Recently, many rules have been proposed to translate fuzzy conditional proposition into fuzzy relations. Most of them are obtained by introducing the well-known implication rules in many valued logic. In these translation rules, the fuzzy relation has been derived by operating membership functions. Many compositional rules of inference, which utilize t-norm operators, have also been proposed. The properties have been well evaluated for applying these translation rules and compositional rules to fuzzy inference. However, definite methods of determining membership functions and selecting t-norm operators have not been clarified. Consequently, when the fuzzy inference based on composition is applied to an actual problem, there are some difficulties in determining fuzzy relations and obtaining reasonable inference results. In this paper, some properties of the max-* composition mapping are investigated with regards to fuzzy inference as the mapping of membership functions. As a result, a new conception is derived where the max-* composition is the many-valued weighted mapping as total spaces correspond. From the conception, it is clarified that the fuzzy relation is a weighted function as total spaces correspond and the t-norm* is a weighted operator which is operated on the fuzzy relation and membership values. Using the conception, a new method is proposed for determining fuzzy relations. In this method, fuzzy relations are directly derived using weighted correspondence without using membership functions of the conditional part. It is shown that the method has some other superior properties compared with conventional methods. In addition, t-norm dependence upon fuzzy inference is also clarified. It is easy to select the suitable t-norm corresponding to actual problems using the result. [In Japanese.]
