Jian-Zhang Wu – författare

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.

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.

Choquet capacities, which provide the weighting mechanism for the Choquet and other fuzzy integrals, model synergistic and antagonistic interactions between variables by assigning value to all subsets rather than individual inputs.  While the flexibility of capacities (also referred to as fuzzy measures and cooperative games) comes at the expense of an exponentially increasing number of parameters, the ability to explain their behavior using various value and interaction indices makes them appealing for applications requiring transparency and interpretability. As well as a number of useful indices that in some way capture the extent to which positive and negative interactions occur, significant progress has been made in addressing the scalability issues that arise in applications.  This book provides a detailed overview of the background concepts relating to capacities and their role in fuzzy integration and aggregation, then presents specialised chapters on most recent results in learning, random sampling and optimization that involve Choquet capacities.Topics and features:·       Fundamentals of Choquet capacities (fuzzy measures) and their use in modeling importance and interaction between variables·       Definitions, properties and mappings between alternative representations that allow capacities and fuzzy integrals to be interpreted and applied in different settings·       Various simplification assumptions, from k-additive, p-symmetric and l-measures to more recent concepts such as k-interactive and hierarchical frameworks·       Capacity learning formulations that allow the diverse types to be elicited from datasets or according to user-specified requirements·       Recent findings related to random sampling and optimisation with Choquet integral objectivesThis book includes illustrative examples and guidance for implementation, including an appendix detailing functions found in the pyfmtools software library. It aims to be useful for practitioners and researchers in decision and data-driven fields, or those who wish to apply these emerging tools to new problems. The authors are all affiliated with the School of Information Technology at Deakin University, Australia. Gleb Beliakov is a professor, Simon James is an Associate Professor, and Jian-Zhang Wu is a Research Fellow.