Rule learning in fuzzy systems using evolutionary programs

Goddard, John C.; Parrazales, Romeo Urbieta; López, Iván Barriuso

doi:10.1109/mwscas.1996.587842

Cited by 9 publications

(5 citation statements)

References 8 publications

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“…We can minimize E by using the partial derivatives of E with respect to the modal points and half-widths of the input and output fuzzy membership functions. We can obtain expressions for these derivatives using (1)- (6). Then, using the differentiation chain rule on (9), we can obtain expressions for the derivative of the error function with respect to the halfwidths and modal points.…”

Section: Fuzzy System Optimization Via H ' Filteringmentioning

confidence: 99%

“…The methods can be broadly divided into two types: those that explicitly use the derivatives of the fuzzy systemÕs performance with respect to the fuzzy parameters, and those that do not use these derivatives. Derivative-free methods include genetic algorithms [1][2][3], neural networks [4,5], evolutionary programming [6], geometric methods [7], fuzzy equivalence relations [8], and heuristic methods [9]. Derivative-based methods include gradient descent [2,10], Kalman filtering [11], the simplex method [12,13], least squares [14,15], backpropagation [16], and other numerical techniques [17].…”

Section: Introductionmentioning

confidence: 99%

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H∞ estimation for fuzzy membership function optimization

Simon

2005

International Journal of Approximate Reasoning

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Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a specific shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a few variables and the membership optimization problem can be reduced to a parameter optimization problem. The parameter optimization problem can then be formulated as a nonlinear filtering problem. In this paper we solve the nonlinear filtering problem using H 1 state estimation theory. However, the membership functions that result from this approach are not (in general) sum normal. That is, the membership function values do not add up to one at each point in the domain. We therefore modify the H 1 filter with the addition of state constraints so that the resulting membership functions are sum normal. Sum normality may be desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The methods proposed in this paper are illustrated on a fuzzy automotive cruise controller and compared to Kalman filtering based optimization.

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Section: Fuzzy System Optimization Via H ' Filteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

H∞ estimation for fuzzy membership function optimization

Simon

2005

International Journal of Approximate Reasoning

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“…The nonlinear system model to which the Kalman filter can be applied is (15) where h(xn) is the fuzzy system's nonlinear mapping from the membership func tion parameters to the single fuzzy system output, and Wn and Vn are artificially added noise processes. The addition of these noise processes is a commonly prac ticed technique in parameter estimation algorithms to increase the stability of the estimator 34 ,36.…”

Section: Extended Kalman Filteringmentioning

confidence: 99%

Sum Normal Optimization of Fuzzy Membership Functions

Simon

2002

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This optimization approach is modified in this paper so that the resulting membership functions are sum normal. Sum normality is desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The sum normal constraint is applied in this paper to both gradient descent optimization and Kalman filter optimization of fuzzy membership functions. The methods are illustrated on a fuzzy automotive cruise controller.

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“…Derivative-based methods for membership optimization include gradient descent, 14,15 Kalman filtering, 16 H ∞ filtering, 17 the simplex method, 18,19 least squares, 20,21 back-propagation 22 and other techniques. 23–25 On the other hand, evolutionary programming 26 such as GAs 27–31 and tabu search (TS), 32 neural networks, like self-organizing feature maps (SOFM), 33–35 geometric methods, 36 fuzzy equivalence relations 37 and other heuristic methods 38–40 are examples of the non-derivative methods used throughout the literature for optimization of membership functions.…”

Section: Introductionmentioning

confidence: 99%

Design of optimized fuzzy model-based controller for nonlinear systems using hybrid intelligent strategies

Kharrati

Khanmohammadi

Zeiaee

et al. 2012

Proceedings of the Institution of Mechanical Engineers, Part I:

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This paper introduces three hybrid methods for the generation and optimization of rules and membership functions of a fuzzy logic controller for nonlinear systems. The proposed methods overcome the deficiency of a systematic approach for optimal design of fuzzy controllers. An optimally designed fuzzy logic controller should have the least number of fuzzy variables and fuzzy rules and the best possible configuration of fuzzy rules in the rule table. The first strategy of this paper is a two-phase optimization problem: in the first phase, the number of fuzzy variables and their arrangement in the rule table are optimized by a genetic algorithm; in the second phase, the parameters of the membership functions are optimized via extended Kalman filtering. The second strategy tries to achieve the goals of the first method all in one phase by modifying the chromosome structure of the genetic algorithm. Then in the next step, a local search algorithm is utilized to improve the obtained results. The third strategy is similar to the second strategy in structure. However, along with optimizing the number of fuzzy variables and membership parameters, the number of fuzzy rules is also optimized. The first and second strategies are obliged to use every possible combination of fuzzy variables in the rule table; however, the third strategy is capable of distinguishing between useful and useless fuzzy rules in the rule table. The introduced strategies are applied to an automotive cruise control system. The results of the simulations show the effectiveness of the proposed methods and the superiority of the latter approaches over the former ones.

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Rule learning in fuzzy systems using evolutionary programs

Cited by 9 publications

References 8 publications

H∞ estimation for fuzzy membership function optimization

H∞ estimation for fuzzy membership function optimization

Sum Normal Optimization of Fuzzy Membership Functions

Design of optimized fuzzy model-based controller for nonlinear systems using hybrid intelligent strategies

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