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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Drewniak, J., Drygaś, P.: Characterization of uninorms locally internal on A(e). Fuzzy Set and Systems (submitted)
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)
Fodor, J., De Baets, B.: A single-point characterization of representable uninorms. Fuzzy Sets and Systems 202, 89–99 (2012)
Fodor, J., Yager, R.R., Rybalov, A.: Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 5, 411–422 (1997)
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)
Hu, S., Li, Z.: The structure of continuous uninorms. Fuzzy Sets and Systems 124, 43–52 (2001)
Karaçal, F., Kesicioğlu, M.N.: A t-partial order obtained from t-norms. Kybernetika 47(2), 300–314 (2011)
Karaçal, F., Khadijev, D.: \(\bigvee\)-distributive and infinitely \(\bigvee\)-distributive t-norms on complete lattices. Fuzzy Sets and Systems 151, 341–352 (2005)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Springer, Heidelberg (2000)
Mesiar, R.: Choquet-like integrals. J. Math. Anal. Appl. 194, 477–488 (1995)
Petrík, M., Mesiar, R.: On the structure of special classes of uninorms. Fuzzy Sets and Systems 240, 22–38 (2014)
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)
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)
Yager, R.R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80, 111–120 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)