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Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators

Part of the Studies in Systems, Decision and Control Book Series (volume 190)

DOI: 10.1007/978-3-030-04287-5

ISBN: 978-3-030-04286-8

Publisher: Springer International Publishing - Springer Journals

Dec 7, 2018

1 - 10 of 17 Chapters

LitStream

Chapter 1Approximation with Rates by Kantorovich–Choquet Quasi-interpolation Neural Network Operators

Anastassiou, George A.

Pages: 1 –21

[In this chapter we present univariate and multivariate basic approximation by Kantorovich–Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous...
LitStream

Chapter 2Approximation with Rates by Perturbed Kantorovich–Choquet Neural Network Operators

Anastassiou, George A.

Pages: 23 –54

[This chapter deals with the determination of the rate of convergence to the unit of Perturbed Kantorovich–Choquet univariate and multivariate normalized neural network operators of one hidden layer. These are given through the univariate and multivariate moduli of continuity of the involved...
LitStream

Chapter 3Approximation with Rates by Shift Invariant Univariate Sublinear-Choquet Operators

Anastassiou, George A.

Pages: 55 –72

[A very general positive sublinear Choquet integral type operator is given through a convolution-like iteration of another general positive sublinear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence...
LitStream

Chapter 4Approximation with Rates by Shift Invariant Multivariate Sublinear-Choquet Operators

Anastassiou, George A.

Pages: 73 –91

[A very general multivariate positive sublinear Choquet integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it sufficient conditions are given for shift invariance,...
LitStream

Chapter 5Hardy Type Inequalities for Choquet Integrals

Anastassiou, George A.

Pages: 93 –108

[Here we present Hardy type integral inequalities for Choquet integrals. These are very general inequalities involving convex and increasing functions. Initially we collect a rich machinery of results about Choquet integrals needed next, and we prove also results of their own merit such as,...
LitStream

Chapter 6Quantitative Approximation by Choquet Integrals

Anastassiou, George A.

Pages: 109 –125

[Here we present the quantitative approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the study of the rate of the convergence of the well-known Bernstein–Kantorovich–Choquet and...
LitStream

Chapter 7Conformable Fractional Approximation by Choquet Integrals

Anastassiou, George A.

Pages: 127 –148

[Here we present the conformable fractional quantitative approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the study of the conformable fractional rate of the convergence of the well-known...
LitStream

Chapter 8Multivariate and Convex Quantitative Approximation by Choquet Integrals

Anastassiou, George A.

Pages: 149 –192

[Here we consider the quantitative approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the study of the rate of the convergence of the well-known Bernstein–Kantorovich–Choquet and...
LitStream

Chapter 9Caputo and Canavati Fractional Quantitative Approximation by Choquet Integrals

Anastassiou, George A.

Pages: 193 –212

[Here we consider the quantitative Caputo and Canavati fractional approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the study of the fractional rate of the convergence of the well-known...
LitStream

Chapter 10Mixed Conformable and Iterated Fractional Quantitative Approximation by Choquet Integrals

Anastassiou, George A.

Pages: 213 –240

[Here we study the quantitative mixed conformable and iterated fractional approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the research of the mixed conformable and iterated fractional rate of...

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