Optimal Size Fuzzy Models

Approximate models using fuzzy rule bases can be made more precise by suitably increasing the size of the rule base and decreasing uncertainty in the rules. A large rule base, however, requires more time for its evaluation and hence the problem arises of determin- ing the size that is good enough for the task at hand, but allows as fast as possible reasoning using the rule base. This trade-off between computation time and precision is significant whenever a prediction is made which can become “out of date” or “too old” if not used in time. The trade off is considered here in the context of tracking a moving target. In this problem, a higher degree of accuracy results in tighter preci- sion of determining target location, but at the cost of longer computation time, during which the target can move further away, thus ultimately requiring a longer search for exact target localisation. This paper exam- ines the problem of determining the optimal rule base size that will yield a minimum total time required to repeatedly re-acquire the moving target, as done by a cat that plays with a mouse. While this problem has no known solution in its general formulation, solutions are shown here for specific contexts.