Abstract
Firstly, we consider modes of reasoning and show that fuzzy reasoning is performed depending on the knowledge of plural rules. Secondly, we introduce an extended logic system employing arithmetic operations together with AND, OR and NOT. On the logic system introduced, we consider infinite multiple-valued switching functions satisfying monotonicity, and then define fuzzy threshold functions. Thirdly we assume monotonicity in modes of reasoning, and represent rule tables of reasoning by means of the fuzzy threshold functions. Next, we propose a method of approximate reasoning using these rule tables. Fourthly, we apply the reasoning method to process control. Through experimental studies by a computer, we show advantages of the control method employing fuzzy threshold functions to the MAX-MIN-CG method which is one of the often used fuzzy-logic-based process control methods. In theoretical discussions, it is shown that fuzzy threshold functions include multiple-valued threshold functions as a special case. This implies that any multiple-valued threshold function may easily be expressed in an extended logical form.
