Aggregation of information is of primary importance in the construction of knowledge based systems in various domains, ranging from medicine, economics, and engineering to decision-making processes, artificial intelligence, robotics, and machine learning. This book gives a broad introduction into the topic of aggregation functions, and provides a concise account of the properties and the main classes of such functions, including classical means, medians, ordered weighted averaging functions, Choquet and Sugeno integrals, triangular norms, conorms and copulas, uninorms, nullnorms, and symmetric sums. It also presents some state-of-the-art techniques, many graphical illustrations and new interpolatory aggregation functions. A particular attention is paid to identification and construction of aggregation functions from application specific requirements and empirical data. This book provides scientists, IT specialists and system architects with a self-contained easy-to-use guide, as well as examples of computer code and a software package. It will facilitate construction of decision support, expert, recommender, control and many other intelligent systems.

Broad introduction into the topic of aggregation functions and discusses in detail the four broad classes of aggregation operators: averaging operators, conjunctive, disjunctive and mixed operators Comes with a software package AOTool, which can be freely downloaded implementing a large number of methods for fitting aggregation functions to empirical data, described in the relevant sections of the book Oriented towards practitioners: computer scientists, software engineers, knowledge engineers Explains the material in a simple way (requires only basic mathematics), with many illustrations and examples Includes supplementary material: sn.pub/extras

Autorentext

Gleb Beliakov is a Professor in Mathematics at Deakin University, Australia. He completed his PhD in 1992 in Moscow and since then worked at various universities, for the last 25 years at Deakin University. His research is focused on computational mathematics, numerical optimisation and aggregation functions. He co-authored three monographs and numerous research papers in this area. Simon James is an Associate Professor in Mathematics at Deakin University. He completed his Ph.D. there on the topic of aggregation functions in 2010 under the supervision of Gleb Beliakov and held an academic position there since 2011. His main research areas of aggregation and capacities (or fuzzy measures) are most commonly applied in computational intelligence and machine learning as prediction and analysis tools. Jian-Zhang Wu was a Research Fellow at Deakin University. He received his PhD in Management Science and Engineering in 2011 from Beijing Institute of Technology and was previously a professor at Ningbo University. He has also worked as a chief data scientist in the finance industry. His research focuses on machine learning, decision-making, and explainable AI, especially using Choquet capacities and fuzzy integrals. He has led several national and provincial research projects in China.

Inhalt
Averaging Functions.- Conjunctive and Disjunctive Functions.- Mixed Functions.- Choice and Construction of Aggregation Functions.- Interpolatory Type Aggregation Functions.- Other Types of Aggregation and Additional Properties.