This paper presents a new approach to the problem of designing Radial Basis Function Neural Networks (RBFNNs) to approximate a given function. The presented algorithm focuses in the first stage of the design where the centers of the RBFs have to be placed. This task has been commonly solved by applying generic clustering algorithms although in other cases, some specific clustering algorithms we...

In contrast to the symbolic approach, neural networks seldom are designed to explain what they have learned. This is a major obstacle for its use in everyday life. With the appearance of neuro-fuzzy systems which use vague, human-like categories the situation has changed. Based on the well-known mechanisms of learning for RBF networks, a special neuro-fuzzy interface is proposed in this paper. ...

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

This paper connects two thoroughly investigated universal approximator techniques to each other. Recently, it has been shown that the input-output function of the general fuzzy KH interpolation method [1, 2] as well as its modification [3] are stable in the mathematical sense, or in other words, they can be considered as universal approximators with respect to the Lp (p ∈ [1,∞]) norm in the spa...

Pulmonary elastance provides an important basis for deciding air pressure parameters of mechanical ventilators, and airway resistance is an important parameter in the diagnosis of respiratory diseases. The authors have proposed a second order nonlinear differential equation model of respiratory system whose elastic and resistant coefficients are expressed by RBF networks with the lung volume as...

[1] K. J. Hunt, R. Hass, and R. Murray-Smith, “Extending the functional equivalence of radial basis function networks and fuzzy inference systems,” IEEE Trans. Neural Networks, vol. 7, pp. 776–781, May 1996. [2] J.-S. R. Jang, C.-T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, MATLAB Curriculum Series. Upper Saddle River, N...

Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...

This study developed a hybrid self-organizing fuzzy and radial basis-function neural-network controller (HSFRBNC) for active suspension systems. The HSFRBNC uses a radial basis function neural-network to adjust the learning rate and the weighting distribution of a self-organizing fuzzy controller (SOFC) in real time, as an alternative to obtain these parameters through trial and error. Therefor...

In this paper, the use of clustering algorithms for decisionlevel data fusion is proposed. Person authentication results coming from several modalities (e.g., still image, speech), are combined by using fuzzy k-means (FKM) and fuzzy vector quantization (FVQ) algorithms, and median radial basis function (MRBF) network. The quality measure of the modalities data is used for fuzzification. Two mod...

In this paper, new definitions of a fuzzy basis and a fuzzy dimension for a fuzzy vector space are presented. A fuzzy basis for a fuzzy vector space (E, μ) is a fuzzy set β on E. The cardinality of a fuzzy basis β is called the fuzzy dimension of (E, μ). The fuzzy dimension of a finite dimensional fuzzy vector space is a fuzzy natural number. For a fuzzy vector space, any two fuzzy bases have t...