Aggregation operators preserving quasiconvexity

Authors:
VladimíR Janiš;Pavol KráL';MagdaléNa RenčOvá
Affiliations:
Department of Mathematics, Faculty of Science, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovak Republic;Institute of Mathematics and Computer Science, Faculty of Science, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovak Republic;Department of Mathematics, Faculty of Science, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovak Republic
Venue:
Information Sciences: an International Journal
Year:
2013

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Abstract

Quasiconvexity of a fuzzy set is the necessary and sufficient condition for its cuts to be convex. We study the class of those two variable aggregation operators that preserve quasiconvexity on a bounded lattice, i.e. A(@m,@n) is quasiconvex for quasiconvex lattice valued fuzzy sets @m, @n. The class of all such aggregation operators is characterized by a lattice identity that they have to fulfill. In case of a unit interval we show the construction of aggregation operators preserving quasiconvexity from a pair of real valued functions on the unit interval. As a consequence we get that the intersection of quasiconvex fuzzy sets is quasiconvex if and only if the intersection is based on the minimum triangular norm.