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Discrete Fuzzy Measures

Computational Aspects

  • Gleb Beliakov
  • Simon James
  • Jian-Zhang Wu

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 1-39
  3. Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 41-54
  4. Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 55-73
  5. Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 75-87
  6. Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 89-133
  7. Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 135-192
  8. Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 193-203
  9. Gleb Beliakov, Simon James, Jian-Zhang Wu
    Pages 205-239
  10. Back Matter
    Pages 241-245

About this book

Introduction

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.

Keywords

Symmetric Fuzzy Measures Nonlinear Integrals Non-additive Integrals Non-additive Measures Nonadditive Ordinal Regression k-maxitive Fuzzy Measures Maximum Entropy Fuzzy Measures Aggregating Data Aggregation Operators Ordered Weighted Averaging (OWA) Induced OWA Averaging Functions Fuzzy Partial Orders Preference Relations Interaction Indices Nonadditivity Indices Non-modularity

Authors and affiliations

  • Gleb Beliakov
    • 1
  • Simon James
    • 2
  • Jian-Zhang Wu
    • 3
  1. 1.Deakin UniversityBurwoodAustralia
  2. 2.Deakin UniversityBurwoodAustralia
  3. 3.Ningbo UniversityNingboChina

Bibliographic information

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