On triangular norms representable as ordinal sums based on interior operators on a bounded meet semilattice

First, we present construction methods for interior operators on a meet semilattice. Second, under the assumption that the underlying meet semilattices constitute the range of an interior operator, we prove an ordinal sum theorem for countably many (finite or countably infinite) triangular norms on bounded meet semilattices, which unifies and generalizes two recent results: one by Dvorak and Holcapek and the other by some of the present authors. We also characterize triangular norms that are representable as the ordinal sum of countably many triangular norms on given bounded meet semilattices. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

In this paper, we first present construction methods for interior operators on a meet semilattice. Then, under the assumption that the underlying meet semilattices constitute the range of an interior operator, we prove an ordinal sum theorem for countably many triangular norms on bounded meet semilattices, and characterize triangular norms that can be represented as the ordinal sum of countably many triangular norms on given bounded meet semilattices.