Abstract
In this paper we introduce the semi-uninorm based ordered weighted averaging (SUOWA) operators, a new class of aggregation functions that integrates weighted means and OWA operators. To do this we take into account that weighted means and OWA operators are particular cases of Choquet integrals. So, the capacities associated to SUOWA operators are defined by using the values of the capacities associated to these functions and idempotent semi-uninorms.
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.
References
Calvo, T., Kolesárová, A., KomornÃková, 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)
Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1953)
Fodor, J., Marichal, J.L., Roubens, M.: Characterization of the ordered weighted averaging operators. IEEE Trans. Fuzzy Syst. 3(2), 236–240 (1995)
Fodor, J., De Baets, B.: Uninorm basics. In: Wang, P.P., Ruan, D., Kerre, E.E. (eds.) Fuzzy Logic: A Spectrum of Theoretical & Practical Issues. STUDFUZZ, vol. 215, pp. 49–64. Springer, Berlin (2007)
Fodor, J.C., Yager, R.R., Rybalov, A.: Structure of uninorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5(4), 411–427 (1997)
Grabisch, M.: Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst. 69(3), 279–298 (1995)
Grabisch, M.: On equivalence classes of fuzzy connectives - the case of fuzzy integrals. IEEE Trans. Fuzzy Syst. 3(1), 96–109 (1995)
Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, New York (2009)
Liu, H.W.: Semi-uninorms and implications on a complete lattice. Fuzzy Sets Syst. 191, 72–82 (2012)
Llamazares, B.: An analysis of some functions that generalizes weighted means and OWA operators. Int. J. Intell. Syst. 28(4), 380–393 (2013)
Murofushi, T., Sugeno, M.: A theory of fuzzy measures. Representation, the Choquet integral and null sets. J. Math. Anal. Appl. 159(2), 532–549 (1991)
Sugeno, M.: Theory of Fuzzy Integrals and its Applications. Phd thesis, Tokyo Institute of Technology (1974)
Torra, V.: The weighted OWA operator. Int. J. Intell. Syst. 12(2), 153–166 (1997)
Torra, V.: On some relationships between the WOWA operator and the Choquet integral. In: Proceedings of the Seventh International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 1998), Paris, France, pp. 818–824 (July 1998)
Torra, V., Narukawa, Y.: Modeling Decisions: Information Fusion and Aggregation Operators. Springer, Berlin (2007)
Yager, R.R.: On ordered weighted averaging operators in multicriteria decision making. IEEE Trans. Syst., Man, Cybern. 18(1), 183–190 (1988)
Yager, R.R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets Syst. 80(1), 111–120 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Llamazares, B. (2013). A New Class of Functions for Integrating Weighting Means and OWA Operators. In: Bielza, C., et al. Advances in Artificial Intelligence. CAEPIA 2013. Lecture Notes in Computer Science(), vol 8109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40643-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-40643-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40642-3
Online ISBN: 978-3-642-40643-0
eBook Packages: Computer ScienceComputer Science (R0)