Alternative approaches to obtain t-norms and t-conorms on bounded lattices

Abstract

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for the clarity. Finally, we show that our construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on an arbitrary bounded lattice, respectively.