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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-642-39165-1_51
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