Abstract: In first-order form systems Lukms，Gödms，∏ms and L^*ms，by introducing the concepts of class of interpretation models and α-logical effective formulas under many-sorted first-order fuzzy language，the theory of class of interpretation models is presented；and then，based on above theory this paper discusses the relation between fuzzy reasoning（CRI arithmetic and Triple I arithmetic） and theory Г-reasoning，consequently the base of theory for fuzzy reasoning is established，and a new fuzzy reasoning arithmetic are given.

Key words: fuzzy reasoning, many-sorted first-order fuzzy language, interpretation model class, α-logical effective formulas

摘要： 首先在多类（many-sorted）一阶形式系统Lukms、Gödms，∏ms和L^*ms中通过引入多类一阶模糊语言Lms的解释模型类及基于解释模型类的α-逻辑有效公式的概念，建立了多类一阶模糊语言的解释模型类理论；然后，基于上述理论探讨了模糊推理算法（CRI及三I算法）与其理论Г-推理的关系，从而进一步奠定了模糊推理的理论基础，同时得到一种新型的模糊推理算法，称为极小三I算法。

关键词: 模糊推理, 多类一阶模糊语言, 解释模型类, α-逻辑有效公式