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DOI:
Journal of Software:2004.15(10):1485-1492

两类模糊推理算法的连续性和逼近性
徐蔚鸿,谢中科,杨静宇,叶有培
(吉首大学,数学与计算机科学学院,湖南,吉首,416000;长沙理工大学,计算机与通信工程学院,湖南,长沙,410077;南京理工大学,计算机科学与技术系,江苏,南京,210094)
Continuity and Approximation Properties of Two Classes of Algorithms for Fuzzy Inference
XU Wei-Hong,XIE Zhong-Ke,YANG Jing-Yu,YE You-Pei
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Received:July 28, 2003    Revised:January 08, 2004
> 中文摘要: 对Zadeh的模糊推理合成法则(CRI算法)和全蕴涵三I算法(三I算法)是否满足连续性和逼近性问题进行了细致的研究,进一步讨论了这两类算法对逼近误差的传播性能.为此,把模糊推理算法看成是模糊集合到模糊集合的映射,选用海明距离作为两模糊集的距离.证明了在模糊假言推理和模糊拒取式推理情形,这两类算法都拥有连续性.指出三I算法在已知规则的前件和后件是正规集的条件下总是满足逼近性,而CRI算法只有当它满足还原性时才拥有逼近性.在满足逼近性的条件下,两类算法都不会放大逼近误差.结果对构建模糊控制系统和模糊专家系统时选用和分析模糊推理算法有一定的指导作用.
Abstract:The authors investigate carefully whether or not two classes of inference algorithms, which are Compositional Rule of Inference (CRI) proposed by L.A.Zadeh and Triple-Implication algorithm (Triple-I) proposed lately, hold the continuity and approximation properties, and moreover, also how the approximation errors are propagated by them. Therefore, a fuzzy inference algorithm is viewed as a mapping from one fuzzy set to another, Hamming distance formula is used as the computing distance between the two fuzzy sets. The authors prove that the two classes of algorithms hold the continuity properties in the cases of fuzzy modus ponens and fuzzy modus tollens. The authors also point out that Triple-I algorithm always holds the approximation property if antecedent and consequence of the known rule are normal fuzzy sets. However CRI algorithm holds approximation property only if CRI holds consistency property. Two classes of algorithms do not make approximation errors magnified when they hold approximation property. The results of the paper are useful for the selection and analysis of algorithms for fuzzy inference when practical fuzzy control and expert systems are designed.
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基金项目:Supported by the National Natural Science Foundation of China under Grant No.60072034(国家自然科学基金);the Natural Science Foundation of Hu'nan Province of China under Grant No.02JJY4060(湖南省自然科学基金) Supported by the National Natural Science Foundation of China under Grant No.60072034(国家自然科学基金);the Natural Science Foundation of Hu'nan Province of China under Grant No.02JJY4060(湖南省自然科学基金)
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徐蔚鸿,谢中科,杨静宇,叶有培.两类模糊推理算法的连续性和逼近性.软件学报,2004,15(10):1485-1492

XU Wei-Hong,XIE Zhong-Ke,YANG Jing-Yu,YE You-Pei.Continuity and Approximation Properties of Two Classes of Algorithms for Fuzzy Inference.Journal of Software,2004,15(10):1485-1492