Abstract
In this paper the characterization of idempotent uninorms given in [21] is revisited and some technical aspects are corrected. Examples clarifying the situation are given and the same characterization is translated in terms of symmetrical functions. The particular cases of left-continuity and right-continuity are studied retrieving the results in [7].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Benítez, J.M., Castro, J.L., Requena, I.: Are artificial neural networks black boxes? IEEE Transactions on Neural Networks 8, 1156–1163 (1997)
Benvenuti, P., Mesiar, R.: Pseudo-arithmetical operations as a basis for the general measure and integration theory. Information Sciences 160, 1–11 (2004)
Bustince, H., Mohedano, V., Barrenechea, E., Pagola, M.: Definition and construction of fuzzy DI-subsethood measures. Information Sciences 176, 3190–3231 (2006)
Bustince, H., Pagola, M., Barrenechea, E.: Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images. Information Sciences 177, 906–929 (2007)
Calvo, T., Mayor, G., Mesiar, R. (eds.): Aggregation operators. New trends and applications, Studies in Fuzziness and Soft Computing, vol. 97. Physica-Verlag, Heidelberg (2002)
Czogala, E., Drewniak, J.: Associative monotonic operations in fuzzy set theory. Fuzzy Sets and Systems 12, 249–269 (1984)
De Baets, B.: Idempotent uninorms. European J. Oper. Res. 118, 631–642 (1999)
De Baets, B., Fodor, J.: Van Melle’s combining function in MYCIN is a representable uninorm: an alternative proof. Fuzzy Sets and Systems 104, 133–136 (1999)
De Baets, B., Fodor, J.C.: Residual operators of uninorms. Soft Computing 3, 89–100 (1999)
De Baets, B., Fodor, J., Ruiz-Aguilera, D., Torrens, J.: Idempotent uninorms on finite ordinal scales. Int. J. of Uncertainty, Fuzziness and Knowledge-based Systems 17, 1–14 (2009)
De Baets, B., Kwasnikowska, N., Kerre, E.: Fuzzy morphology based on uninorms. In: Seventh IFSA World Congress, Prague, pp. 215–220 (1997)
Drygaś, P.: Discussion of the structure of uninorms. Kybernetika 41, 213–226 (2005)
Drygaś, P.: Remarks about idempotent uninorms. Journal of Electrical Engineering 57, 92–94 (2006)
Fodor, J.C., Yager, R.R., Rybalov, A.: Structure of Uninorms. Int. J. Uncertainty, Fuzziness, Knowledge-based Systems 5, 411–427 (1997)
Gabbay, D., Metcalfe, G.: Fuzzy logics based on [0,1)-continuous uninorms. Arch. Math. Logic 46, 425–449 (2007)
González, M., Mir, A.: Noise Reduction Using Alternate Filters Generated by Fuzzy Mathematical Operators Using Uninorms (ΦMM-U Morphology). In: Proceedings of EUROFUSE 2009, Pamplona, pp. 233–238 (2009)
González, M., Mir, A., Ruiz-Aguilera, D., Torrens, J.: Edge-Images using a Uninorm-Based Fuzzy Mathematical Morphology. Opening and Closing. In: Tavares, J., Jorge, N. (eds.) Advances in Computational Vision and Medical Image Processing, pp. 137–157. Springer, Netherlands (2009)
Klement, E.P., Mesiar, R., Pap, E.: Integration with respect to decomposable measures, based on a conditionally distributive semiring on the unit interval. Int. J. Uncertainty, Fuzziness, Knowledge-Based Systems 8, 701–717 (2000)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, London (2000)
Maes, K.C., De Baets, B.: Orthosymmetrical monotone functions. Bulletin of the Belgian Mathematical Society - Simon Stevin 14, 99–116 (2007)
Martín, J., Mayor, G., Torrens, J.: On locally internal monotonic operations. Fuzzy Sets and Systems 137, 27–42 (2003)
Mayor, G., Torrens, J.: Triangular norms in discrete settings. In: Klement, E.P., Mesiar, R. (eds.) Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, pp. 189–230. Elsevier, Amsterdam (2005)
Pap, E.: Pseudo-additive measures and their applications. In: Pap, E. (ed.) A Handbook of Measure Theory, pp. 1403–1468. Elsevier, Amsterdam (2002)
Ruiz-Aguilera, D., Torrens, J.: Distributive idempotent uninorms. Int. J. Uncertainty, Fuzziness, Knowledge-based Systems 11, 413–428 (2003)
Ruiz-Aguilera, D., Torrens, J.: Residual implications and co-implications from idempotent uninorms. Kybernetika 40, 21–38 (2004)
Takács, M.: Approximate reasoning in fuzzy systems based on pseudo-analysis and uninorm residuum. Acta Polytechnica Ungarica 1, 49–62 (2004)
Yager, R.R.: Uninorms in fuzzy systems modeling. Fuzzy Sets and Systems 122, 167–175 (2001)
Yager, R.R., Kreinovich, V.: On the relation between two approaches to combining evidence: Ordered abelian groups and uninorms. J. Intell. Fuzzy Syst. 14, 7–12 (2003)
Yager, R.R., Kreinovich, V.: Universal approximation theorem for uninorm-based fuzzy systems modelling. Fuzzy Sets and Systems 140, 331–339 (2003)
Yager, R.R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80, 111–120 (1996)
Yan, P., Chen, G.: Discovering a cover set of ARsi with hierarchy from quantitative databases. Information Sciences 173, 319–336 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ruiz-Aguilera, D., Torrens, J., De Baets, B., Fodor, J. (2010). Some Remarks on the Characterization of Idempotent Uninorms. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_44
Download citation
DOI: https://doi.org/10.1007/978-3-642-14049-5_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14048-8
Online ISBN: 978-3-642-14049-5
eBook Packages: Computer ScienceComputer Science (R0)