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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 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 collects the extended abstracts of 45 contributions of
participants to the Seventh International Summer School on
Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20,
2013. These contributions cover a very broad range, from the purely
theoretical ones to those with a more applied focus. Moreover, the
summaries of the plenary talks and tutorials given at the same
workshop are included. Together they provide a good overview of
recent trends in research in aggregation functions which can be of
interest to both researchers in Physics or Mathematics working on
the theoretical basis of aggregation functions, and to engineers
who require them for applications.
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