N. Roschke, P.-Y. Lin, and C.-H. Loh, "GA-optimized fuzzy logic control of a large-scale building for seismic loads," Eng. Struct., vol. 30, no. 2, pp. 436-449, 2008.
106. R. Munoz-Salinas, E. Aguirre, O. Cord́on, and M. Garcia-Silvente, "Automatic tuning of a fuzzy visual system using evolutionary-algorithms: Single-objective versus multiobjective approaches," IEEE Trans. Fuzzy Syst., vol. 16, no. 2, pp. 485-501, Apr. 2008.
107. L. J. Eshelman and J. D. Schaffer, "Real-coded genetic algorithms and interval-schemata," Found. Genet. Algorithms, vol. 2, 1993, pp. 187-202.
108. D. Daum and N.Morel, "Identifying important state variables for a blind controller," Build. Environ., vol. 45, no. 4, pp. 887-900, 2010.
109. M. Ebner, P. Stalph, M. Michel, and R. Benz, "Evolutionary parameter optimization of a fuzzy controller which is used to control a sewage treatment plant," Water Sci. Technol., vol. 61, pp. 53-66, 2010.
110. A. L. Blumel, E. J. Hughes, and B. A.White, "Multi-objective evolutionary design of fuzzy autopilot controller," in EvolutionaryMulti- Criterion Optimization, E. Zitzler L. Thiele K. Deb C. Coello D. Corne, Eds., Berlin/Heidelberg, Germany: Springer-Verlag, 2001, pp. 668-680.
111. P. Stewart, D. A. Stone, and P. J. Fleming, "Design of robust fuzzy-logic control systems by multi-objective evolutionary methods with hardware in the loop," Eng. Appl. Artif. Intell., vol. 17, no. 3, pp. 275-284, 2004.
112. P. Fazendeiro, J. V. Oliveira, andW. Pedrycz, "A multiobjective design of a patient and anaesthetist-friendly neuromuscular blockade controller," IEEE Trans. Biomed. Eng., vol. 54, no. 9, pp. 1667-1678, Sep. 2007.
113. W. C. Chen, N.-B. Chang, and J.-C. Chen, "GA-based fuzzy neural controller design for municipal incinerators," Fuzzy Sets Syst., vol. 129, pp. 343-369, 2002.
114. G. L. O. Serra and C. P. Bottura, "Multiobjective evolution based fuzzy PI controller design for nonlinear systems," Eng. Appl. Artif. Intell., vol. 19, no. 2, pp. 157-167, 2006.
115. M. Kaya, "Multi-objective genetic algorithm based approaches for mining optimized fuzzy association rules," Soft Comput., vol. 10, pp. 578-586, 2006.
116. C.-H. Chen, T.-P. Hong, V. S. Tseng, and L.-C. Chen, "A multi-objective genetic-fuzzy mining algorithm," in Proc. IEEE Int. Conf. Granular Comput., Aug. 2008, pp. 115-120.
117. R. Alhajj and M. Kaya, "Multi-objective genetic algorithms based automated clustering for fuzzy association rules mining," J. Intell. Inf. Syst., vol. 31, pp. 243-264, 2008.
118. P. S. Thilagam and V. S. Ananthanarayana, "Extraction and optimization of fuzzy association rules using multi-objective genetic algorithm," Pattern Anal. Appl., vol. 11, no. 2, pp. 159-168, 2008.
119. J. Casillas and F. J. Martinez-Lopez, "Mining uncertain data with multiobjective genetic fuzzy systems to be applied in consumer behaviour modelling," Expert Syst. Appl., vol. 36, no. 2, Part 1, pp. 1645-1659, 2009.
120. C. J. Carmona, P. Gonzalez, M. J. del Jesus, and F. Herrera, "NMEEFSD: Non-dominated multiobjective evolutionary algorithm for extracting fuzzy rules in subgroup discovery," IEEE Trans. Fuzzy Syst., vol. 18, no. 5, pp. 958-970, Oct. 2010.
121. C. M. Fonseca and P. J. Fleming, "On the performance assessment and comparison of stochastic multiobjective optimizers," in Parallel Problem Solving From Nature, H.-M. Voigt,W. Ebeling, I. Rechenberg, and H.-P. Schwefel, Eds. Berlin/Heidelberg Germany: Springer-Verlag, 1996, pp. 584-593.
122. E. Zitzler and L. Thiele, "Multiobjective optimization using evolutionary algorithms-A comparative case study," in Parallel Problem Solving from Nature, A. Eiben, T. Bck, M. Schoenauer, and H.-P. Schwefel, Eds. Berlin/Heidelberg, Germany: Springer-Verlag, 1998, pp. 292-301.
123. E. Zitzler, L. Thiele, M. Laumanns, C. Fonseca, and V. da Fonseca, "Performance assessment of multiobjective optimizers: An analysis and review," IEEE Trans. Evol. Comput., vol. 7, no. 2, pp. 117-132, Apr. 2003.
124. J. Alonso and L. Magdalena, "HILK++: An interpretability-guided fuzzy modeling methodology for learning readable and comprehensible fuzzy rule-based classifiers," Soft Comput., vol. 15, no. 10, pp. 1959-1980, 2011.
125. H. Ishibuchi, N. Tsukamoto, and Y. Nojima, "Evolutionary manyobjective optimization," in Proc. 3rd Int. Workshop Genet. Evolving Syst., 2008, pp. 47-52.
126. Y. Jin, "Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement," IEEE Trans. Fuzzy Syst., vol. 8, no. 2, pp. 212-221, Apr. 2000.
127. N. V. Chawla, N. Japkowicz, and A. Kotcz, "Editorial: special issue on learning from imbalanced data sets," SIGKDD Explor. Newsl., vol. 6, pp. 1-6, 2004.
128. H. Ishibuchi, Y. Nakashima, and Y. Nojima, "Double cross-validation for performance evaluation of multi-objective genetic fuzzy systems," in Proc. 5th IEEE Int. Workshop Genet. Evol. Fuzzy Syst., 2011, pp. 31-38.
129. P. Bonissone, "Research issues in multi criteria decision making (MCDM): The impact of uncertainty in solution evaluation," in Proc. 12th Int. Conf. Proc. Manag. Uncert. Knowl.-Based Syst., 2008, pp. 1409-1416.
130. Y. Nojima and H. Ishibuchi, "Incorporation of user preference intomultiobjective genetic fuzzy rule selection for pattern classification problems," Artif. Life Rob., vol. 14, pp. 418-421, 2009.
131. N. Karnik, J.Mendel, and Q. Liang, "Type-2 fuzzy logic systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 6, pp. 643-658, Dec. 1999.
132. L. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning I," Inf. Sci., vol. 8, no. 3, pp. 199-249, 1975.
133. S. Park and H. Lee-Kwang, "Designing fuzzy logic controllers by genetic algorithms considering their characteristics," in Proc. Cong. Evol. Comput., 2000, vol. 1, pp. 683-690.
134. C. Wagner and H. Hagras, "A genetic algorithm based architecture for evolving type-2 fuzzy logic controllers for realworld autonomous mobile robots," in Proc. IEEE Fuzzy Syst. Conf., 2007, pp. 1-6.
135. O. Castillo, P. Melin, A. Alanis, O. Montiel, and R. Sepulveda, "Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms," Soft Comput., vol. 15, no. 6, pp. 1145-1160, 2011.
136. P. Melin, D. Sanchez, and L. Cervantes, "Hierarchical genetic algorithms for optimal type-2 fuzzy system design," in Proc. Annu. Meeting North Amer. Fuzzy Inf. Process. Soc., 2011, pp. 1-6.