A Review of the Application of Multiobjective Evolutionary Fuzzy Systems: Current Status and Further Directions

Over the past few decades, fuzzy systems have been widely used in several application fields, thanks to their ability to model complex systems. The design of fuzzy systems has been successfully performed by applying evolutionary and, in particular, genetic algorithms, and recently, this approach has been extended by using multiobjective evolutionary algorithms, which can consider multiple conflicting objectives, instead of a single one. The hybridization between multiobjective evolutionary algorithms and fuzzy systems is currently known as multiobjective evolutionary fuzzy systems. This paper presents an overview of multiobjective evolutionary fuzzy systems, describing the main contributions on this field and providing a two-level taxonomy of the existing proposals, in order to outline a well-established framework that could help researchers who work on significant further developments. Finally, some considerations of recent trends and potential research directions are presented.

[1]  Hisao Ishibuchi,et al.  Double cross-validation for performance evaluation of multi-objective genetic fuzzy systems , 2011, 2011 IEEE 5th International Workshop on Genetic and Evolutionary Fuzzy Systems (GEFS).

[2]  Peter J. Fleming,et al.  Fuzzy scheduling control of a gas turbine aero-engine: a multiobjective approach , 2002, IEEE Trans. Ind. Electron..

[3]  Ludmila I. Kuncheva,et al.  Fuzzy Classifier Design , 2000, Studies in Fuzziness and Soft Computing.

[4]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[5]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[6]  Patricia Melin,et al.  Hierarchical genetic algorithms for optimal type-2 fuzzy system design , 2011, 2011 Annual Meeting of the North American Fuzzy Information Processing Society.

[7]  Beatrice Lazzerini,et al.  On reducing computational overhead in multi-objective genetic Takagi-Sugeno fuzzy systems , 2011, Appl. Soft Comput..

[8]  Francisco Herrera,et al.  Increasing fuzzy rules cooperation based on evolutionary adaptive inference systems , 2007, Int. J. Intell. Syst..

[9]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[10]  Hannu Koivisto,et al.  A Dynamically Constrained Multiobjective Genetic Fuzzy System for Regression Problems , 2010, IEEE Transactions on Fuzzy Systems.

[11]  Gregory Piatetsky-Shapiro,et al.  Knowledge Discovery in Databases: An Overview , 1992, AI Mag..

[12]  Martin Atzmüller,et al.  Subgroup discovery , 2005, Künstliche Intell..

[13]  Ebrahim Mamdani,et al.  Applications of fuzzy algorithms for control of a simple dynamic plant , 1974 .

[14]  Hisao Ishibuchi,et al.  Three-objective genetics-based machine learning for linguistic rule extraction , 2001, Inf. Sci..

[15]  Witold Pedrycz,et al.  A Multiobjective Design of a Patient and Anaesthetist-Friendly Neuromuscular Blockade Controller , 2007, IEEE Transactions on Biomedical Engineering.

[16]  José M. Alonso,et al.  Multi-objective design of highly interpretable fuzzy rule-based classifiers with semantic cointension , 2011, 2011 IEEE 5th International Workshop on Genetic and Evolutionary Fuzzy Systems (GEFS).

[17]  H. Ishibuchi,et al.  Performance evaluation of fuzzy rule-based classification systems obtained by multi-objective genetic algorithms , 1998 .

[18]  V. S. Ananthanarayana,et al.  Extraction and optimization of fuzzy association rules using multi-objective genetic algorithm , 2008, Pattern Analysis and Applications.

[19]  Jorge Casillas,et al.  Learning consistent, complete and compact sets of fuzzy rules in conjunctive normal form for regression problems , 2008, Soft Comput..

[20]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[21]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[22]  Hyun-Su Kim,et al.  GA-fuzzy control of smart base isolated benchmark building using supervisory control technique , 2007, Adv. Eng. Softw..

[23]  Francisco Herrera,et al.  Tuning fuzzy logic controllers by genetic algorithms , 1995, Int. J. Approx. Reason..

[24]  Antonio F. Gómez-Skarmeta,et al.  Improving interpretability in approximative fuzzy models via multiobjective evolutionary algorithms , 2007, EUSFLAT Conf..

[25]  John H. Holland,et al.  COGNITIVE SYSTEMS BASED ON ADAPTIVE ALGORITHMS1 , 1978 .

[26]  José M. Alonso,et al.  An Empirical Study on Interpretability Indexes through Multi-objective Evolutionary Algorithms , 2011, WILF.

[27]  Chuen-Chien Lee FUZZY LOGIC CONTROL SYSTEMS: FUZZY LOGIC CONTROLLER - PART I , 1990 .

[28]  Héctor Pomares,et al.  Improving the accuracy while preserving the interpretability of fuzzy function approximators by means of multi-objective evolutionary algorithms , 2007, Int. J. Approx. Reason..

[29]  José Valente de Oliveira,et al.  Semantic constraints for membership function optimization , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[30]  Francisco Herrera,et al.  A three-stage evolutionary process for learning descriptive and approximate fuzzy-logic-controller knowledge bases from examples , 1997, Int. J. Approx. Reason..

[31]  Peter J. Fleming,et al.  Evolutionary algorithms in control systems engineering: a survey , 2002 .

[32]  Marc Ebner,et al.  Evolutionary parameter optimization of a fuzzy controller which is used to control a sewage treatment plant. , 2010, Water science and technology : a journal of the International Association on Water Pollution Research.

[33]  Hisao Ishibuchi,et al.  Incorporation of user preference into multi-objective genetic fuzzy rule selection for pattern classification problems , 2009, Artificial Life and Robotics.

[34]  Jesús Alcalá-Fdez,et al.  A Proposal for the Genetic Lateral Tuning of Linguistic Fuzzy Systems and Its Interaction With Rule Selection , 2007, IEEE Transactions on Fuzzy Systems.

[35]  Hannu Koivisto,et al.  Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms , 2008, Int. J. Approx. Reason..

[36]  Francisco Herrera,et al.  Integration of an Index to Preserve the Semantic Interpretability in the Multiobjective Evolutionary Rule Selection and Tuning of Linguistic Fuzzy Systems , 2010, IEEE Transactions on Fuzzy Systems.

[37]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[38]  Hannu Koivisto,et al.  Developing a bioaerosol detector using hybrid genetic fuzzy systems , 2008, Eng. Appl. Artif. Intell..

[39]  Oscar Castillo,et al.  Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms , 2011, Soft Comput..

[40]  Peter J. Fleming,et al.  On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers , 1996, PPSN.

[41]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[42]  P. Bonissone Research Issues in Multi Criteria Decision Making (MCDM): The Impact of Uncertainty in Solution Evaluation , 2008 .

[43]  Francisco Herrera,et al.  Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems , 2008, Soft Comput..

[44]  Ananth Ramaswamy,et al.  Multiobjective Optimal Structural Vibration Control using Fuzzy Logic Control System , 2001 .

[45]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[46]  Rafael Muñoz-Salinas,et al.  Automatic Tuning of a Fuzzy Visual System Using Evolutionary Algorithms: Single-Objective Versus Multiobjective Approaches , 2008, IEEE Transactions on Fuzzy Systems.

[47]  Beatrice Lazzerini,et al.  Learning concurrently data and rule bases of Mamdani fuzzy rule-based systems by exploiting a novel interpretability index , 2011, Soft Comput..

[48]  Ni-Bin Chang,et al.  GA-based fuzzy neural controller design for municipal incinerators , 2002, Fuzzy Sets Syst..

[49]  José M. Alonso,et al.  HILK: A new methodology for designing highly interpretable linguistic knowledge bases using the fuzzy logic formalism , 2008, Int. J. Intell. Syst..

[50]  Francisco Herrera,et al.  Multiobjective genetic fuzzy rule selection of single granularity-based fuzzy classification rules and its interaction with the lateral tuning of membership functions , 2011, Soft Comput..

[51]  Ananth Ramaswamy,et al.  Multiobjective Optimal Fuzzy Logic Controller Driven Active and Hybrid Control Systems for Seismically Excited Nonlinear Buildings , 2004 .

[52]  Stephen F. Smith,et al.  A learning system based on genetic adaptive algorithms , 1980 .

[53]  C. L. Karr,et al.  Fuzzy control of pH using genetic algorithms , 1993, IEEE Trans. Fuzzy Syst..

[54]  Ramasamy Uthurusamy,et al.  Data mining and knowledge discovery in databases , 1996, CACM.

[55]  José M. Alonso,et al.  Embedding HILK in a three-objective evolutionary algorithm with the aim of modeling highly interpretable fuzzy rule-based classifiers , 2010, 2010 4th International Workshop on Genetic and Evolutionary Fuzzy Systems (GEFS).

[56]  Hani Hagras,et al.  A Genetic Algorithm Based Architecture for Evolving Type-2 Fuzzy Logic Controllers for Real World Autonomous Mobile Robots , 2007, 2007 IEEE International Fuzzy Systems Conference.

[57]  Z. Xing,et al.  On Generating Fuzzy Systems based on Pareto Multi-objective Cooperative Coevolutionary Algorithm , 2007 .

[58]  Jesús Alcalá-Fdez,et al.  Improving fuzzy logic controllers obtained by experts: a case study in HVAC systems , 2009, Applied Intelligence.

[59]  Ananth Ramaswamy,et al.  Multi‐objective optimal design of FLC driven hybrid mass damper for seismically excited structures , 2002 .

[60]  Francisco Herrera,et al.  Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base , 2001, IEEE Trans. Fuzzy Syst..

[61]  Francisco Herrera,et al.  A multi-objective evolutionary algorithm for an effective tuning of fuzzy logic controllers in heating, ventilating and air conditioning systems , 2012, Applied Intelligence.

[62]  A. S. Ahlawat,et al.  Multiobjective optimal fuzzy logic control system for response control of wind-excited tall buildings , 2004 .

[63]  John Q. Gan,et al.  Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling , 2008, Fuzzy Sets Syst..

[64]  Chin-Hsiung Loh,et al.  GA-optimized fuzzy logic control of a large-scale building for seismic loads , 2008 .

[65]  Jan Paredis,et al.  Coevolutionary Computation , 1995, Artificial Life.

[66]  Daniel Sánchez,et al.  Fuzzy association rules: general model and applications , 2003, IEEE Trans. Fuzzy Syst..

[67]  Bart Kosko,et al.  Fuzzy Systems as Universal Approximators , 1994, IEEE Trans. Computers.

[68]  Hisao Ishibuchi,et al.  Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning , 2007, Int. J. Approx. Reason..

[69]  Francisco Herrera,et al.  A Multi-Objective Genetic Algorithm for Tuning and Rule Selection to Obtain Accurate and Compact Linguistic Fuzzy Rule-Based Systems , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[70]  María José del Jesús,et al.  NMEEF-SD: Non-dominated Multiobjective Evolutionary Algorithm for Extracting Fuzzy Rules in Subgroup Discovery , 2010, IEEE Transactions on Fuzzy Systems.

[71]  José M. Alonso,et al.  HILK++: an interpretability-guided fuzzy modeling methodology for learning readable and comprehensible fuzzy rule-based classifiers , 2011, Soft Comput..

[72]  Francisco Herrera,et al.  A Fast and Scalable Multiobjective Genetic Fuzzy System for Linguistic Fuzzy Modeling in High-Dimensional Regression Problems , 2011, IEEE Transactions on Fuzzy Systems.

[73]  Beatrice Lazzerini,et al.  A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems , 2007, Soft Comput..

[74]  Ginalber Luiz de Oliveira Serra,et al.  Multiobjective evolution based fuzzy PI controller design for nonlinear systems , 2006, Eng. Appl. Artif. Intell..

[75]  Hisao Ishibuchi,et al.  Evolutionary multiobjective optimization for the design of fuzzy rule-based ensemble classifiers , 2006, Int. J. Hybrid Intell. Syst..

[76]  Fernando José Von Zuben,et al.  Hierarchical genetic fuzzy systems , 2001, Inf. Sci..

[77]  Evan J. Hughes,et al.  Multi-objective Evolutionary Design of Fuzzy Autopilot Controller , 2001, EMO.

[78]  Francisco Herrera,et al.  A Multiobjective Evolutionary Approach to Concurrently Learn Rule and Data Bases of Linguistic Fuzzy-Rule-Based Systems , 2009, IEEE Transactions on Fuzzy Systems.

[79]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[80]  Francisco Herrera,et al.  Interpretability of linguistic fuzzy rule-based systems: An overview of interpretability measures , 2011, Inf. Sci..

[81]  Shichao Zhang,et al.  Association Rule Mining: Models and Algorithms , 2002 .

[82]  Beatrice Lazzerini,et al.  Multi-objective evolutionary learning of granularity, membership function parameters and rules of Mamdani fuzzy systems , 2009, Evol. Intell..

[83]  John H. Holland,et al.  Cognitive systems based on adaptive algorithms , 1977, SGAR.

[84]  Luis Magdalena,et al.  A Multiobjective Genetic Learning Process for joint Feature Selection and Granularity and Contexts Learning in Fuzzy Rule-Based Classification Systems , 2003 .

[85]  Oscar Cordón,et al.  International Journal of Approximate Reasoning a Historical Review of Evolutionary Learning Methods for Mamdani-type Fuzzy Rule-based Systems: Designing Interpretable Genetic Fuzzy Systems , 2022 .

[86]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[87]  R. K. Ursem Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[88]  Francisco Herrera,et al.  Increasing fuzzy rules cooperation based on evolutionary adaptive inference systems: Research Articles , 2007 .

[89]  Chuen-Chien Lee,et al.  Fuzzy logic in control systems: fuzzy logic controller. I , 1990, IEEE Trans. Syst. Man Cybern..

[90]  Hideo Tanaka,et al.  Construction of fuzzy classification systems with rectangular fuzzy rules using genetic algorithms , 1994, CVPR 1994.

[91]  Alessio Botta,et al.  Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index , 2008, Soft Comput..

[92]  Hisao Ishibuchi,et al.  Selecting fuzzy if-then rules for classification problems using genetic algorithms , 1995, IEEE Trans. Fuzzy Syst..

[93]  Nicolas Morel,et al.  Identifying important state variables for a blind controller , 2010 .

[94]  Antonio A. Márquez,et al.  Rule Base and Inference System Cooperative Learning of Mamdani Fuzzy Systems with Multiobjective Genetic Algorithms , 2009, IFSA/EUSFLAT Conf..

[95]  Francisco Jurado,et al.  Enhancing the electrical performance of a solid oxide fuel cell using multiobjective genetic algorithms , 2005 .

[96]  Giovanni Corsini,et al.  Solving the ocean color inverse problem by using evolutionary multi-objective optimization of neuro-fuzzy systems , 2008, Int. J. Knowl. Based Intell. Eng. Syst..

[97]  Beatrice Lazzerini,et al.  Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets , 2010, Soft Comput..

[98]  Ananth Ramaswamy,et al.  Multiobjective optimal FLC driven hybrid mass damper system for torsionally coupled, seismically excited structures , 2002 .

[99]  Lucien Duckstein,et al.  Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological and Engineering Systems , 1995 .

[100]  Hisao Ishibuchi,et al.  Classification and modeling with linguistic information granules - advanced approaches to linguistic data mining , 2004, Advanced information processing.

[101]  José M. Alonso,et al.  Looking for a good fuzzy system interpretability index: An experimental approach , 2009, Int. J. Approx. Reason..

[102]  Mehmet Kaya,et al.  Multi-objective genetic algorithm based approaches for mining optimized fuzzy association rules , 2006, Soft Comput..

[103]  Francisco Herrera,et al.  Building fuzzy graphs: Features and taxonomy of learning for non-grid-oriented fuzzy rule-based systems , 2001, J. Intell. Fuzzy Syst..

[104]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[105]  Hong Chen,et al.  Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks , 1993, IEEE Trans. Neural Networks.

[106]  Magne Setnes,et al.  Rule-based modeling: precision and transparency , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[107]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[108]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems , 1999, IEEE Trans. Fuzzy Syst..

[109]  Hisao Ishibuchi,et al.  Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining , 2004, Fuzzy Sets Syst..

[110]  Francisco Herrera,et al.  Genetic Fuzzy Systems - Evolutionary Tuning and Learning of Fuzzy Knowledge Bases , 2002, Advances in Fuzzy Systems - Applications and Theory.

[111]  Yaochu Jin,et al.  Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement , 2000, IEEE Trans. Fuzzy Syst..

[112]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[113]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[114]  Philip R. Thrift,et al.  Fuzzy Logic Synthesis with Genetic Algorithms , 1991, ICGA.

[115]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[116]  Antonio A. Márquez,et al.  A multi-objective evolutionary algorithm with an interpretability improvement mechanism for linguistic fuzzy systems with adaptive defuzzification , 2010, International Conference on Fuzzy Systems.

[117]  Q GanJohn,et al.  Low-level interpretability and high-level interpretability , 2008 .

[118]  Bernard P. Zeigler,et al.  Designing fuzzy net controllers using genetic algorithms , 1995 .

[119]  Serge Guillaume,et al.  Designing fuzzy inference systems from data: An interpretability-oriented review , 2001, IEEE Trans. Fuzzy Syst..

[120]  Hisao Ishibuchi,et al.  Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems , 1997, Fuzzy Sets Syst..

[121]  Padhraic Smyth,et al.  From Data Mining to Knowledge Discovery in Databases , 1996, AI Mag..

[122]  Hyun-Su Kim,et al.  Fuzzy Control of Base‐Isolation System Using Multi‐Objective Genetic Algorithm , 2006, Comput. Aided Civ. Infrastructure Eng..

[123]  Chengqi Zhang,et al.  Association Rule Mining , 2002, Lecture Notes in Computer Science.

[124]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization , 2008, 2008 3rd International Workshop on Genetic and Evolving Systems.

[125]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[126]  Marcelo Simoes Introduction to Fuzzy Control , 2003 .

[127]  Reda Alhajj,et al.  Multi-objective genetic algorithms based automated clustering for fuzzy association rules mining , 2008, Journal of Intelligent Information Systems.

[128]  Francisco Herrera,et al.  Genetic fuzzy systems: taxonomy, current research trends and prospects , 2008, Evol. Intell..

[129]  Kim-Fung Man,et al.  Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction , 2005, Fuzzy Sets Syst..

[130]  Beatrice Lazzerini,et al.  Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework , 2009, Int. J. Approx. Reason..

[131]  Frank Hoffmann,et al.  Evolutionary algorithms for fuzzy control system design , 2001, Proc. IEEE.

[132]  Ali Belmehdi,et al.  Multi-objective optimization of TSK fuzzy models , 2008, 2008 5th International Multi-Conference on Systems, Signals and Devices.

[133]  Chuen-Chien Lee,et al.  Fuzzy logic in control systems: fuzzy logic controller. II , 1990, IEEE Trans. Syst. Man Cybern..

[134]  Giovanna Castellano,et al.  Distinguishability quantification of fuzzy sets , 2007, Inf. Sci..

[135]  H. Lee-Kwang,et al.  Designing fuzzy logic controllers by genetic algorithms considering their characteristics , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[136]  Nitesh V. Chawla,et al.  Editorial: special issue on learning from imbalanced data sets , 2004, SKDD.

[137]  Tzung-Pei Hong,et al.  A multi-objective genetic-fuzzy mining algorithm , 2008, 2008 IEEE International Conference on Granular Computing.

[138]  Francisco J. Martínez-López,et al.  Mining uncertain data with multiobjective genetic fuzzy systems to be applied in consumer behaviour modelling , 2009, Expert Syst. Appl..

[139]  Beatrice Lazzerini,et al.  Learning knowledge bases of multi-objective evolutionary fuzzy systems by simultaneously optimizing accuracy, complexity and partition integrity , 2011, Soft Comput..

[140]  Yung C. Shin,et al.  Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems , 1994, IEEE Trans. Neural Networks.

[141]  Christian Setzkorn,et al.  On the use of multi-objective evolutionary algorithms for the induction of fuzzy classification rule systems. , 2005, Bio Systems.

[142]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[143]  Peter J. Fleming,et al.  Design of robust fuzzy-logic control systems by multi-objective evolutionary methods with hardware in the loop , 2004, Eng. Appl. Artif. Intell..