Discrete Fuzzy Measures: Computational Aspects

Description

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. Front Matter ....Pages i-xiv Introduction (Gleb Beliakov, Simon James, Jian-Zhang Wu)....Pages 1-39 Types of Fuzzy Measures (Gleb Beliakov, Simon James, Jian-Zhang Wu)....Pages 41-54 Value and Interaction Indices (Gleb Beliakov, Simon James, Jian-Zhang Wu)....Pages 55-73 Representations (Gleb Beliakov, Simon James, Jian-Zhang Wu)....Pages 75-87 Fuzzy Integrals (Gleb Beliakov, Simon James, Jian-Zhang Wu)....Pages 89-133 Symmetric Fuzzy Measures: OWA (Gleb Beliakov, Simon James, Jian-Zhang Wu)....Pages 135-192 k–Order Fuzzy Measures and k–Order Aggregation Functions (Gleb Beliakov, Simon James, Jian-Zhang Wu)....Pages 193-203 Learning Fuzzy Measures (Gleb Beliakov, Simon James, Jian-Zhang Wu)....Pages 205-239 Back Matter ....Pages 241-245