Towards a General Description of Interval Multiplications: Algebraic Analysis and Its Relation to t-Norms

AbstractIt is well known that interval computations are very important, both by themselves (as a method for processing data known with interval uncertainty) and as a way to process fuzzy data. In general, the problem of computing the range of a given function under interval uncertainty is computationally difcult (NP-hard). As a result, there exist different methods for estimating such a range: some methods require a longer computation time and lead to more accurate results, other methods lead to somewhat less accurate results but are much faster than the more accurate techniques. In particular, different methods exist for interval multiplication, i.e., for computin