Optimal Size Fuzzy Models

Abstract

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 determining 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 This trade-off between computation time and precision is significant whenever a prediction is made which can become “out of date” or “too old” if not used in time.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 precision 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 examines 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.