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.

This book offers a comprehensive report on the state-of-the art in the broadly-intended field of "intelligent systems". After introducing key theoretical issues, it describes a number of promising models for data and system analysis, decision making, and control. It discusses important theories, including possibility theory, the Dempster-Shafer theory, the theory of approximate reasoning, as well as computing with words, together with novel applications in various areas, such as information aggregation and fusion, linguistic data summarization, participatory learning, systems modeling, and many others. By presenting the methods in their application contexts, the book shows how granular computing, soft computing and fuzzy logic techniques can provide novel, efficient solutions to real-world problems. It is dedicated to Professor Ronald R. Yager for his great scientific and scholarly achievements, and for his long-lasting service to the fuzzy logic, and the artificial and computational intelligence communities. It has been motivated by the authors' appreciation of his original thinking and groundbreaking ideas, with a special thought to his valuable research on the computerized implementation of various aspects of human cognition for decision-making and problem-solving.

A broad introduction to the topic of aggregation functions is to be found in this book. It also provides a concise account of the properties and the main classes of such functions. Some state-of-the-art techniques are presented, along with many graphical illustrations and new interpolatory aggregation functions. Particular attention is paid to identification and construction of aggregation functions from application specific requirements and empirical data.

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.

This book offers a comprehensive report on the state-of-the art in the broadly-intended field of "intelligent systems". After introducing key theoretical issues, it describes a number of promising models for data and system analysis, decision making, and control. It discusses important theories, including possibility theory, the Dempster-Shafer theory, the theory of approximate reasoning, as well as computing with words, together with novel applications in various areas, such as information aggregation and fusion, linguistic data summarization, participatory learning, systems modeling, and many others. By presenting the methods in their application contexts, the book shows how granular computing, soft computing and fuzzy logic techniques can provide novel, efficient solutions to real-world problems. It is dedicated to Professor Ronald R. Yager for his great scientific and scholarly achievements, and for his long-lasting service to the fuzzy logic, and the artificial and computational intelligence communities. It has been motivated by the authors' appreciation of his original thinking and groundbreaking ideas, with a special thought to his valuable research on the computerized implementation of various aspects of human cognition for decision-making and problem-solving.

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.

This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general aggregation operator. That simplicity, generality and implementability of the OWA operators, combined with their intuitive appeal, have triggered much research both in the foundations and extensions of the OWA operators, and in their applications to a wide variety of problems in various fields of science and technology.

Part I: Methods includes papers on theoretical foundations of OWA operators and their extensions. The papers in Part II: Applications show some more relevant applications of the OWA operators, mostly means, as powerful yet general aggregation operators. The application areas are exemplified by environmental modeling, social networks, image analysis, financial decision making and water resource management."

A broad introduction to the topic of aggregation functions is to be found in this book. It also provides a concise account of the properties and the main classes of such functions. Some state-of-the-art techniques are presented, along with many graphical illustrations and new interpolatory aggregation functions. Particular attention is paid to identification and construction of aggregation functions from application specific requirements and empirical data.

This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general aggregation operator. That simplicity, generality and implementability of the OWA operators, combined with their intuitive appeal, have triggered much research both in the foundations and extensions of the OWA operators, and in their applications to a wide variety of problems in various fields of science and technology.

Part I: Methods includes papers on theoretical foundations of OWA operators and their extensions. The papers in Part II: Applications show some more relevant applications of the OWA operators, mostly means, as powerful yet general aggregation operators. The application areas are exemplified by environmental modeling, social networks, image analysis, financial decision making and water resource management."