中文摘要：

基于若干条模糊规则的模糊推理的数学本质是将有限个模糊集之间的对应延拓成整个模糊空间上的映射，sup-＊合成推理算法和inf-→合成推理算法都是实现这种延拓的有效途径．研究了：1）基于一种sup-＊合成的模糊关系方程组Ai°mR=Bi（i=1，…，n），给出了最大解（最优近似解）的公式，并将此最大解用于构造模糊控制器，证明了以此解构造的模糊控制器具有插值函数的泛逼近性；2）基于一种inf°合成的模糊关系方程组Ai⊙mR=Bi（i=1，…，n），证明了在模糊划分意义下解的存在性，给出了最小解的公式，并将此最小解用于设计模糊控制器，证明了以此解构造的模糊控制器具有插值函数的泛逼近性．由于合成运算中引进了一种连续可变的T范数和蕴涵算子，即SchweizerT范数和Schweizer蕴涵算子，因而得到了2个基于已知模糊规则的具有良好柔性和泛逼近性的连续可变的模糊控制器簇的构造方法，这个结果对模糊系统设计与优化有重要意义．

英文摘要：

The essence of fuzzy reasoning based on some fuzzy rules is to extend a mapping on a finite group of fuzzy sets to a mapping on the whole fuzzy space. Both sup- ＊ and inf- → composition algorithms are effective ways to realize this extension. The main results of this paper are the following： 1） The system of fuzzy relation equations（SRE） Ai°mR =Bi （i= 1, ..., n） in which every equation is based on sup-＊-composition is studied and the formula of its greatest solution（or best approximate solution） is given. Furthermore, with this solution a new type of fuzzy controllers is constructed, these controllers＇ universal approximation property is proved. 2） The SRE Ai⊙mR =Bi （i= 1, …,n） in which every equation is based on inf- → -composition is studied. It is proved that under the conditions of fuzzy partition this SRE is solvable, and the formula of it＇s smallest solution is presented. Furthermore, with this solution a new type of fuzzy controllers is constructed, these controllers＇ universal approximation property is proved. Since a kind of continuous variable implication operator and T-norm （i. e. Schweizer implication operator and Schweizer T-norm） are used in the composition operations, two clusters of flexible fuzzy systems which are both universal approximators with respect to continuous systems are obtained. This is significant in design and optimization of fuzzy systems.