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Advocating the use of imprecisely observed data in genetic fuzzy systems
 in Proc. GFS 2005
, 2005
"... Abstract—In our opinion, and in accordance with current literature, the precise contribution of genetic fuzzy systems to the corpus of the machine learning theory has not been clearly stated yet. In particular, we question the existence of a set of problems for which the use of fuzzy rules, in combi ..."
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Abstract—In our opinion, and in accordance with current literature, the precise contribution of genetic fuzzy systems to the corpus of the machine learning theory has not been clearly stated yet. In particular, we question the existence of a set of problems for which the use of fuzzy rules, in combination with genetic algorithms, produces more robust models, or classifiers that are inherently better than those arising from the Bayesian point of view. We will show that this set of problems actually exists, and comprises interval and fuzzy valued datasets, but it is not being exploited. Current genetic fuzzy classifiers deal with crisp classification problems, where the role of fuzzy sets is reduced to give a parametric definition of a set of discriminant functions, with a convenient linguistic interpretation. Provided that the customary use of fuzzy sets in statistics is vague data, we propose to test genetic fuzzy classifiers over imprecisely measured data and design experiments well suited to these problems. The same can be said about genetic fuzzy models: the use of a scalar fitness function assumes crisp data, where fuzzy models, a priori, do not have advantages over statistical regression. Index Terms—Fuzzy fitness function, fuzzy rulebased classifiers, fuzzy rulebased models, genetic fuzzy systems, vague data. I.
A review of the application of MultiObjective Evolutionary Fuzzy systems: Current status and further directions
 IEEE Trans. Fuzzy Syst
"... Abstract—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 app ..."
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Abstract—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 twolevel taxonomy of the existing proposals, in order to outline a wellestablished framework that could help researchers who work on significant further developments. Finally, some considerations of recent trends and potential research directions are presented. Index Terms—Accuracy–interpretability tradeoff, fuzzy association rule mining, fuzzy control, fuzzy rulebased systems (FRBSs), multiobjective evolutionary algorithms (EAs), multiobjective evolutionary fuzzy systems (MOEFSs). I.
Interpretability Improvements to Find the Balance InterpretabilityAccuracy in Fuzzy Modeling: An Overview
"... Abstract. System modeling with fuzzy rulebased systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to fa ..."
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Abstract. System modeling with fuzzy rulebased systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to faithfully represent the real system. While linguistic FM (mainly developed by linguistic FRBSs) is focused on the interpretability, precise FM (mainly developed by TakagiSugenoKang FRBSs) is focused on the accuracy. Since both criteria are of vital importance in system modeling, the balance between them has started to pay attention in the fuzzy community in the last few years. The chapter analyzes mechanisms to find this balance by improving the interpretability in linguistic FM: selecting input variables, reducing the fuzzy rule set, using more descriptive expressions, or performing linguistic approximation; and in precise FM: reducing the fuzzy rule set, reducing the number of fuzzy sets, or exploiting the local description of the rules. 1
Fuzzy rule basedsystems (FRBS) have become a wide choice when addressing modeling and system identification problems [1, 2, 3, 4]. One of the most popular
"... Abstract. The tuning of Fuzzy RuleBased Systems is often applied to improve their performance as a postprocessing stage once an appropriate set of fuzzy rules has been extracted. This optimization problem can become a hard one when the size of the considered system in terms of the number of variab ..."
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Abstract. The tuning of Fuzzy RuleBased Systems is often applied to improve their performance as a postprocessing stage once an appropriate set of fuzzy rules has been extracted. This optimization problem can become a hard one when the size of the considered system in terms of the number of variables, rules and, particularly, data samples is big. Distributed Genetic Algorithms are excellent optimization algorithms which exploit the nowadays available parallel hardware (multicore microprocessors and clusters) and could help to alleviate this growth in complexity. In this work, we present a study on the use of the Distributed Genetic Algorithms for the tuning of Fuzzy RuleBased Systems. To this end, we analyze the application of a specific Gradual Distributed RealCoded Genetic Algorithm which employs eight subpopulations in a hypercube topology. The empirical performance in solution quality and computing time is assessed by comparing its results with those from a highly effective sequential tuning algorithm. We applied both, the highly effective sequential algorithm and the distributed method, for the modeling of four wellknown regression problems. The results show
A Hierarchical Fuzzy Rulebased Learning System based on an Information Theoretic Approach
"... This paper proposes a new novel method for the online construction of a Hierarchical Fuzzy Rule Based System (FRBS) to accurately model a function while retaining a level of human interpretability. The algorithm uses an information theoretic approach to limit the amount of uncertainty within each de ..."
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This paper proposes a new novel method for the online construction of a Hierarchical Fuzzy Rule Based System (FRBS) to accurately model a function while retaining a level of human interpretability. The algorithm uses an information theoretic approach to limit the amount of uncertainty within each decision and to determine when a rule does not effectively model the underlying decision space. Experimental results are provided which compare the performance of the proposed system with existing approaches.
Approximate Versus Linguistic Representation in FuzzyUCS
"... Abstract. This paper introduces an approximate fuzzy representation to FuzzyUCS, a Michiganstyle Learning FuzzyClassifier System that evolves linguistic fuzzy rules, and studies whether the flexibility provided by the approximate representation results in a significant improvement of the accuracy ..."
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Abstract. This paper introduces an approximate fuzzy representation to FuzzyUCS, a Michiganstyle Learning FuzzyClassifier System that evolves linguistic fuzzy rules, and studies whether the flexibility provided by the approximate representation results in a significant improvement of the accuracy of the models evolved by the system. We test FuzzyUCS with both approximate and linguistic representation on a large collection of reallife problems and compare the results in terms of training and test accuracy and interpretability of the evolved rule sets.
Genetic Tuning of Fuzzy RuleBased Systems Integrating Linguistic Hedges ∗
"... Tuning fuzzy rulebased systems for linguistic modeling is an interesting and widely developed task. It involves adjusting the membership functions composing the knowledge base. To do that, as changing the parameters defining each membership function as using linguistic hedges to slightly modify ..."
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Tuning fuzzy rulebased systems for linguistic modeling is an interesting and widely developed task. It involves adjusting the membership functions composing the knowledge base. To do that, as changing the parameters defining each membership function as using linguistic hedges to slightly modify them may be considered. This contribution introduces a genetic tuning process for jointly making these two tuning approaches. The experimental results show that our method obtain accurate linguistic models in both approximation and generalization aspects. 1
Fuzzy Evolutionary Algorithms and Genetic Fuzzy Systems: A Positive Collaboration between Evolutionary Algorithms and Fuzzy Systems
"... Abstract. There are two possible ways for integrating fuzzy logic and evolutionary algorithms. The first one involves the application of evolutionary algorithms for solving optimization and search problems related with fuzzy systems, obtaining genetic fuzzy systems. The second one concerns the use ..."
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Abstract. There are two possible ways for integrating fuzzy logic and evolutionary algorithms. The first one involves the application of evolutionary algorithms for solving optimization and search problems related with fuzzy systems, obtaining genetic fuzzy systems. The second one concerns the use of fuzzy tools and fuzzy logicbased techniques for modelling different evolutionary algorithm components and adapting evolutionary algorithm control parameters, with the goal of improving performance. The evolutionary algorithms resulting from this integration are called fuzzy evolutionary algorithms. In this chapter, we shortly introduce genetic fuzzy systems and fuzzy evolutionary algorithms, giving a short state of the art, and sketch our vision of some hot current trends and prospects. In essence, we paint a complete picture of these two lines of research with the aim of showing the benefits derived from the synergy between evolutionary algorithms and fuzzy logic. 1