On Generating Functions of Two-Dimensional T-Norms

t-norms are significant operations employed in various fields including fuzzy theories. There exist many types of t-norms. t-norms defined on discrete domains and continuous domains have rather different properties. It is known that continuous and strictly monotone t-norms defined on continuous domains have generating functions [1, 4, 5]. Generating functions are important functions that characterize the properties of t-norms. In this article, tow-dimensional t-norms are proposed, and their properties are studied. Furthermore, it is shown that if a tow-dimensional t-norm satisfies particular conditions, it could be decomposed into Cartesian product of two one-dimensional t-norms and each one-dimensional t-norm have a generating function. Applications of two-dimensional t-norms are briefly discussed at the last of this article [2, 3].