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Stability in Aggregation Operators

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 299))

Abstract

Aggregation functions have been widely studied in literature. Nevertheless, few efforts have been dedicated to analyze those properties related with the family of operators in a global way. In this work, we analyze the stability in a family of aggregation operators The stability property for a family of aggregation operators tries to force a family to have a stable/continuous definition in the sense that the aggregation of n − 1 items should be similar to the aggregation of n items if the last item is the aggregation of the previous n − 1 items. Following this idea some definitions and results are given.

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References

  1. Amo, A., Montero, J., Molina, E.: Representation of consistent recursive rules. European Journal of Operational Research 130, 29–53 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions, a Guide to Practitioners. Springer, Berlin (2007)

    Google Scholar 

  3. Calvo, T., Kolesarova, A., Komornikova, M., Mesiar, R.: Aggregation operators, properties, classes and construction methods. In: Calvo, T., et al. (eds.) Aggregation Operators New trends ans Aplications, pp. 3–104. Physica-Verlag, Heidelberg (2002)

    Google Scholar 

  4. Calvo, T., Mayor, G., Torrens, J., Suer, J., Mas, M., Carbonell, M.: Generation of weighting triangles associated with aggregation fuctions. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8(4), 417–451 (2000)

    MathSciNet  MATH  Google Scholar 

  5. Cutello, V., Montero, J.: Hierarchical aggregation of OWA operators: basic measures and related computational problems. Uncertainty, Fuzzinesss and Knowledge-Based Systems 3, 17–26 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cutello, V., Montero, J.: Recursive families of OWA operators. In: Proceedings FUZZ-IEEE Conference, pp. 1137–1141. IEEE Press, Piscataway (1994)

    Google Scholar 

  7. Cutello, V., Montero, J.: Recursive connective rules. International Journal of Intelligent Systems 14, 3–20 (1999)

    Article  MATH  Google Scholar 

  8. Gómez, D., Montero, J.: A discussion of aggregation functions. Kybernetika 40, 107–120 (2004)

    MathSciNet  MATH  Google Scholar 

  9. Gómez, D., Montero, J., Yáñez, J., Poidomani, C.: A graph coloring algorithm approach for image segmentation. Omega 35, 173–183 (2007)

    Article  Google Scholar 

  10. Gómez, D., Montero, J., Yánez, J.: A coloring algorithm for image classification. Information Sciences 176, 3645–3657 (2006)

    Article  MATH  Google Scholar 

  11. Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation Functions. Encyclopedia of Mathematics and its Applications (2009)

    Google Scholar 

  12. Kolesárová, A.: Sequential aggregation. In: González, M., et al. (eds.) Proceedings of the Fifth International Summer School on Aggregation Operators, AGOP, pp. 183–187. Universitat de les Illes Balears, Palma de Mallorca (2009)

    Google Scholar 

  13. Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets and Systems 158, 2429–2442 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Montero, J., López, V., Gómez, D.: The Role of Fuzziness in Decision Making. STUDFUZZ, vol. 215, pp. 337–349. Springer, Heidelberg (2007)

    Google Scholar 

  15. Rojas, K., Gómez, D., Rodríguez, J.T., Montero, J.: Some Properties of Consistency in the Families of Aggregation Operators. In: Melo-Pinto, P., Couto, P., Serôdio, C., Fodor, J., De Baets, B. (eds.) Eurofuse 2011. AISC, vol. 107, pp. 169–176. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Yager, R.R., Rybalov, A.: Nonconmutative self-identity aggregation. Fuzzy Sets and Systems 85, 73–82 (1997)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Escuela de Estadística, Complutense University, Av. Puerta de Hierro s/n, 28050, Madrid, Spain

    Daniel Gómez

  2. Facultad de Ciencias Matematicas, Complutense University, Plz. Ciencias s/n, 28050, Madrid, Spain

    Javier Montero, J. Tinguaro Rodríguez & Karina Rojas

Authors
  1. Daniel Gómez
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  2. Javier Montero
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  3. J. Tinguaro Rodríguez
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  4. Karina Rojas
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Gómez, D., Montero, J., Rodríguez, J.T., Rojas, K. (2012). Stability in Aggregation Operators. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_33

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  • DOI: https://doi.org/10.1007/978-3-642-31718-7_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31717-0

  • Online ISBN: 978-3-642-31718-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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