Aggregation of weakly quasi-convex fuzzy sets

Abstract

Weakly quasi-convex fuzzy sets have been defined as an extension of the class of quasi-convex fuzzy sets. We study the binary commutative aggregation operators which preserve weak quasi-convexity. It is shown, that there is only one such aggregation operator and it is the trivial (the largest) one. As a corollary we obtain that in general the intersection of weakly quasi-convex fuzzy sets is not weakly quasi-convex. © 2012 Springer-Verlag Berlin Heidelberg.