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Discrete Fuzzy Measures

Computational Aspects

  • Book
  • © 2020

Overview

Authors:
  1. Gleb Beliakov

    1. Deakin University, Burwood, Australia

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    You can also search for this author in PubMed   Google Scholar

  2. Simon James

    1. Deakin University, Burwood, Australia

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  3. Jian-Zhang Wu

    1. Ningbo University, Ningbo, China

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    You can also search for this author in PubMed   Google Scholar

  • Presents new findings concerning aggregation of inputs
  • Offers new insights into computational aspects of fuzzy measures
  • Explains all the necessary mathematical concepts

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 382)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    • Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 1-39

  3. Types of Fuzzy Measures

    • Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 41-54

  4. Value and Interaction Indices

    • Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 55-73

  5. Representations

    • Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 75-87

  6. Fuzzy Integrals

    • Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 89-133

  7. Symmetric Fuzzy Measures: OWA

    • Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 135-192

  8. k–Order Fuzzy Measures and k–Order Aggregation Functions

    • Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 193-203

  9. Learning Fuzzy Measures

    • Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 205-239

  10. Back Matter

    Pages 241-245
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Keywords

About this book

This book addresses computer scientists, IT specialists, mathematicians, knowledge engineers and programmers, who are engaged in research and practice of multicriteria decision making. Fuzzy measures, also known as capacities, allow one to combine degrees of preferences, support or fuzzy memberships into one representative value, taking into account interactions between the inputs. The notions of mutual reinforcement or redundancy are modeled explicitly through coefficients of fuzzy measures, and fuzzy integrals, such as the Choquet and Sugeno integrals combine the inputs. Building on previous monographs published by the authors and dealing with different aspects of aggregation, this book especially focuses on the Choquet and Sugeno integrals. It presents a number of new findings concerning computation of fuzzy measures, learning them from data and modeling interactions. The book does not require substantial mathematical background, as all the relevant notions are explained. It is intended as concise, timely and self-contained guide to the use of fuzzy measures in the field of multicriteria decision making.

Authors and Affiliations

  • Deakin University, Burwood, Australia

    Gleb Beliakov, Simon James

  • Ningbo University, Ningbo, China

    Jian-Zhang Wu

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