Constructions of quotient algebras via triangular norms

In this paper, properties of certain real-valued mappings Δ on binary systems X which satisfy versions of the triangle inequality are investigated. For example, via a quotient construction using Ker Δ = {x: Δ(x) = 0} it is shown that X/Ker Δ is a d-algebra if X is a d-algebra. In addition fuzzy versions of these triangular norms and their properties are considered as well. Finally boundedness conditions on Δ and a concept of magnitude are both introduced and some consequences are derived.