Soft Computing Explains Heuristic Numerical Methods in Data Processing and in Logic Programming

We show that fuzzy logic and other soft computing approaches explain and justify heuristic numerical methods used in data processing and in logic programming, in particular, M-methods in robust statistics, regularization techniques, metric fixed point theorems, etc. Introduction What is soft computing good for? Traditional viewpoint. When are soft computing methods (fuzzy, neural, etc.) mostly used now? Let us take, as an example, control, which is one of the major success stories of soft computing (especially of fuzzy methods; see, e.g., (Klir 1995)). ffl In control, if we know the exact equations that describe the controlled system, and if we know the exact objective function of the control, then we can often apply the optimal control techniques developed in traditional (crisp) control theory and compute the optimal control. Even in these situations, we can, in principle, use soft computing methods instead: e.g., we can use simpler fuzzy control rules instead of (more complicated..