Convergence of t-norms

Abstract

When we introduced several important families of t-norms in Chapter 4, we mentioned already (without proof) that all these families are continuous with respect to the parameter, i.e., that we have pointwise convergence of the t-norms if the corresponding parameters converge (some of these statements are trivial, some of them follow directly from [Dombi 1982, 1986]).

An exact description of any real situation is virtually impossible. This is a fact we have had to accept and adjust to. As a result, one of the major problems in description (essential to communication, decision making, and, in a broader sense, to any human activity) is to reduce the necessary imprecision to a level of relative unimportance. We must balance the needs for exactness and simplicity, and reduce complexity without oversimplification in order to match the level of detail at each step with the problem we face.

Richard E. Bellman