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

  • George A. Anastassiou

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 190)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. George A. Anastassiou
    Pages 93-108
  3. George A. Anastassiou
    Pages 109-125
  4. George A. Anastassiou
    Pages 127-148
  5. George A. Anastassiou
    Pages 307-316

About this book

Introduction

Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences.

The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.

Keywords

Non-Additive Integrals Neural Network Operators Choquet Integral Approximators Shilkret Integral Approximators Sugeno Integral Approximators Kantorovich-Choquet Quasi-Interpolation

Authors and affiliations

  • George A. Anastassiou
    • 1
  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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