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On Capacities Characterized by Two Weight Vectors

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Book cover Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 610))

Abstract

We are interested in aggregation function based on two weights vectors: the criteria weights p and the rank weights w. The main drawback of the existing proposals based on p and w (in particular the Weighted OWA (WOWA) and the Semi-Uninorm OWA (SUOWA) operators) is that their expression is rather complex and the contribution of the weights p and w in the aggregation is obscure as there is no clear interpretation of these weights. We propose a new approach to define aggregation functions based on the weights p and w. We consider the class of capacities (which subsumes the WOWA and SUOWA). We start by providing clear interpretations of these weights that are seen as constraints on the capacity. We consider thus the whole class of capacities fulfilling these constraints. A simulation shows that the WOWA and SUOWA almost never satisfy these constraints in a strict sense.

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References

  1. Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Yager, R.R.: Quantifier guided aggregation using OWA operators. Int. J. Intell. Syst. 11, 49–73 (1996)

    Article  Google Scholar 

  3. Labreuche, C., Mayag, B., Duqueroie, B.: Extension of the MACBETH approach to elicit an owa operator. EURO J. Decis. Processes 3, 65–105 (2015)

    Article  Google Scholar 

  4. Torra, V.: The weighted owa operator. Int. J. Intell. Syst. 12, 153–166 (1997)

    Article  MATH  Google Scholar 

  5. Xu, Z., Dai, Q.: An overview of operators for aggregating information. Int. J. Intell. Syst. 18, 953–969 (2003)

    Article  MATH  Google Scholar 

  6. Llamazares, B.: An analysis of some functions that generalize weighted means and OWA operators. Int. J. Intell. Syst. 28, 380–393 (2013)

    Article  Google Scholar 

  7. Merigo, J.: A unified model between the weighted average and the induced owa operator. Expert Syst. Appl. 38, 11560–11572 (2011)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Sugeno, M.: Fuzzy measures and fuzzy integrals. Trans. SICE 8(2), 95–102 (1972)

    Google Scholar 

  10. Shapley, L.S.: A value for \(n\)-person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, Vol. II. Annals of Mathematics Studies, vol. 28, pp. 307–317. Princeton University Press, Princeton (1953)

    Google Scholar 

  11. Marichal, J.L.: Tolerant or intolerant character of interacting criteria in aggregation by the choquet integral. Eur. J. Oper. Res. 155(3), 771–791 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Marichal, J.L.: k-intolerant capacities and choquet integrals. Eur. J. Oper. Res. 177(3), 1453–1468 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Grabisch, M.: The application of fuzzy integrals in multicriteria decision making. Eur. J. Oper. Res. 89, 445–456 (1996)

    Article  MATH  Google Scholar 

  14. Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  15. Yager, R.R.: Families of OWA operators. Fuzzy Sets Syst. 55, 255–271 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Llamazares, B.: Constructing choquet integral-based operators that generalize weighted means and OWA operators. Information Fusion 23, 131–138 (2015)

    Article  Google Scholar 

  17. Llamazares, B.: SUOWA operators: Constructing semi-uninorms and analyzing specific cases. Fuzzy Sets and Systems

    Google Scholar 

  18. Kojadinovic, I., Marichal, J.L., Roubens, M.: An axiomatic approach to the definition of the entropy of a discrete Choquet capacity. Inform. Sci. 172, 131–153 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work has been supported by the European project FP7-SEC-2013-607697, PREDICT “PREparing the Domino effect In crisis siTuations”.

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Authors and Affiliations

  1. Thales Research & Technology, 1 avenue Augustin Fresnel, 91767, Palaiseau Cedex, France

    Christophe Labreuche

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  1. Christophe Labreuche
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Correspondence to Christophe Labreuche .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Machine Intelligence Institute, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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© 2016 Springer International Publishing Switzerland

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Labreuche, C. (2016). On Capacities Characterized by Two Weight Vectors. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-40596-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40595-7

  • Online ISBN: 978-3-319-40596-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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