Approximate realization of fuzzy mappings by regression models, neural networks and rule-based systems

Ishibuchi, Hisao; Nii, Manabu; Oh, Chi-Hyon

doi:10.1109/fuzzy.1999.793078

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…In Algorithm 2, by solving following constraint type minimum problem we can find a suitable learning constant (see (20) Subject to (20) At first, by , (20) can be transformed into unconstrained one [22] ( 21) where . To guarantee the error sequence will not fluctuate, excessively, let the learning constant belong to .…”

Section: B Ga For Finding Optimal Learning Constantmentioning

confidence: 99%

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Efficient Learning Algorithms for Three-Layer Regular Feedforward Fuzzy Neural Networks

Liu

2004

IEEE Trans. Neural Netw.

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A key step of using gradient descend methods to develop learning algorithms of a regular feedforward fuzzy neural network (FNN) is to differentiate max--min functions, which contain max and min operations. The paper aims at several objectives. First, investigate further the differentiation of max--min functions. Second, employ general fuzzy numbers, which include triangular and trapezoidal fuzzy numbers as special cases to define a three-layer regular FNN. The general fuzzy numbers related can be approximately determined by their corresponding finite level sets. So, we can approximately represent the input-output (I/O) relationship of the regular FNN as functions of the endpoints of all finite level sets. Third, a fuzzy back-propagation algorithm is presented. And to speed up the convergence of the learning algorithm, a fuzzy conjugate gradient algorithm for fuzzy weights and biases is developed, furthermore, the convergence of the algorithm is analyzed, systematically. Finally, some real simulations demonstrate the efficiency of our learning algorithms. The regular FNN is applied to the approximate realization of fuzzy inference rules and fuzzy functions defined on given compact sets.

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Section: B Ga For Finding Optimal Learning Constantmentioning

confidence: 99%

“…If a real system maps fuzzy inputs to fuzzy outputs, we can employ regular FNNs not neuro-fuzzy networks to realize such a system, approximately [21]. Furthermore, applying regular FNNs we can solve the overfitting problem [11].…”

Section: Introductionmentioning

confidence: 97%