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Abstract

This paper is devoted to studying of (pre-)orders of the unit interval generated by uninorms. We present properties of such generated pre-orders. Further we give a condition under which the generated relation is just a pre-order, i.e., under which it is not anti-symmetric. We present also a new type of uninorms, which is interesting from the point of view of generated pre-orders.

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References

  1. Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: Properties, classes and construction methods. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation Operators, pp. 3–104. Physica-Verlag, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Drewniak, J., Drygaś, P.: Characterization of uninorms locally internal on A(e). Fuzzy Set and Systems (submitted)

    Google Scholar 

  3. Drygaś, P.: On monotonic operations which are locally internal on some subset of their domain. In: Štepnička, et al. (eds.) New Dimensions in Fuzzy Logic and Related Technologies, Proceedings of the 5th EUSFLAT Conference 2007, vol. II, pp. 359–364. Universitas Ostraviensis, Ostrava (2007)

    Google Scholar 

  4. Fodor, J., De Baets, B.: A single-point characterization of representable uninorms. Fuzzy Sets and Systems 202, 89–99 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fodor, J., Yager, R.R., Rybalov, A.: Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 5, 411–422 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hliněná, D., Kalina, M., Král’, P.: Non-representable uninorms. In: EUROFUSE 2013, Uncertainty and Imprecision Modelling in Decision Making, pp. 131–138, Servicio de Publicaciones de la Universidad de Oviedo, Oviedo (2013)

    Google Scholar 

  7. Hu, S., Li, Z.: The structure of continuous uninorms. Fuzzy Sets and Systems 124, 43–52 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Karaçal, F., Kesicioğlu, M.N.: A t-partial order obtained from t-norms. Kybernetika 47(2), 300–314 (2011)

    MATH  MathSciNet  Google Scholar 

  9. Karaçal, F., Khadijev, D.: \(\bigvee\)-distributive and infinitely \(\bigvee\)-distributive t-norms on complete lattices. Fuzzy Sets and Systems 151, 341–352 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Springer, Heidelberg (2000)

    Book  MATH  Google Scholar 

  11. Mesiar, R.: Choquet-like integrals. J. Math. Anal. Appl. 194, 477–488 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Petrík, M., Mesiar, R.: On the structure of special classes of uninorms. Fuzzy Sets and Systems 240, 22–38 (2014)

    Article  MathSciNet  Google Scholar 

  13. Ruiz-Aguilera, D., Torrens, J., De Baets, B., Fodor, J.: Some remarks on the characterization of idempotent uninorms. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS (LNAI), vol. 6178, pp. 425–434. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Smutná, D.: Limit t-norms as a basis for the construction of a new t-norms. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 9(2), 239–247 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Yager, R.R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80, 111–120 (1996)

    Article  MATH  MathSciNet  Google Scholar 

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Hliněná, D., Kalina, M., Král, P. (2014). Pre-orders and Orders Generated by Conjunctive Uninorms. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_32

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  • DOI: https://doi.org/10.1007/978-3-319-08852-5_32

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08851-8

  • Online ISBN: 978-3-319-08852-5

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