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Modeling Decisions:
Information Fusion and Aggregation Operators
 Vicenç Torra, Yasuo Narukawa
 Springer, 2007, Approx. 300 p. (ISBN: 978-3-540-68789-4).
 https://doi.org/10.1007/978-3-540-68791-7
http://www.mdai.cat/ifao

Catalan translation from UAB University Press
V. Torra, Y. Narukawa (2007) Modelització de decisions: fusió d'informació i operadors d'agregació. Edicions UAB, ISBN: 978-84-490-2529-7.

The book
This book covers the underlying science and application issues related to aggregation operators, focusing on tools used in practical applications that involve numerical information. Starting with detailed introductions to information fusion and integration, measurement and probability theory, fuzzy sets, and functional equations, the authors then cover the following topics in detail: synthesis of judgements, fuzzy measures, weighted means and fuzzy integrals, indices and evaluation methods, model selection, and parameter extraction. The methods are illustrated with representative examples throughout, and there are extensive bibliographies and reading suggestions.
The book contains the following chapters: 1. Introduction, 2. Basic Notions, 3. Introduction to Functional Equations, 4. Synthesis of Judgements, 5. Fuzzy Measures, 6. From the Weighted Mean to Fuzzy Integrals, 7. Indices and Evaluation Methods, 8. Model Selection; Appendices: A. Properties, B. Some Aggregation Operators
Slides Click here
Definitions A few definitions of aggregation operators. Click here
Software Programs to implement aggregation operators and for parameter determination from examples.
  • Software in python for fuzzy measures and integrals, and fuzzy measure identification: prog.choquet.web.txt (requires prog.vectors.matrices.web.txt )
  • Software in JAVA for the OWA and WOWA operators can be found here
  • Implementations for some aggregation operators (AM, WM, OWA, QAM), as well as some examples of Chapter 8 using R (R project) can be found. This includes parameter (weight) determination from examples. here
  • Implementations for the WOWA operator using R (R project) can be found here
  • Implementations for the Choquet integral in Scala can be found here
  • Implementations in R (R project) of numerical integration for the Choquet integral on continuous domains. here
    Details in our paper Torra, V., Narukawa, Y. (2016) Numerical integration for the Choquet integral, Information fusion 31 137-145. http://dx.doi.org/10.1016/j.inffus.2016.02.007
Flyer A flyer of the book (by 05/Jan/2007) can be found here

 


Vicenç Torra

Modeling Decisions for Artificial Intelligence
Last modified: 14 : 11 December 01 2022.