M. Mizumoto. " Fuzzy Inference Using Max-a Composition in the Com- Positional Rule of Inference. " in Approxrnmte Reusonrng 111

with conventional expert systems, it is clear that 1) 2) 3) AARS can reduce the size of the rule base; AARS uses linguistic variables rather than quantitative variables; AARS increases the system's flexibility. In future research, we expect to 1) associate observation P,' and rule R , with certainty factors CF, and CF, and derive a certainty factor for consequent experiment with other forms of similarity measures and modification functions, and extend AARS to other inference modes. Modus Tollens. REFERENCES W. Bandler and L. J. Kohout. " The four modes of inference in fuzzy expert systems, " Cvhernetics und Stwenis Reseurch. Membership functions I: Comparing methods of measurement. " Int. On distances between fuzzy points and their use for plausible reasoning. " in Proc.-, " Fuzzy logics and the generalized modus ponens revisited, I n t. J C r h m ~. A method of inference in approximate reasoning hased on interval-valued fuzzy sets, " Furrr Sets, A linear decision rule for production and employment scheduling. Application of fuzzy logic to approximate reasoning using linguistic systems, " IEEE Truns. A model for the measurement of membership and the consequences of its empirical implementation. " Expert system on a chip: An engine for real-time approximate reasoning, " IEEE Expert. ~, " Approximate reasoning with interval valued fuzzy sets, " in Proc.