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A Characterization of Fuzzy Integrals Invariant with Respect to Permutation Groups

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 300))

Abstract

This contribution studies isomorphisms of fuzzy measure spaces and related notions, namely cardinal fuzzy measure spaces and fuzzy measure spaces closed under isomorphisms with respect to permutation groups. By these special fuzzy measure spaces, a characterization of ⊙-fuzzy integrals that are for a given function invariant with respect to permutations from a group of permutations is provided.

This work was supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070).

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References

  1. Bělohlávek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic Publisher, New York (2002)

    MATH  Google Scholar 

  2. Dvořák, A., Holčapek, M.: On convergence of fuzzy integrals over complete residuated lattices. In: Proceedings of EUSFLAT-LFA, Aix-les-Bains, France, July 18-22, pp. 98–105 (2011)

    Google Scholar 

  3. Dvořák, A., Holčapek, M.: Type 〈1,1〉 fuzzy quantifiers determined by fuzzy measures, Part I: Basic definitions and examples. Submitted to Fuzzy Sets and Systems

    Google Scholar 

  4. Dvořák, A., Holčapek, M.: Type 〈1,1〉 fuzzy quantifiers determined by fuzzy measures, Part II: Permutation and isomorphism invariances. Submitted to Fuzzy Sets and Systems

    Google Scholar 

  5. Dvořák, A., Holčapek, M.: Type 〈1, 1〉 fuzzy quantifiers determined by fuzzy measures. In: Proceedengs of WCCI 2010 IEEE World Congress on Computational Intelligence, CCIB, Barcelona, Spain, July 18-23, pp. 3168–3175 (2010)

    Google Scholar 

  6. Dvořák, A., Holčapek, M.: Fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices. Information Sciences 185(1), 205–229 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mišík, L., Tóth, J.: On asymptotic behaviour of universal fuzzy measure. Kybernetika 42(3), 379–388 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical principles of fuzzy logic. Kluwer Academic Publisher, Boston (1999)

    Book  MATH  Google Scholar 

  9. Ward, M., Dilworth, R.: Residuated lattices. Transactions of the American Mathematical Society 45, 335–354 (1939)

    Article  MathSciNet  Google Scholar 

  10. Wygralak, M.: Generalized cardinal numbers and operations on them. Fuzzy Sets and Systems 53(1), 49–85 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wygralak, M.: Vaguely defined objects. Representations, fuzzy sets and nonclassical cardinality theory. Theory and Decision Library. Series B: Mathematical and Statistical Methods, vol. 33. Kluwer Academic Publisher, Dordrecht (1996)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Centre of Excellence IT4Innovations Division of UO, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 70103, Ostrava, Czech Republic

    Antonín Dvořák & Michal Holčapek

Authors
  1. Antonín Dvořák
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  2. Michal Holčapek
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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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Dvořák, A., Holčapek, M. (2012). A Characterization of Fuzzy Integrals Invariant with Respect to Permutation Groups. 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 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_22

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  • DOI: https://doi.org/10.1007/978-3-642-31724-8_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31723-1

  • Online ISBN: 978-3-642-31724-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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