Radko Mesiar's Books

Aggregation Functions

By: Michel Grabisch,Jean-Luc Marichal,Radko Mesiar,Endre Pap

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Aggregation Functions

By: Michel Grabisch,Jean-Luc Marichal,Radko Mesiar,Endre Pap

Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science, and many applied fields (economics and finance, pattern recognition and image processing, data fusion, etc.). This is a comprehensive, rigorous and self-contained exposition of aggregation functions. Classes of aggregation functions covered include triangular norms and conorms, copulas, means and averages, and those based on nonadditive integrals. The properties of each method, as well as their interpretation and analysis, are studied in depth, together with construction methods and practical identification methods. Special attention is given to the nature of scales on which values to be aggregated are defined (ordinal, interval, ratio, bipolar). It is an ideal introduction for graduate students and a unique resource for researchers.

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Page Count

481

Publisher

Cambridge University Press

Published Date

ISBN 10

1139643223

ISBN 13

9781139643221

Triangular Norms

By: Erich Peter Klement,Radko Mesiar,Endre Pap

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Triangular Norms

By: Erich Peter Klement,Radko Mesiar,Endre Pap

This book discusses the theory of triangular norms and surveys several applied fields in which triangular norms play a significant part: probabilistic metric spaces, aggregation operators, many-valued logics, fuzzy logics, sets and control, and non-additive measures together with their corresponding integrals. It includes many graphical illustrations and gives a well-balanced picture of theory and applications. It is for mathematicians, computer scientists, applied computer scientists and engineers.

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Page Count

387

Publisher

Springer

Published Date

ISBN 10

9401595410

ISBN 13

9789401595414

New Trends in Aggregation Theory

By: Radomâir Halaés,Marek Gagolewski,Radko Mesiar

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New Trends in Aggregation Theory

By: Radomâir Halaés,Marek Gagolewski,Radko Mesiar

This book collects the contributions presented at AGOP 2019, the 10th International Summer School on Aggregation Operators, which took place in Olomouc (Czech Republic) in July 2019. It includes contributions on topics ranging from the theory and foundations of aggregation functions to their various applications. Aggregation functions have numerous applications, including, but not limited to, data fusion, statistics, image processing, and decision-making. They are usually defined as those functions that are monotone with respect to each input and that satisfy various natural boundary conditions. In particular settings, these conditions might be relaxed or otherwise customized according to the user's needs. Noteworthy classes of aggregation functions include means, t-norms and t-conorms, uninorms and nullnorms, copulas and fuzzy integrals (e.g., the Choquet and Sugeno integrals). This book provides a valuable overview of recent research trends in this area.

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Page Count

348

Published Date

ISBN 10

3030194957

ISBN 13

9783030194956

Book's by Radko Mesiar

Aggregation Functions

Aggregation Functions

Triangular Norms

Triangular Norms

New Trends in Aggregation Theory

New Trends in Aggregation Theory

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