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A Practical Guide to Averaging Functions

  • Gleb Beliakov
  • Humberto Bustince Sola
  • Tomasa Calvo

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 329)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Gleb Beliakov, Humberto Bustince Sola, Tomasa Calvo Sánchez
    Pages 1-53
  3. Gleb Beliakov, Humberto Bustince Sola, Tomasa Calvo Sánchez
    Pages 55-99
  4. Gleb Beliakov, Humberto Bustince Sola, Tomasa Calvo Sánchez
    Pages 101-144
  5. Gleb Beliakov, Humberto Bustince Sola, Tomasa Calvo Sánchez
    Pages 145-181
  6. Gleb Beliakov, Humberto Bustince Sola, Tomasa Calvo Sánchez
    Pages 183-205
  7. Gleb Beliakov, Humberto Bustince Sola, Tomasa Calvo Sánchez
    Pages 207-250
  8. Gleb Beliakov, Humberto Bustince Sola, Tomasa Calvo Sánchez
    Pages 251-304
  9. Gleb Beliakov, Humberto Bustince Sola, Tomasa Calvo Sánchez
    Pages 305-345
  10. Back Matter
    Pages 347-352

About this book

Introduction

This book offers an easy-to-use and practice-oriented reference guide to mathematical averages. It presents different ways of aggregating input values given on a numerical scale, and of choosing and/or constructing aggregating functions for specific applications. Building on a previous monograph by Beliakov et al. published by Springer in 2007, it outlines new aggregation methods developed in the interim, with a special focus on the topic of averaging aggregation functions. It examines recent advances in the field, such as aggregation on lattices, penalty-based aggregation and weakly monotone averaging, and extends many of the already existing methods, such as: ordered weighted averaging (OWA), fuzzy integrals and mixture functions. A substantial mathematical background is not called for, as all the relevant mathematical notions are explained here and reported on together with a wealth of graphical illustrations of distinct families of aggregation functions. The authors mainly focus on practical applications and give central importance to the conciseness of exposition, as well as the relevance and applicability of the reported methods, offering a valuable resource for computer scientists, IT specialists, mathematicians, system architects, knowledge engineers and programmers, as well as for anyone facing the issue of how to combine various inputs into a single output value.

Keywords

Constructing Aggregation Functions Mixed Aggregation Functions Aggregation Operators Gini Mean Bonferroni Mean Counter-Harmonic Means Choquet and Sugeno Integrals Intuitionistic OWA Triangular Norms and Conforms Aggregation on Product Lattices Multiple Attribute Decision Making

Authors and affiliations

  • Gleb Beliakov
    • 1
  • Humberto Bustince Sola
    • 2
  • Tomasa Calvo
    • 3
  1. 1.Deakin University School of Information TechnologyBurwoodAustralia
  2. 2.Departamento de Automática yUniversidad Pública de NavarraPamplonaSpain
  3. 3.Universidad de Alcalá de HenaresMadridSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-24753-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-24751-9
  • Online ISBN 978-3-319-24753-3
  • Series Print ISSN 1434-9922
  • Series Online ISSN 1860-0808
  • Buy this book on publisher's site
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