Constructions of overlap functions on bounded lattices.

In this paper, we present two methods for constructing new overlap functions on bounded lattices from given ones. At first, we introduce the notion of overlap functions on bounded lattices, which is a generalization of overlap functions on the real unit interval. Then we provide the ∧-extension of an overlap function on a subinterval and give the necessary and sufficient conditions for the ∧-extension to be an overlap function. Finally, we propose a definition of ordinal sum of finitely many overlap functions on subintervals of a bounded lattice, where the endpoints of the subintervals constitute a chain. Necessary and sufficient conditions for the ordinal sum yielding again an overlap function are provided. [ABSTRACT FROM AUTHOR]