Continuous fuzzy conjunctions and disjunctions

Several functions have been used to implement conjunction and disjunction in fuzzy logic and to implement intersection and union in fuzzy set theory. Usually t-norms and t-conorms are used, but for some applications these may not be the best function classes. In this paper, I propose specific requirements which a function should satisfy if it is to be used to implement conjunction (or intersection) or disjunction (or union) and compare the functions proposed for conjunction to t-norms. In addition to stating basic properties of the resulting function classes, I give theorems on polynomial approximation within each class and on the existence of functions in either class with specified values at particular points.