An order induced by the direct product of t-norms

Abstract

In this paper, we study the direct product of triangular norms (t-norms) on bounded lattices. We define an order induced by t-norms, which is a direct product of two t-norms on bounded lattices, and properties of introduced order are deeply investigated. We explore some properties of the direct product of two t-norms on bounded lattices. We investigate the properties of the set of comparable and incomparable elements with respect to the $\preceq_T $ partial order.