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Aggregation Functions
Abstract
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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Cited by
Yager, R. R. (2013) · 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS) · doi:10.1109/ifsa-nafips.2013.6608375 · Cited by 2,703
Senapati, T., & Yager, R. R. (2019) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2019.05.012 · Cited by 451
Intuitionistic Fuzzy Information Aggregation Using Einstein Operations
Wang, W., & Liu, X. (2012) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2012.2189405 · Cited by 416
On averaging operators for Atanassov’s intuitionistic fuzzy sets
Beliakov, G., Bustince, H., Goswami, D. P., Mukherjee, U. K., & Pal, N. R. (2011) · Information Sciences · doi:10.1016/j.ins.2010.11.024 · Cited by 290
Greco, S., Ishizaka, A., Matarazzo, B., & Torrisi, G. (2018) · Regional Studies · doi:10.1080/00343404.2017.1347612 · Cited by 90
Metadata
- Authors
- Grabisch, M., Marichal, J.-L., Mesiar, R., & Pap, E.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2009-07-09
- OpenAlex
- W4252793191
- Cited by
- 1,588
- References
- 0
- FWCI
- 15.48
- Type
- book
- Language
- en
- Open access
- closed
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