Abstract
Aggregation of intuitionistic fuzzy sets is studied from the point of view of preserving convexity.We focus on those aggregation functions for IF-sets, that are results of separate aggregation of the membership and of nonmembership functions, that is, the representable aggregation functions. A sufficient and necessary condition for an aggregation function is given in order to fulfil that the aggregation of two IF-sets preserves the convexity of cuts.
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
Atanassov, K.: Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia (1983) (in Bulgarian)
Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)
Atanassov, K.: Intuitionistic Fuzzy Sets, Theory and Applications. Physica-Verlag, Heidelberg (1999)
Ammar, E., Metz, J.: On convexity and parametric optimization. Fuzzy Sets and Systems 49, 135–141 (1992)
Iglesias, T., Montes, I., Janiš, V., Montes, S.: T-convexity for lattice-valued fuzzy sets. In: Proceedings of the ESTYLF Conference (2012)
Janiš, V.: T-norm based cuts of intuitionistic fuzzy sets. Information Sciences 180(7), 1134–1137 (2010)
Janiš, V., Kráľ, P., Renčová, M.: Aggregation operators preserving quasiconvexity. Information Sciences 228, 37–44 (2013)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice-Hall, New Jersey (1995)
Martinetti, D., Janiš, V., Montes, S.: Cuts of intuitionistic fuzzy sets respecting fuzzy connectives. Information Sciences (2013), doi: http://dx.doi.org/10.1016/j.ins.2012.12.026
Pan, X.: Graded Intuitionistic Fuzzy Convexity with Application to Fuzzy Decision Making. In: Zeng, D. (ed.) Advances in Information Technology and Industry Applications. LNEE, vol. 136, pp. 709–716. Springer, Heidelberg (2012)
Saminger-Platz, S., Mesiar, R., Dubois, D.: Aggregation operators and Commuting. IEEE Transactions on Fuzzy Systems 15(6), 1032–1045 (2007)
Syau, Y.-R., Lee, E.S.: Fuzzy Convexity with Application to Fuzzy Decision Making. In: Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 5221–5226 (2003)
Xu, W., Liu, Y., Sun, W.: On Starshaped Intuitionistic Fuzzy Sets. Applied Mathematics 2, 1051–1058 (2011)
Zadeh, L.A.: Fuzzy sets. Inform. and Control 8, 338–353 (1965)
Zhang, C., Xiao, P., Wang, S., Liu, X. (s,t]-intuitionistic convex fuzzy sets. In: Cao, B.-Y., Wang, G.-J., Guo, S.-Z., Chen, S.-L. (eds.) Fuzzy Information and Engineering 2010. AISC, vol. 78, pp. 75–84. Springer, Heidelberg (2010)
Zhang, C., Su, Q., Zhao, Z., Xiao, P.: From three-valued nested sets to interval-valued (or intuitionistic) fuzzy sets. International Journal of Information and Systems Sciences 7(1), 11–21 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Janiš, V., Montes, S. (2013). Aggregation of Convex Intuitionistic Fuzzy Sets. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_51
Download citation
DOI: https://doi.org/10.1007/978-3-642-39165-1_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39164-4
Online ISBN: 978-3-642-39165-1
eBook Packages: EngineeringEngineering (R0)