The Algebraic Properties Of Triangular-norms

The triangular-norm can be thoroughly, painstakingly and systematically investigated from the view of the function, which has two variables, and algebra, respectively. In this dissertation, we mainly study the basic algebraic properties of triangular norms, such as Archimedean, strict monotone and nilpotent properties and provide some methods about construction of t-norms.In chapter one, we introduce some basic knowledge and related notations about t-norms. In chapter two, we discuss the basic algebraic properties such as the continuity, strict monotone, cancellation law, conditional cancellation law, Archimedean and limit property and investigate the relationship among the sets associated to a t-norm of elements. In chapter three, we give some characterizations of the De Morgan triple(T,S,N). In chapter four, we introduce some examples about t-norms and provide some methods about construction of t-norms. In chapter five, we study the relationship between t-norms and a special commutative semiring.