On ordinal sums of countably many [formula omitted]- and [formula omitted]-overlap functions on complete lattices

Abstract

Concepts of CR- and CL-overlap functions on a complete lattice were introduced by extending the underlying truth value set from the unit interval to an arbitrary complete lattice. Then, ordinal sums of a finite set of (CR- and CL-) overlap functions on subintervals of complete lattices were investigated, the endpoints of which are comparable. Based on these work, we further explore ordinal sums of countably many (including finite or countably infinite cases of) CR- and CL-overlap functions on a complete lattice under additional constraints, where the endpoints are comparable in this paper.