模糊推理算法的数学原理  

Mathematical Principle of the Algorithms of Fuzzy Reasoning

作　　者：潘正华[1] 

机构地区：[1]江南大学理学院数理研究所,无锡214122

出　　处：《计算机研究与发展》2008年第z1期165-168,共4页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(60575038)

摘　　要：模糊推理算法在自动控制等领域不断得到成功应用,但其理论基础却是贫弱的.从数学与逻辑的角度对模糊推理算法的基础进行研究分析,提出并证明了3个定理.结果表明在各种模糊推理模式中,前提与结论之间存在一个数学关系(有界实函数),模糊推理的各种算法都是这一函数的不同构造形式.所以,模糊推理的算法其基础是可靠的.Algorithm of fuzzy reasoning has been successful applied in the automatic control, but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper, structure of basic algorithms of fuzzy reasoning was studied, its rationality was discussed from the viewpoint of logic and mathematics, and three theorems were proved. These theorems shows that there always exists a mathematical relation (that is, a bounded real function)between the premises and the conclusion for fuzzy reasoning, and in fact various algorithms of fuzzy reasoning are specific forms of this function. Thus these results show that algorithms of fuzzy reasoning are theoretic reliable.

关 键 词：模糊推理 糊推理算法 模糊假言推理 CRI算法 3I算法 

分 类 号：TP273+.4[自动化与计算机技术—检测技术与自动化装置]