A construction method for t-norms on bounded lattices

Abstract

In this paper, a construction method on a bounded lattice from a given t-norm on a subinterval of the bounded lattice is presented. the supremum distributivity of the constructed t-norm by the mentioned method has been proven under some special conditions. Giving an example, the constructed t-norm need not be supremum-distributive on any bounded lattice is shown. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.