Aggregation Functions

by Beliakov, Gleb; Pradera, Ana; Calvo, Tomasa

• ISBN13: 9783540737209
• ISBN10: 3540737200
• Format: Hardcover
• Copyright: 2008-02-03
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Introduction	p. 1
Averaging functions	p. 39
Conjunctive and disjunctive functions	p. 123
Mixed functions	p. 197
Choice and construction of aggregation functions	p. 261
Interpolatory type aggregation functions	p. 271
Other types of aggregation and additional properties	p. 297
Tools for approximation and optimization	p. 305
References	p. 341
Index	p. 355
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