Skip to main content

Aggregation Operators and Soft Computing

  • Reference work entry
Encyclopedia of Complexity and Systems Science

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 3,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

Information integration:

The whole process of obtaining some information from different sources and then using this information to achieve a concrete task.

Information fusion:

A  general term that defines the whole area that studies techniques and methods to combine information for achieving a particular goal.

Aggregation operators:

Particular operators that are actually used for combining the information.

Bibliography

Primary Literature

  1. Aczél J (1966) Lectures on functional equations and their applications. Academic, New York, London

    Google Scholar 

  2. Aczél J (1987) A short course on functional equations. Reidel, Dordrecht

    Google Scholar 

  3. Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York

    MATH  Google Scholar 

  4. Arrow KJ (1951) Social choice and individual values, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  5. Arrow KJ, Sen AK, Suzumura K (eds) (2002) Handbook of social choice and welfare. Elsevier, Amsterdam

    Google Scholar 

  6. Bajraktarević M (1958) Sur une équation fonctionnelle aux valeurs moyennes. Glasnik Mat Fiz I Astr 13(4):243–248

    Google Scholar 

  7. Barthelemy JP, McMorris FR (1986) The median procedure for n-trees. J Classif 3:329–334

    MATH  Google Scholar 

  8. Bouyssou D, Marchant T, Pirlot M, Perny P, Tsoukiàs A, Vincke P (2000) Evaluation and decision models: A critical perspective. Kluwer's International Series. Kluwer, Dordrecht

    Google Scholar 

  9. Bullen PS (2003) Handbook of means and their inequalities. Kluwer, Dordrecht

    MATH  Google Scholar 

  10. Bullen PS, Mitrinović DS, Vasić PM (1988) Means and their Inequalities. Reidel, Dordrecht

    Google Scholar 

  11. Choquet G (1953) Theory of capacities. Ann Inst Fourier 5:131–295

    MathSciNet  Google Scholar 

  12. Fishburn PC, Rubinstein A (1986) Aggregation of equivalence relations. J Classif 3:61–65

    MathSciNet  MATH  Google Scholar 

  13. Fodor J, Roubens M (1994) Fuzzy preference modelling and multicriteria decision support. Kluwer, Dordrecht

    MATH  Google Scholar 

  14. Grabisch M, Murofushi T, Sugeno M (2000) Fuzzy measures and integrals: Theory and applications. Physica, Heidelberg

    Google Scholar 

  15. Hardy GH, Littlewood JE, Pólya G (1934) Inequalities, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  16. Hirsch JE (2005) An index to quantify an individual's scientific research output. Proc Natl Acad Sci 102(45):16569–16572

    ADS  Google Scholar 

  17. Narukawa Y, Torra V (2004) Twofold integral and Multi-step Choquet integral. Kybernetika 40(1):39–50

    MathSciNet  MATH  Google Scholar 

  18. Mitchell HB (2007) Multi-sensor data fusion. An introduction. Springer, Heidelberg

    Google Scholar 

  19. Pappus (1982) La collection mathématique. Librairie Scientifique et Technique Albert Blanchard, Paris

    Google Scholar 

  20. Roy B (1996) Multicriteria methodology for decision aiding. Kluwer, Dordrecht

    MATH  Google Scholar 

  21. Ruspini EH, Bonissone PP, Pedrycz W (1998) Handbook of fuzzy computation. IOP, London

    MATH  Google Scholar 

  22. Sugeno M (1974) Theory of fuzzy integrals and its applications. Ph D dissertation, Tokyo Institute of Technology, Japan

    Google Scholar 

  23. Torra V (1997) The weighted OWA operator. Int J Intell Syst 12:153–166

    MATH  Google Scholar 

  24. Torra V (2003) La integral doble o twofold integral: Una generalització de les integrals de Choquet i Sugeno. Butlletí de l'Associació Catalana d'Intel·ligència Artificial 29:13–19. Preliminary version in English: Twofold integral: A generalization of Choquet and Sugeno integral. IIIA Technical Report TR-2003-08

    Google Scholar 

  25. Torra V, Narukawa Y (2007) Modeling decisions: Information fusion and aggregation operators. Springer, Heidelberg

    Google Scholar 

  26. Torra V, Narukawa Y (2008) The h-index and the number of citations: Two fuzzy integrals. IEEE Trans Fuzzy Syst 16(3):795–797

    MathSciNet  Google Scholar 

Books and Reviews

  1. [26] gives a general description of the field of aggregation operators, it defines the main operators and discusses a few practical topics about their applications (e. g. parameter determination). (Calvo et al, 2002) is an edited book that contains state-of-the-art chapter on different topics related with aggregation and fusion. A few properties on the aggregation operators (mainly related with inequalities) can be found in the books by Bullen [9] and Bullen, Mitrinović and Vasić [10], and the excellent book by Hardy, Littlewood and Pólya [34]. [14] is an edited volume on fuzzy measures and fuzzy integrals.

    Google Scholar 

  2. [18] is an introduction to multisensor data fusion, a topic very much related with aggregation operators

    Google Scholar 

  3. Alsina C, Frank MJ, Schweizer B (2006) Associative functions: Triangular norms and copulas. World Scientific, Singapore

    Google Scholar 

  4. Calvo T, Mayor G, Mesiar R (2002) Aggregation operators. Physica, Heidelberg

    MATH  Google Scholar 

  5. Pap E (2002) Handbook of measure theory, vols I, II. North-Holland, Amsterdam

    Google Scholar 

  6. Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18:183–190

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag

About this entry

Cite this entry

Torra, V. (2009). Aggregation Operators and Soft Computing. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_15

Download citation

Publish with us

Policies and ethics