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Aggregation Operators and Soft Computing

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Encyclopedia of Complexity and Systems Science
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Glossary

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.

Definition of the Subject

Aggregation operators are the particular functions used for combining information in systems where several information sources have to be taken into consideration for achieving a particular goal.

Formally, aggregation operators are the particular techniques of information fusion which can be mathematically expressed in a relatively simple way. They are part of the more general process of information integration. That is the process that goes from the acquisition of data to the accomplishment of the final task.

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Bibliography

Primary Literature

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

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

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

    Book  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • 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 

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

    Book  MATH  Google Scholar 

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

    Article  Google Scholar 

Books and Reviews

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

    Book  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  • Mitchell (2007b) is an introduction to multisensor data fusion, a topic very much related with aggregation operators

    Google Scholar 

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

    Google Scholar 

  • Torra and Narukawa (2008b) 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 (2003) and Bullen, Mitrinović and Vasić (1988), and the excellent book by Hardy, Littlewood and Pólya (1934). Grabisch et al. (2000) is an edited volume on fuzzy measures and fuzzy integrals

    Google Scholar 

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

    Article  MATH  Google Scholar 

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Correspondence to Vicenç Torra .

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Torra, V. (2022). Aggregation Operators and Soft Computing. In: Meyers, R.A. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_15-3

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_15-3

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  • Print ISBN: 978-3-642-27737-5

  • Online ISBN: 978-3-642-27737-5

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