Aggregation functions

Author(s)

• Grabisch, Michel

Bibliographic Information

Aggregation functions

Michel Grabisch ... [et al.]

（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 127）

Cambridge University Press, 2009

• : hardback

Note

Includes bibliographical references (p. 428-453) and index

Description and Table of Contents

Description

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.

Table of Contents

• Preface
• 1. Introduction
• 2. Properties for aggregation
• 3. Conjunctive and disjunctive aggregation functions
• 4. Means and averages
• 5. Aggregation functions based on nonadditive integrals
• 6. Construction methods
• 7. Aggregation on specific scale types
• 8. Aggregation on ordinal scales
• 9. Aggregation on bipolar scales
• 10. Behavioral analysis of aggregation functions
• 11. Identification of aggregation functions
• A. Aggregation of infinitely many arguments
• B. Examples and applications
• List of symbols
• Bibliography
• Index.

by "Nielsen BookData"

Details

• NCID: BA90666368
• ISBN:
  • 9780521519267
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge
• Pages/Volumes: xvii, 460 p.
• Size: 24 cm
• Classification:
  • LCC : QA246
  • DC22 : 512
• Subject Headings:
  • LCSH : Numerical functions
  • LCSH : Aggregation operators
• Parent Bibliography ID:
  • BA00064663