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109
Selforganized fuzzy system generation from training examples
 IEEE Trans. Fuzzy Syst
, 2000
"... Abstract—In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. This paper presents a methodology to automatically perform these two steps in conjunction using a threephase approach to construct a fu ..."
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Cited by 23 (10 self)
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Abstract—In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. This paper presents a methodology to automatically perform these two steps in conjunction using a threephase approach to construct a fuzzy system from numerical data. Phase 1 outlines the membership functions and system rules for a specific structure, starting from a very simple initial topology. Phase 2 decides a new and more suitable topology with the information received from the previous step; it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located. This, in turn, decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased. Phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set. The accuracy and complexity of the fuzzy system derived by the proposed selforganized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation. Simulation results are compared with other methodologies such as artificial neural networks, neurofuzzy systems, and genetic algorithms. Index Terms—Function approximation, fuzzy system design, generation of membership functions and rules. I.
A FuzzyGenetic Approach to Breast Cancer Diagnosis
, 1999
"... The automatic diagnosis of breast cancer is an important, realworld medical problem. In this paper we focus on the Wisconsin breast cancer diagnosis (WBCD) problem, combining two methodologiesfuzzy systems and evolutionary algorithmsso as to automatically produce diagnostic systems. We find t ..."
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Cited by 23 (7 self)
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The automatic diagnosis of breast cancer is an important, realworld medical problem. In this paper we focus on the Wisconsin breast cancer diagnosis (WBCD) problem, combining two methodologiesfuzzy systems and evolutionary algorithmsso as to automatically produce diagnostic systems. We find that our fuzzygenetic approach produces systems exhibiting two prime characteristics: first, they attain high classification performance (the best shown to date), with the possibility of attributing a confidence measure to the output diagnosis; second, the resulting systems involve a few simple rules, and are therefore (human) interpretable. 1999 Elsevier Science B.V. All rights reserved. Keywords: Fuzzy systems; Genetic algorithms; Breast cancer diagnosis www.elsevier.com/locate/artmed 1.
Accuracybased Neuro and NeuroFuzzy Classifier Systems
 IN
, 2002
"... Learning Classifier Systems traditionally use a binary representation with wildcards added to allow for generalizations over the problem encoding. However, the simple scheme can be limiting in complex domains. In this paper we present results from the use of neural networkbased representation schem ..."
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Cited by 23 (5 self)
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Learning Classifier Systems traditionally use a binary representation with wildcards added to allow for generalizations over the problem encoding. However, the simple scheme can be limiting in complex domains. In this paper we present results from the use of neural networkbased representation schemes within the accuracybased XCS. Here each rule's condition and action are represented by a small neural network, evolved through the actions of the genetic algorithm. After describing the changes required to the standard production system functionality, optimal performance is presented using multilayered perceptrons to represent the individual rules. Results from the use of fuzzy logic through radial basis fuction networks are then presented. In particular, the new representation scheme is shown to produce systems where outputs are a function of the inputs.
Modified GathGeva Fuzzy Clustering for Identification of TakagiSugeno Fuzzy Models
 IEEE Transactions on Systems, Man, and Cybernetics
, 2001
"... The construction of interpretable TakagiSugeno (TS) fuzzy models by means of clustering is addressed. First, it is shown how the antecedent fuzzy sets and the corresponding consequent parameters of the TS model can be derived from clusters obtained by the GathGeva algorithm. To preserve the part ..."
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Cited by 21 (6 self)
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The construction of interpretable TakagiSugeno (TS) fuzzy models by means of clustering is addressed. First, it is shown how the antecedent fuzzy sets and the corresponding consequent parameters of the TS model can be derived from clusters obtained by the GathGeva algorithm. To preserve the partitioning of the antecedent space, linearly transformed input variables can be used in the model. This may, however, complicate the interpretation of the rules. To form an easily interpretable model that does not use the transformed input variables, a new clustering algorithm is proposed, based on the Expectation Maximization (EM) identification of Gaussian mixture models. This new technique is applied to two wellknown benchmark problems: the MPG (miles per gallon) prediction and a simulated secondorder nonlinear process. The obtained results are compared with results from the literature.
Fuzzy CoCo: A CooperativeCoevolutionary Approach to Fuzzy Modeling
, 2001
"... Coevolutionary algorithms have received increased attention in the past few years within the domain of evolutionary computation. In this paper, we combine the search power of coevolutionary computation with the expressive power of fuzzy systems, introducing a novel algorithm, Fuzzy CoCo: Fuzzy Coope ..."
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Cited by 18 (7 self)
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Coevolutionary algorithms have received increased attention in the past few years within the domain of evolutionary computation. In this paper, we combine the search power of coevolutionary computation with the expressive power of fuzzy systems, introducing a novel algorithm, Fuzzy CoCo: Fuzzy Cooperative Coevolution. We demonstrate the efficacy of Fuzzy CoCo by applying it to a hard, realworld problembreast cancer diagnosisobtaining the best results to date while expending less computational effort than formerly. Analyzing our results, we derive guidelines for setting the algorithm's parameters given a (hard) problem to solve. We hope Fuzzy CoCo proves to be a powerful tool in the fuzzy modeler's toolkit.
A systematic approach to a selfgenerating fuzzy ruletable for function approximation
 IEEE Trans Syst., Man, Cybern
, 2000
"... Abstract—In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the iden ..."
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Cited by 16 (10 self)
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Abstract—In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A fourstep approach to build a fuzzy system automatically is presented: Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration. Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation. Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography. Index Terms—Function approximation, fuzzy system construction, fuzzy system design, knowledge acquisition. I.
Visualizing Fuzzy Points in Parallel Coordinates
, 1999
"... The ability to visualize data often leads to new insights. Data that is more than three dimensional must be visualized as a series of projections or transformed into some other representation which usually causes a loss of details. Parallel coordinates allows one to visualize data in two dimensions ..."
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Cited by 15 (5 self)
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The ability to visualize data often leads to new insights. Data that is more than three dimensional must be visualized as a series of projections or transformed into some other representation which usually causes a loss of details. Parallel coordinates allows one to visualize data in two dimensions without a loss of information. In this paper, we discuss the use of parallel coordinates to visualize fuzzy data. Fuzzy data may consist of fuzzy rules, which can be viewed as cutting a swath through an ndimensional space. Fuzzy clusters may also be considered fuzzy data in a similar way. Examples are given from three domains. The examples show that parallel coordinates can be used to nd extraneous fuzzy rules, separate fuzzy clusters as well as validate previous ndings about data sets.
Flexible neurofuzzy systems
 IEEE TRANS. NEURAL NETW
, 2003
"... In this paper, we derive new neurofuzzy structures called flexible neurofuzzy inference systems or FLEXNFIS. Based on the input–output data, we learn not only the parameters of the membership functions but also the type of the systems (Mamdani or logical). Moreover, we introduce: 1) softness to f ..."
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Cited by 15 (3 self)
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In this paper, we derive new neurofuzzy structures called flexible neurofuzzy inference systems or FLEXNFIS. Based on the input–output data, we learn not only the parameters of the membership functions but also the type of the systems (Mamdani or logical). Moreover, we introduce: 1) softness to fuzzy implication operators, to aggregation of rules and to connectives of antecedents; 2) certainty weights to aggregation of rules and to connectives of antecedents; and 3) parameterized families of Tnorms and Snorms to fuzzy implication operators, to aggregation of rules and to connectives of antecedents. Our approach introduces more flexibility to the structure and design of neurofuzzy systems. Through computer simulations, we show that Mamdanitype systems are more suitable to approximation problems, whereas logicaltype systems may be preferred for classification problems.
Evolving Fuzzy Rules for Breast Cancer Diagnosis
, 1998
"... We present an evolutionary approach for discovering fuzzy systems for breast cancer diagnosis. By judiciously designing an appropriate representation scheme (genome) and fitness function, the genetic algorithm is then able to produce successful systems. These surpass the best known systems to date i ..."
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Cited by 14 (9 self)
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We present an evolutionary approach for discovering fuzzy systems for breast cancer diagnosis. By judiciously designing an appropriate representation scheme (genome) and fitness function, the genetic algorithm is then able to produce successful systems. These surpass the best known systems to date in terms of combined performance and simplicity. I. Introduction Fuzzy logic is a computational paradigm that provides a mathematical tool for dealing with the uncertainty and the imprecision typical of human reasoning [1]. A prime characteristic of fuzzy logic is its capability of expressing knowledge in a linguistic way, allowing a system to be described by simple, "humanfriendly" rules. A fuzzy inference system is a rulebased system that uses fuzzy logic, rather than boolean logic, to reason about data [1]. Its basic structure comprises four main components: (1) a fuzzifier, which translates crisp (realvalued) inputs into fuzzy values, (2) an inference engine that applies a fuzzy reaso...
Input Selection for ANFIS Learning
 IN PROCEEDINGS OF THE IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS
, 1996
"... We present a quick and straightfoward way of input selection for neurofuzzy modeling using ANFIS. The method is tested on two realworld problems: the nonlinear regression problem of automobile MPG (miles per gallon) prediction, and the nonlinear system identification using the Box and Jenkins gas ..."
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Cited by 14 (0 self)
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We present a quick and straightfoward way of input selection for neurofuzzy modeling using ANFIS. The method is tested on two realworld problems: the nonlinear regression problem of automobile MPG (miles per gallon) prediction, and the nonlinear system identification using the Box and Jenkins gas furnace data [1].