Aggregation of convex intuitionistic fuzzy sets

Aggregation of intuitionistic fuzzy sets is studied from the point of view of preserving various kinds of convexity. We focus on aggregation functions for intuitionistic fuzzy sets. These functions correspond to simultaneous separate aggregations of the membership as well as of the nonmembership indicators. It is performed by means of the so-called representable functions. Sufficient and necessary conditions are analyzed in order to guarantee that the composition of two intuitionistic fuzzy sets preserves convexity.