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KEEL: A Software Tool to Assess Evolutionary Algorithms for Data Mining Problems ⋆
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Genetic Tuning of Fuzzy Rule Deep Structures for Linguistic Modeling
 IEEE TRANS. ON FUZZY SYSTEMS
, 2001
"... Tuning fuzzy rulebased systems for Linguistic Modeling is an interesting and widely developed task. It involves adjusting some of the components composing the knowledge base without completely redefining it. To do that, as the fuzzy rule symbolic representations (known as fuzzy rule surface structu ..."
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Cited by 50 (13 self)
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Tuning fuzzy rulebased systems for Linguistic Modeling is an interesting and widely developed task. It involves adjusting some of the components composing the knowledge base without completely redefining it. To do that, as the fuzzy rule symbolic representations (known as fuzzy rule surface structures) as the meaning of the involved membership functions (which together with the surface structures are known as fuzzy rule deep structures) may be modified. This contribution introduces a genetic tuning process for jointly fitting these two components, i.e., whole deep structures. To adjust the symbolic representations, we propose to use linguistic hedges to perform slight modifications keeping a good interpretability. To change the membership function meanings, two different ways considering basic or extended expressions are proposed. As the accomplished experimental study shows, the good performance of our proposal mainly lies in the consideration of this tuning approach performed at two different levels of significance.
Generating the knowledge base of a fuzzy rulebased system by the genetic learning of the data base
 IEEE Tran. Fuzzy Systems
"... Abstract—A new method is proposed to automatically learn the knowledge base (KB) by finding an appropiate data base (DB) by means of a genetic algorithm while using a simple generation method to derive the rule base (RB). Our genetic process learns the number of linguistic terms per variable and the ..."
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Cited by 46 (14 self)
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Abstract—A new method is proposed to automatically learn the knowledge base (KB) by finding an appropiate data base (DB) by means of a genetic algorithm while using a simple generation method to derive the rule base (RB). Our genetic process learns the number of linguistic terms per variable and the membership function parameters that define their semantics, while a rule base generation method learns the number of rules and their composition. Index Terms—Fuzzy rulebased systems, data base, learning, genetic algorithms. I.
A proposal for improving the accuracy of linguistic modeling
 IEEE Trans. Fuzzy Systems
, 2000
"... Abstract—In this paper, we propose accurate linguistic modeling, a methodology to design linguistic models that are accurate to a high degree and may be suitably interpreted. This approach will be based on two main assumptions related to the interpolative reasoning developed by fuzzy rulebased syst ..."
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Cited by 43 (23 self)
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Abstract—In this paper, we propose accurate linguistic modeling, a methodology to design linguistic models that are accurate to a high degree and may be suitably interpreted. This approach will be based on two main assumptions related to the interpolative reasoning developed by fuzzy rulebased systems: a small change in the structure of the linguistic model based on allowing the linguistic rule to have two consequents associated and a different way to obtain the knowledge base based on generating a preliminary fuzzy rule set composed of a large number of rules and then selecting the subset of them best cooperating. Moreover, we will introduce two variants of an automatic design method for these kinds of linguistic models based on two wellknown inductive fuzzy rule generation processes and a genetic process for selecting rules. The accuracy of the proposed methods will be compared with other linguistic modeling techniques with different characteristics when solving of three different applications. Index Terms—Descriptive Mamdanitype fuzzy rulebased systems, doubleconsequent linguistic rules, genetic algorithms, inductive fuzzy rule generation, linguistic modeling, rule selection. I.
A proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection
 IEEE Transactions on Fuzzy Systems
, 2007
"... Abstract—Linguistic fuzzy modeling allows us to deal with the modeling of systems by building a linguistic model which is clearly interpretable by human beings. However, since the accuracy and the interpretability of the obtained model are contradictory properties, the necessity of improving the acc ..."
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Cited by 40 (22 self)
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Abstract—Linguistic fuzzy modeling allows us to deal with the modeling of systems by building a linguistic model which is clearly interpretable by human beings. However, since the accuracy and the interpretability of the obtained model are contradictory properties, the necessity of improving the accuracy of the linguistic model arises when complex systems are modeled. To solve this problem, one of the research lines in recent years has led to the objective of giving more accuracy to linguistic fuzzy modeling without losing the interpretability to a high level. In this paper, a new postprocessing approach is proposed to perform an evolutionary lateral tuning of membership functions, with the main aim of obtaining linguistic models with higher levels of accuracy while maintaining good interpretability. To do so, we consider a new rule representation scheme base on the linguistic 2tuples representation model which allows the lateral variation of the involved labels. Furthermore, the cooperation of the lateral tuning together with fuzzy rule reduction mechanisms is studied in this paper, presenting results on different real applications. The obtained results show the good performance of the proposed approach in highdimensional problems and its ability to cooperate with methods to remove unnecessary rules. Index Terms—Fuzzy rulebased systems, genetic algorithms, interpretability, linguistic 2tuples representation, rule selection, tuning. I.
A methodology to improve ad hoc datadriven linguistic rule learning methods by inducing cooperation among rules
, 2000
"... Abstract—This paper introduces a new learning methodology to quickly generate accurate and simple linguistic fuzzy models, the cooperative rules (COR) methodology. It acts on the consequents of the fuzzy rules to find those best cooperating. Instead of selecting the consequent with the highest perfo ..."
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Cited by 35 (19 self)
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Abstract—This paper introduces a new learning methodology to quickly generate accurate and simple linguistic fuzzy models, the cooperative rules (COR) methodology. It acts on the consequents of the fuzzy rules to find those best cooperating. Instead of selecting the consequent with the highest performance in each fuzzy input subspace as ad hoc datadriven methods usually do, the COR methodology considers the possibility of using another consequent, different from the best one, when it allows the fuzzy model to be more accurate thanks to having a rule set with best cooperation. Our proposal has shown good results solving three different applications when compared to other methods. Index Terms—Accuracy improvement, cooperative rules, linguistic fuzzy rulebased modeling, simulated annealing. I.
A twostage evolutionary process for designing TSK fuzzy rulebased systems
 IEEE Trans. Syst., Man, Cybern. B
, 1999
"... Abstract—Nowadays, fuzzy rulebased systems are successfully applied to many different realworld problems. Unfortunately, relatively few wellstructured methodologies exist for designing them and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the ..."
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Cited by 28 (11 self)
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Abstract—Nowadays, fuzzy rulebased systems are successfully applied to many different realworld problems. Unfortunately, relatively few wellstructured methodologies exist for designing them and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the form of fuzzy rules. Takagi–Sugeno –Kang (TSK) fuzzy rulebased systems were enunciated in order to solve this design problem because they are usually identified using numerical data. In this paper we present a twostage evolutionary process for designing TSK fuzzy rulebased systems from examples combining a generation stage based on a ( ;)evolution strategy, in which the fuzzy rules with different consequents compete among themselves to form part of a preliminary knowledge base, and a refinement stage, in which both the antecedent and consequent parts of the fuzzy rules in this previous knowledge base are adapted by a hybrid evolutionary process composed of a genetic algorithm and an evolution strategy to obtain the final Knowledge Base whose rules cooperate in the best possible way. Some aspects make this process different from others proposed until now: the design problem is addressed in two different stages, the use of an angular coding of the consequent parameters that allows us to search across the whole space of possible solutions, and the use of the available knowledge about the system under identification to generate the initial populations of the Evolutionary Algorithms that causes the search process to obtain good solutions more quickly. The performance of the method proposed is shown by solving two different problems: the fuzzy modeling of some threedimensional surfaces and the computing of the maintenance costs of electrical medium line in Spanish towns. Results obtained are compared with other kind of techniques, evolutionary learning processes to design TSK and Mamdanitype fuzzy rulebased systems in the first case, and classical regression and neural modeling in the second. Index Terms — Evolution strategies, evolutionary algorithms, genetic algorithms, learning, Takagi–Sugeno –Kang (TSK) fuzzy
A Genetic Learning Process for the Scaling Factors, Granularity and Contexts of the Fuzzy RuleBased System Data Base
"... Fuzzy RuleBased Systems are knowledgebased systems, incorporating human knowledge into their knowledge base through fuzzy rules (Rule Base) and fuzzy membership functions (Data Base). In these kinds of systems, the Data Base is usually defined by choosing a specific membership function type, unifo ..."
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Cited by 28 (13 self)
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Fuzzy RuleBased Systems are knowledgebased systems, incorporating human knowledge into their knowledge base through fuzzy rules (Rule Base) and fuzzy membership functions (Data Base). In these kinds of systems, the Data Base is usually defined by choosing a specific membership function type, uniformly partitioning the variable domains into a number of linguistic labels and assigning a fuzzy set to each partition. This operation mode can significantly decrease the FRBS performance. To solve this problem, in this contribution, we propose a genetic process to automatically learn the whole Data Base definition from examples, using an adhoc data covering learning method to obtain the Rule Base. Our process learns an appropiate number of labels for each variable primary fuzzy partition and a good distribution for the membership functions (using a nonlinear scaling function to de ne the fuzzy partition contexts). Moreover, it tries to improve the final performance o...
Linguistic modeling by hierarchical systems of linguistic rules
 IEEE Trans. Fuzzy Systems
"... Linguistic modeling by hierarchical systems of linguistic rules ..."
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Cited by 28 (12 self)
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Linguistic modeling by hierarchical systems of linguistic rules
A multiobjective evolutionary approach to concurrently learn rule and data bases of Linguistic . . .
, 2009
"... In this paper, we propose the use of a multiobjective evolutionary approach to generate a set of linguistic fuzzyrulebased systems with different tradeoffs between accuracy and interpretability in regression problems. Accuracy and interpretability are measured in terms of approximation error and r ..."
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Cited by 24 (4 self)
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In this paper, we propose the use of a multiobjective evolutionary approach to generate a set of linguistic fuzzyrulebased systems with different tradeoffs between accuracy and interpretability in regression problems. Accuracy and interpretability are measured in terms of approximation error and rule base (RB) complexity, respectively. The proposed approach is based on concurrently learning RBs and parameters of the membership functions of the associated linguistic labels. To manage the size of the search space, we have integrated the linguistic twotuple representation model, which allows the symbolic translation of a label by only considering one parameter, with an efficient modification of the wellknown (2 + 2) Pareto Archived Evolution Strategy (PAES). We tested our approach on nine realworld datasets of different sizes and with different numbers of variables. Besides the (2 + 2)PAES, we have also used the wellknown nondominated sorting genetic algorithm (NSGAII) and an accuracydriven singleobjective evolutionary algorithm (EA). We employed these optimization techniques both to concurrently learn rules and parameters and to learn only rules. We compared the different approaches by applying a nonparametric statistical test for pairwise comparisons, thus taking into consideration three representative points from the obtained Pareto fronts in the case of the multiobjective EAs. Finally, a datacomplexity measure, which is typically used in pattern recognition to evaluate the data density in terms of average number of patterns per variable, has been introduced to characterize regression problems. Results confirm the effectiveness of our approach, particularly for (possibly highdimensional) datasets with high values of the complexity metric.