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Aggregation Operators for Evaluating Alternatives

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Fuzzy Optimization

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 254))

Abstract

This chapter reviews the use of aggregation functions and operators in the field of decision making. We first present an overview of main decision making problems, and, then, we show that aggregation operators are in common use for solving them. Once having presented their interest, we describe the major aggregation operators, their properties and their major differences.

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References

  1. Bouyssou, D., Marchant, T., Pirlot, M., Perny, P., Tsoukiàs, A., Vincke, P.: Evaluation and Decision Models: A Critical Perspective. Kluwer’s International Series. Kluwer Academic Publishers, Dordrecht (2000)

    MATH  Google Scholar 

  2. Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1953/1954)

    MathSciNet  Google Scholar 

  3. Figuera, J., Mousseau, V., Roy, B.: Electre Methods. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multi Criteria Decision Analysis: State of the Art Surveys. Springer, Heidelberg (2005)

    Google Scholar 

  4. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)

    MATH  Google Scholar 

  5. Geldermann, J., Rentz, O.: Bridging the Gap between American and European MADM-Approaches? In: Proc. of the 51st Meeting of the European Working Group “Multicriteria Aid for Decisions”, Madrid (2000)

    Google Scholar 

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

    MathSciNet  Google Scholar 

  7. Narukawa, Y., Torra, V.: Graphical interpretation of the twofold integral and its generalization. Int. J. of Unc., Fuzz. and Knowledge Based Systems 13(4), 415–424 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Rapoport, A.: Decision Theory and Decision Behavior. Kluwer Academic Publishers, Dordrecht (1989)

    Google Scholar 

  9. Roy, B.: Multicriteria Methodology for Decision Aiding. Kluwer Academic Publishers, Dordrecht (1996)

    MATH  Google Scholar 

  10. Roy, B., Vanderpooten, D.: The European school of MCDA: Emergence, basic features and current works. J. of Multi-Criteria Decision Analysis 5(1), 22–38 (1998)

    Article  Google Scholar 

  11. Sugeno, M.: Theory of Fuzzy Integrals and its Applications. Ph. D. Dissertation, Tokyo Institute of Technology, Tokyo, Japan (1974)

    Google Scholar 

  12. Tanino, T., Tanaka, T., Inuiguchi, M. (eds.): Multi-Objective Programming and Goal Programming. Springer, Heidelberg (2002)

    Google Scholar 

  13. Torra, V.: The weighted OWA operator. Int. J. of Intel. Syst. 12, 153–166 (1997)

    Article  MATH  Google Scholar 

  14. Torra, V.: The WOWA operator and the interpolation function W*: Chen and Otto’s interpolation method revisited. Fuzzy Sets and Systems 113(3), 389–396 (2000)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  16. Torra, V., Lv: On the WOWA operator and its interpolation function. Int. J. of Intel. Systems (2009) (in press), doi:10.1002/int.20371

    Google Scholar 

  17. Torra, V., Narukawa, Y.: The interpretation of fuzzy integrals and their application to fuzzy systems. Int. J. of Approx. Reasoning 41(1), 43–58 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  19. Torra, V., Narukawa, Y.: Modelització de decisions: fusió d’informació i operadors d’agregació. UAB Press (2007)

    Google Scholar 

  20. Valls, A.: ClusDM: A Multiple Criteria Decision Making Method for Heterogeneous Data Sets. Monografies de l’IIIA (2003)

    Google Scholar 

  21. Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. on Systems, Man and Cybernetics 18, 183–190 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  22. Yager, R.R., Kacprzyk, J. (eds.): The Ordered Weighted Averaging Operators: Theory and Applications. Springer, Heidelberg (1997)

    Google Scholar 

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Author information

Authors and Affiliations

  1. IIIA-CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

Authors
  1. Vicenç Torra
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Editor information

Editors and Affiliations

  1. Department of Mathemaitical and Statistical Sciences, University of Colorado Denver, PO Box 173364, 80217-3364, Colorado, Denver, USA

    Weldon A. Lodwick

  2. Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

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Torra, V. (2010). Aggregation Operators for Evaluating Alternatives. In: Lodwick, W.A., Kacprzyk, J. (eds) Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13935-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-13935-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13934-5

  • Online ISBN: 978-3-642-13935-2

  • eBook Packages: EngineeringEngineering (R0)

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