Measuring fuzzy specificity using fuzzy unit hypercube

2018 ◽  
Vol 5 (1) ◽  
pp. 39-47
Author(s):  
Geoffrey O. Barini ◽  
Livingstone M. Ngoo ◽  
Ronald M. Waweru
Keyword(s):  
Unit Hypercube

The distribution of the sequence {nξ}(n = 0, 1, 2, …)

1965 ◽  
Vol 61 (3) ◽  
pp. 665-670 ◽  
Author(s):  
John H. Halton
Keyword(s):  
Unit Interval ◽  
Simple Generalization ◽  
Unit Hypercube

Introduction and statement of results. We shall describe how, for successive integers N, the points {nξ}, with n = 0, 1, …,N – 1, are distributed in the closed unit interval U = [0, 1]; by showing how successive points {Nξ,} modify the partition of U produced by the previous points. The simple generalization to the k-dimensional sequence {nξ} = ({nξ(1)},{nξ(2)}, …,{nξ(k)}), in the unit hypercube Uk, is also made.

Application of a fuzzy unit hypercube in cardiovascular risk classification

2019 ◽  
Vol 23 (23) ◽  
pp. 12521-12527
Author(s):  
Geoffrey O. Barini ◽  
Livingstone M. Ngoo ◽  
Ronald W. Mwangi
Keyword(s):  
Cardiovascular Risk ◽  
Risk Classification ◽  
Unit Hypercube

Bounding the stochastic performance of continuum structure functions. II

1987 ◽  
Vol 24 (03) ◽  
pp. 609-618 ◽  
Author(s):  
Laurence A. Baxter ◽  
Chul Kim
Keyword(s):  
Structure Function ◽  
Random Variables ◽  
Structure Functions ◽  
Unit Interval ◽  
Modular Decomposition ◽  
Associated Random Variables ◽  
Unit Hypercube ◽  
Continuum Structure

A continuum structure function γ is a non-decreasing mapping from the unit hypercube to the unit interval. Block and Savits (1984) use the sets and to determine bounds on the distribution of γ (X) when X is a vector of associated random variables. It is shown that, if γ admits of a modular decomposition, improved bounds may be obtained.

Continuum structures. II

1986 ◽  
Vol 99 (2) ◽  
pp. 331-338 ◽  
Author(s):  
Laurence A. Baxter
Keyword(s):  
Structure Function ◽  
Unit Interval ◽  
Continuum Structures ◽  
Unit Hypercube ◽  
Continuum Structure ◽  
The Subject ◽  
Nondecreasing Mapping

AbstractA continuum structure function is a nondecreasing mapping from the unit hypercube to the unit interval. This paper continues the author's work on the subject, extending Griffith's definitions of coherency to such functions and studying the analytic properties of a continuum structure function based on Natvig's ‘second suggestion’.

Approximation Capability of Layered Neural Networks with Sigmoid Units on Two Layers

1994 ◽  
Vol 6 (6) ◽  
pp. 1233-1243 ◽  
Author(s):  
Yoshifusa Ito
Keyword(s):  
Neural Networks ◽  
Feedforward Neural Networks ◽  
Constructive Method ◽  
Heaviside Function ◽  
Supremum Norm ◽  
Sigmoid Function ◽  
Unit Hypercube ◽  
Approximation Capability ◽  
Special Case ◽  
Accuracy Of Approximation

Using only an elementary constructive method, we prove the universal approximation capability of three-layered feedforward neural networks that have sigmoid units on two layers. We regard the Heaviside function as a special case of sigmoid function and measure accuracy of approximation in either the supremum norm or in the Lp-norm. Given a continuous function defined on a unit hypercube and the required accuracy of approximation, we can estimate the numbers of necessary units on the respective sigmoid unit layers. In the case where the sigmoid function is the Heaviside function, our result improves the estimation of Kůrková (1992). If the accuracy of approximation is measured in the LP-norm, our estimation also improves that of Kůrková (1992), even when the sigmoid function is not the Heaviside function.

scholarly journals Minimizing the L2 and L∞ star discrepancies of a single point in the unit hypercube

2006 ◽  
Vol 197 (1) ◽  
pp. 282-285 ◽  
Author(s):  
Tim Pillards ◽  
Bart Vandewoestyne ◽  
Ronald Cools
Keyword(s):  
Single Point ◽  
Unit Hypercube

scholarly journals A Universal Approximation Theorem for Mixture-of-Experts Models

2016 ◽  
Vol 28 (12) ◽  
pp. 2585-2593 ◽  
Author(s):  
Hien D. Nguyen ◽  
Luke R. Lloyd-Jones ◽  
Geoffrey J. McLachlan
Keyword(s):  
Network Architecture ◽  
Approximation Theorem ◽  
Target Function ◽  
Continuous Functions ◽  
Universal Approximation ◽  
Mixture Of Experts ◽  
Neural Network Architecture ◽  
Alternative Result ◽  
Unit Hypercube ◽  
Uniformly Convergent

The mixture-of-experts (MoE) model is a popular neural network architecture for nonlinear regression and classification. The class of MoE mean functions is known to be uniformly convergent to any unknown target function, assuming that the target function is from a Sobolev space that is sufficiently differentiable and that the domain of estimation is a compact unit hypercube. We provide an alternative result, which shows that the class of MoE mean functions is dense in the class of all continuous functions over arbitrary compact domains of estimation. Our result can be viewed as a universal approximation theorem for MoE models. The theorem we present allows MoE users to be confident in applying such models for estimation when data arise from nonlinear and nondifferentiable generative processes.

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