模糊推理三I算法的逻辑基础

The Logic Foundation of the Triple I Algorithms in Fuzzy Reasoning

在模糊推理理论中 ,近期问世的三 I推理方法以逻辑蕴涵运算取代传统的合成运算 ,从根本上改进了传统的合成推理规则 (即 CRI方法 )。本文基于模糊命题逻辑的形式演绎系统 L* 和模糊谓词逻辑的一阶系统 K* ,构建了一个完备的多型变元一阶系统 K*ms,并且将三 I算法完全纳入了模糊逻辑的框架之中 ,从而为模糊推理奠定了严格的逻辑基础。

In the theory of fuzzy reasoning, the full implication triple I algorithms proposed recently (efficiently) improve the conventional CRI algorithms. By the method of partial valuations, the triple I algorithm can be put into the fremework of fuzzy logic semantically. In this paper, based on the (researches) of the formal deductive system L~* of fuzzy propositional logic and the first-order systems K~*, a multiple-sorted first-order system K~* (ms) of fuzzy predicate logic is proposed, and moreover, based on the theory of the system K~* (ms), the triple I algorithms are put into the framework of fuzzy logic (syntactically.) Thus a solid logic foundation of fuzzy reasoning is built up.