## A Two-Stage Evolutionary Process for Designing TSK Fuzzy Rule-Based Systems (1996)

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Venue: | IEEE Trans. on Systems, Man, and Cybernetics |

Citations: | 19 - 10 self |

### BibTeX

@ARTICLE{Cordon96atwo-stage,

author = {O. Cordon and F. Herrera and Francisco Herrera},

title = {A Two-Stage Evolutionary Process for Designing TSK Fuzzy Rule-Based Systems},

journal = {IEEE Trans. on Systems, Man, and Cybernetics},

year = {1996},

volume = {29},

pages = {703--715}

}

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### Abstract

Nowadays, Fuzzy Rule-Based Systems are successfully applied to many different real-world problems. Unfortunatelly, relatively few well-structured 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. TSK Fuzzy Rule-Based Systems were enunciated in order to solve this design problem because they are usually identified using numerical data. In this paper we present a two-stage evolutionary process for designing TSK Fuzzy Rule-Based 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 ...

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Citation Context ...y rule-based systems, TSK knowledge base. I. INTRODUCTION FUZZY rule-based systems (FRBS’s) are now considered as one of the most important applications of fuzzy set theory suggested by Zadeh in 1965 =-=[1]-=-. These kinds of systems constitute an extension of the classical rule-based systems because they deal with fuzzy rules instead of classical logic rules. Thanks to this, they have been successfully ap... |

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Citation Context ...en rules. This has forced researchers to develop automatic techniques for performing this task. Over the last few years, many different approaches have been presented taking genetic algorithms (GA’s) =-=[4]-=- as their base, obtaining the so called genetic fuzzy systems (GFS’s) [5], [6] or, more generically, evolutionary fuzzy systems (EFS’s) when an Evolutionary Algorithm (EA) [7] is used instead of a GA.... |

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Citation Context ...enetic algorithms (GA’s) [4] as their base, obtaining the so called genetic fuzzy systems (GFS’s) [5], [6] or, more generically, evolutionary fuzzy systems (EFS’s) when an Evolutionary Algorithm (EA) =-=[7]-=- is used instead of a GA. For a wider description of some of these approaches refer to [5], [6], [8], and for an extensive bibliography see [9]. In this paper, we present a two-stage evolutionary proc... |

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Citation Context ...lecting different tables of the results obtained in the fuzzy modeling of the three functions, respectively, are presented. II. TSK FUZZY RULE-BASED SYSTEMS The TSK fuzzy model was first presented in =-=[14]-=-. It is based on rules in which the consequent is not a linguistic variable, as in the Mamdani-type fuzzy model, but a function of the input variables. This kind of rule usually presents the following... |

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Citation Context ...techniques have been employed until now to derive the TSK KB from examples since Takagi and Sugeno first presented a process based on the least squares method [14]. For example, Neural Networks [15], =-=[16]-=- and gradient descent methods [17] have been considered. The use of EA’s, either specific, GA’s [12], [18] and EE’s [19]; or hybrid [19], [20], has increased over the last few years. Fig. 1. Examples ... |

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Citation Context ...ands for the number of rules in the KB and for the number of consequent parameters for TSK fuzzy rule: D. Genetic Operators The selection procedure considered is Baker’s stochastic universal sampling =-=[23]-=-, in which the number of any structure offspring is limited by the floor and ceiling of the expected number of offspring, together with the elitist selection. As regards the genetic operators, the one... |

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Citation Context ...he first case, results obtained are compared with other Mamdani and TSK-type FRBS evolutionary design processes (a Mamdani-type two-stage EFS based on the Wang and Mendel fuzzy rule generation method =-=[10]-=-, a three-stage Mamdani-type EFS [11], and a TSK-type EFS [12], [13]). In the second application, the same EFS’s are considered, and 1083–4419/99$10.00 © 1999 IEEE704 IEEE TRANSACTIONS ON SYSTEMS, MA... |

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Citation Context ...ngeniería Informática, University of Granada, 18071 Granada, Spain (e-mail: ocordon@decsai.ugr.es). Publisher Item Identifier S 1083-4419(99)08063-2. have been obtained by the fuzzy logic controllers =-=[3]-=-, the FRBS’s for control problems. Several tasks have to be performed in order to design an intelligent system of this kind for a concrete application. They can be grouped into two main tasks: to desi... |

252 |
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Citation Context ...eural network models. The parameters of the polynomial models were fitted by Levenberg–Marquardt method and the neural model (a three-layer perceptron) was trained with the QuickPropagation Algorithm =-=[30]-=-. The number of neurons in the hidden layer was chosen to minimize the test error; note that the training error could be made much lower than the shown, but not without making the test error higher. W... |

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Citation Context ...orming this task. Over the last few years, many different approaches have been presented taking genetic algorithms (GA’s) [4] as their base, obtaining the so called genetic fuzzy systems (GFS’s) [5], =-=[6]-=- or, more generically, evolutionary fuzzy systems (EFS’s) when an Evolutionary Algorithm (EA) [7] is used instead of a GA. For a wider description of some of these approaches refer to [5], [6], [8], a... |

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Citation Context ...ompared with other Mamdani and TSK-type FRBS evolutionary design processes (a Mamdani-type two-stage EFS based on the Wang and Mendel fuzzy rule generation method [10], a three-stage Mamdani-type EFS =-=[11]-=-, and a TSK-type EFS [12], [13]). In the second application, the same EFS’s are considered, and 1083–4419/99$10.00 © 1999 IEEE704 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETIC... |

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Citation Context ...i and TSK-type FRBS evolutionary design processes (a Mamdani-type two-stage EFS based on the Wang and Mendel fuzzy rule generation method [10], a three-stage Mamdani-type EFS [11], and a TSK-type EFS =-=[12]-=-, [13]). In the second application, the same EFS’s are considered, and 1083–4419/99$10.00 © 1999 IEEE704 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 29, NO. 6, DECEMB... |

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Citation Context ..., we have selected the minimum t-norm playing the role of the implication and conjunctive operators, and the center of gravity weighted by the matching strategy acting as the defuzzification operator =-=[28]-=-. In the TSK-type ones obtained from processes T1 and T2, the role of conjunctive operator is played by the minimum t-norm as well. We have performed different runs of the proposed process, T2, using ... |

48 | Completeness and consistency conditions for learning fuzzy rules - González, Pérez - 1998 |

45 | A learning process for fuzzy control rules using genetic algorithms. Fuzzy Sets and Systems - Herrera, Lozano, et al. - 1997 |

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Citation Context ...own electrical needs in each moment. Therefore, we need to solve the problem using other kinds of techniques, which are able to relate some characteristics of a certain town with its maintenance cost =-=[29]-=-. In this paper, we consider evolutionary fuzzy modeling techniques and compare its behavior with classical regression and neural techniques. To solve the problem, we were provided with data related t... |

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Citation Context ...use they deal with fuzzy rules instead of classical logic rules. Thanks to this, they have been successfully applied to a wide range of problems presenting uncertainty and vagueness in different ways =-=[2]-=-. In particular, the most promising results Manuscript received March 1, 1998; revised May 10, 1999. This work was supported by CICYT under Grant TIC96-0778. This paper was recommended by Associate Ed... |

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Citation Context ...uzzy systems (EFS’s) when an Evolutionary Algorithm (EA) [7] is used instead of a GA. For a wider description of some of these approaches refer to [5], [6], [8], and for an extensive bibliography see =-=[9]-=-. In this paper, we present a two-stage evolutionary process to automatically learn Takagi–Sugeno –Kang (TSK) KB’s from examples. The learning process is divided into two stages: the generation and re... |

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Citation Context ... later stages. 2) Crossover: We shall work with another genetic operator which has shown good behavior for real-coded GA’s, the max-min-arithmetical crossover. This crossover operator was proposed in =-=[24]-=- and has been widely used in the field of EFS’s [11], [25]–[27]. It works as follows. If and are to be crossed, the following four offspring are generated: with with This operator can use a parameter ... |

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Citation Context ...consequent and the antecedent parts of the fuzzy rules in the preliminary KB obtained from the first stage. The second process is composed of a special real-coded GA (a genetic local search algorithm =-=[22]-=-) which includes an ( )-ES [7] as a genetic operator to improve the search process. The algorithm works on chromosomes encoding the whole preliminary definition of the KB obtained and globally adjusts... |

27 | Hybridizing genetic algorithms with sharing scheme and evolution strategies for designing fuzzy rule-based systems,” Fuzzy Sets and Systems
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Citation Context ...netic operator which has shown good behavior for real-coded GA’s, the max-min-arithmetical crossover. This crossover operator was proposed in [24] and has been widely used in the field of EFS’s [11], =-=[25]-=-–[27]. It works as follows. If and are to be crossed, the following four offspring are generated: with with This operator can use a parameter which is either a constant, or a variable whose value depe... |

18 |
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Citation Context ...erent techniques have been employed until now to derive the TSK KB from examples since Takagi and Sugeno first presented a process based on the least squares method [14]. For example, Neural Networks =-=[15]-=-, [16] and gradient descent methods [17] have been considered. The use of EA’s, either specific, GA’s [12], [18] and EE’s [19]; or hybrid [19], [20], has increased over the last few years. Fig. 1. Exa... |

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Citation Context ...l now to derive the TSK KB from examples since Takagi and Sugeno first presented a process based on the least squares method [14]. For example, Neural Networks [15], [16] and gradient descent methods =-=[17]-=- have been considered. The use of EA’s, either specific, GA’s [12], [18] and EE’s [19]; or hybrid [19], [20], has increased over the last few years. Fig. 1. Examples of angular coding. III. A NEW CODI... |

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Citation Context ... performing this task. Over the last few years, many different approaches have been presented taking genetic algorithms (GA’s) [4] as their base, obtaining the so called genetic fuzzy systems (GFS’s) =-=[5]-=-, [6] or, more generically, evolutionary fuzzy systems (EFS’s) when an Evolutionary Algorithm (EA) [7] is used instead of a GA. For a wider description of some of these approaches refer to [5], [6], [... |

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Citation Context ...cess based on the least squares method [14]. For example, Neural Networks [15], [16] and gradient descent methods [17] have been considered. The use of EA’s, either specific, GA’s [12], [18] and EE’s =-=[19]-=-; or hybrid [19], [20], has increased over the last few years. Fig. 1. Examples of angular coding. III. A NEW CODING SCHEME TO REPRESENT TSK RULE CONSEQUENTS There is a problem when designing TSK FRBS... |

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Citation Context ...oblem solution since the value of some of the parameters may lie outside the intervals considered. In this section, we propose a new coding scheme, called angular coding, which was first presented in =-=[21]-=-. It is based on encoding the values of the angles instead of the tangent values for each TSK rule consequent parameter, thus allowing us to have all the variables lying in the same fixed interval and... |

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Citation Context ...resented a process based on the least squares method [14]. For example, Neural Networks [15], [16] and gradient descent methods [17] have been considered. The use of EA’s, either specific, GA’s [12], =-=[18]-=- and EE’s [19]; or hybrid [19], [20], has increased over the last few years. Fig. 1. Examples of angular coding. III. A NEW CODING SCHEME TO REPRESENT TSK RULE CONSEQUENTS There is a problem when desi... |

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Citation Context ...t squares method [14]. For example, Neural Networks [15], [16] and gradient descent methods [17] have been considered. The use of EA’s, either specific, GA’s [12], [18] and EE’s [19]; or hybrid [19], =-=[20]-=-, has increased over the last few years. Fig. 1. Examples of angular coding. III. A NEW CODING SCHEME TO REPRESENT TSK RULE CONSEQUENTS There is a problem when designing TSK FRBS’s using EA’s. Usually... |

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Citation Context ... operator which has shown good behavior for real-coded GA’s, the max-min-arithmetical crossover. This crossover operator was proposed in [24] and has been widely used in the field of EFS’s [11], [25]–=-=[27]-=-. It works as follows. If and are to be crossed, the following four offspring are generated: with with This operator can use a parameter which is either a constant, or a variable whose value depends o... |