Numerical analysis of the learning of fuzzified neural networks from fuzzy if–then rules

Ishibuchi, Hisao; Nii, Manabu

doi:10.1016/s0165-0114(99)00070-6

Cited by 55 publications

(27 citation statements)

References 14 publications

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“…Ishibuchi et al [33] presented a comparison between real numbers, and different fuzzy numbers such as symmetric triangular, asymmetric triangular and symmetric trapezoidal as weights in the connections between layers in a neural network. Karnik et al [34] presented mathematical operations of type-2 fuzzy sets for obtaining the join and meet under t-norm.…”

Section: Proposed Methodologymentioning

confidence: 99%

Comparison of T-Norms and S-Norms for Interval Type-2 Fuzzy Numbers in Weight Adjustment for Neural Networks

et al. 2017

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Abstract:A comparison of different T-norms and S-norms for interval type-2 fuzzy number weights is proposed in this work. The interval type-2 fuzzy number weights are used in a neural network with an interval backpropagation learning enhanced method for weight adjustment. Results of experiments and a comparative research between traditional neural networks and the neural network with interval type-2 fuzzy number weights with different T-norms and S-norms are presented to demonstrate the benefits of the proposed approach. In this research, the definitions of the lower and upper interval type-2 fuzzy numbers with random initial values are presented; this interval represents the footprint of uncertainty (FOU). The proposed work is based on recent works that have considered the adaptation of weights using type-2 fuzzy numbers. To confirm the efficiency of the proposed method, a case of data prediction is applied, in particular for the Mackey-Glass time series (for τ = 17). Noise of Gaussian type was applied to the testing data of the Mackey-Glass time series to demonstrate that the neural network using a interval type-2 fuzzy numbers method achieves a lower susceptibility to noise than other methods.

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Section: Proposed Methodologymentioning

confidence: 99%

Comparison of T-Norms and S-Norms for Interval Type-2 Fuzzy Numbers in Weight Adjustment for Neural Networks

et al. 2017

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“…Substituting these into equations (Ishibuchi et al 1995;Ishibuchi and Nii 2001;Rumelhart and McClelland 1986), we obtain…”

Section: Learning Fuzzy Neural Networkmentioning

confidence: 99%

Numerical solution of fully fuzzy linear systems by fuzzy neural network

2011

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In this paper, a new hybrid method based on fuzzy neural network (FNN) for approximate solution of fuzzy linear systems of the form Ax ¼ d; where A is a square matrix of fuzzy coefficients, x and d are fuzzy number vectors, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution of an n Â n system of fuzzy linear equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of the FNN is proposed. Finally, we illustrate our approach by some numerical examples.

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“…We call such fuzzified neural networks to be regular FNNs [2], [24]- [27]. The regular FNNs have successfully applied to many real problems that are inherent uncertain and imprecise, involving adaptive control, system identification, and pattern classification [11], [16], [17]- [19]. Similarly with crisp neural networks in approximation capability [4], [32], the regular FNNs can provide universal approximation to general Manuscript fuzzy functions [2], [12], [24]- [27], including monotone increasing continuous fuzzy functions that are cut-preserving.…”

Section: Introductionmentioning

confidence: 99%

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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Numerical analysis of the learning of fuzzified neural networks from fuzzy if–then rules

Cited by 55 publications

References 14 publications

Comparison of T-Norms and S-Norms for Interval Type-2 Fuzzy Numbers in Weight Adjustment for Neural Networks

Comparison of T-Norms and S-Norms for Interval Type-2 Fuzzy Numbers in Weight Adjustment for Neural Networks

Numerical solution of fully fuzzy linear systems by fuzzy neural network

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

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