Aggregation Functions in Theory and in Practice
Aggregation Functions in Theory and in Practice

Author: Vicenç Torra

Publisher: Springer

Published: 2017-05-17

Total Pages: 288

ISBN-13: 3319593064

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This book collects the abstracts of the contributions presented at AGOP 2017, the 9th International Summer School on Aggregation Operators. The conference took place in Skövde (Sweden) in June 2017. Contributions include works from theory and fundamentals of aggregation functions to their use in applications. Aggregation functions are usually defined as those functions that are monotonic and that satisfy the unanimity condition. In particular settings these conditions are relaxed. Aggregation functions are used for data fusion and decision making. Examples of these functions include means, t-norms and t-conorms, copulas and fuzzy integrals (e.g., the Choquet and Sugeno integrals).

Aggregation Functions in Theory and in Practise
Aggregation Functions in Theory and in Practise

Author: Humberto Bustince Sola

Publisher: Springer Science & Business Media

Published: 2013-06-20

Total Pages: 535

ISBN-13: 3642391656

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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.

Aggregation Functions in Theory and in Practise
Aggregation Functions in Theory and in Practise

Author: Humberto Bustince

Publisher: Springer

Published: 2013-06-26

Total Pages: 552

ISBN-13: 9783642391668

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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.

An Introduction to Data Analysis using Aggregation Functions in R
An Introduction to Data Analysis using Aggregation Functions in R

Author: Simon James

Publisher: Springer

Published: 2016-11-07

Total Pages: 205

ISBN-13: 331946762X

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This textbook helps future data analysts comprehend aggregation function theory and methods in an accessible way, focusing on a fundamental understanding of the data and summarization tools. Offering a broad overview of recent trends in aggregation research, it complements any study in statistical or machine learning techniques. Readers will learn how to program key functions in R without obtaining an extensive programming background. Sections of the textbook cover background information and context, aggregating data with averaging functions, power means, and weighted averages including the Borda count. It explains how to transform data using normalization or scaling and standardization, as well as log, polynomial, and rank transforms. The section on averaging with interaction introduces OWS functions and the Choquet integral, simple functions that allow the handling of non-independent inputs. The final chapters examine software analysis with an emphasis on parameter identification rather than technical aspects. This textbook is designed for students studying computer science or business who are interested in tools for summarizing and interpreting data, without requiring a strong mathematical background. It is also suitable for those working on sophisticated data science techniques who seek a better conception of fundamental data aggregation. Solutions to the practice questions are included in the textbook.

New Trends in Aggregation Theory
New Trends in Aggregation Theory

Author: Radomír Halaš

Publisher: Springer

Published: 2019-05-16

Total Pages: 348

ISBN-13: 3030194949

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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.

Aggregation Functions
Aggregation Functions

Author: Michel Grabisch

Publisher: Cambridge University Press

Published: 2009-07-09

Total Pages: 481

ISBN-13: 1139643223

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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.

New Trends in Aggregation Theory
New Trends in Aggregation Theory

Author: Radomâir Halaés

Publisher:

Published: 2019

Total Pages: 348

ISBN-13: 9783030194956

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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.

Aggregation Functions: A Guide for Practitioners
Aggregation Functions: A Guide for Practitioners

Author: Gleb Beliakov

Publisher: Springer

Published: 2009-09-02

Total Pages: 361

ISBN-13: 9783540841180

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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.

Aggregation Functions Considering Criteria Interrelationships in Fuzzy Multi-Criteria Decision Making: State-of-the-Art
Aggregation Functions Considering Criteria Interrelationships in Fuzzy Multi-Criteria Decision Making: State-of-the-Art

Author: LE SUN

Publisher: Infinite Study

Published:

Total Pages: 33

ISBN-13:

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Aggregation function is an important component in an information aggregation or information fusion system. Interrelationships usually exist between the input arguments (e.g., the criteria in the multicriteria decision making) of an aggregation function. In this paper, we make a comprehensive survey on the aggregation operators (AOs) that consider the argument interrelationships in crisp and fuzzy settings. In particular, we discuss the mechanisms of modeling the argument interrelationships of the Choquet integral (CI), the power average (PA), the Bonferroni mean (BM), the Heronian mean (HM), and the Maclaurin symmetric mean (MSM) operators, and introduce their extended (e.g., generalized or weighted) forms and their applications in different fuzzy sets. In addition, we compare these ve types of operators and summarize their advantages and disadvantages. Furthermore, we discuss the applications of these operators. Finally, we identify some future research directions in the AOs considering the argument interrelationships. The reviewed papers are mainly about the development of the CI, the PA, the BM, the HM, and the MSM in (fuzzy) MCDMs, most of which fall in the period of 20092018.

Aggregation
Aggregation

Author: Franklin M. Fisher

Publisher: MIT Press (MA)

Published: 1993-01-01

Total Pages: 280

ISBN-13: 9780262061520

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Aggregation lies at the heart of macroeconomics. Economists using such aggregates as capital, investment, labor, and even output or GNP assume that such constructions have a sound analytic foundation. The question of the existence of aggregate production functions is not only part of the foundation of macroeconomic theory and policy but also played a central role in the "Cambridge vs. Cambridge" debate, which challenged long-held assumptions about the foundations of neoclassical microeconomics. In this third collection of his essays Franklin M. Fisher settles the question of the conditions for the existence of aggregate production functions. He examines the conditions for approximate aggregation and, through simulation experiments, considers why aggregate production functions appear to work in practice. He also explores related topics involving price aggregation and aggregation in international trade.