摘要
列举了模糊规则发生摄动的常见情形,建立了一般性的模糊推理算法对规则摄动的鲁棒性的概念;就多重、链式和多维模糊推理情形,重点研究了一般性的模糊蕴涵算子对几个重要的模糊推理算法的这种鲁棒性的影响,并分别给出了相应的充分必要条件;初步尝试了通过一定的摄动制约来改善这种鲁棒性;同时指出了很多现有的模糊蕴涵算子使得所讨论的这些推理算法拥有好的鲁棒性,此时,即使规则中的隶属度有适度的粗糙或摄动,推理仍是可行的、安全的.文中工作对模糊系统的分析、模糊蕴涵算子的选择以及规则获取过程有一定的指导意义.
The authors list several common cases when fuzzy rules may perturb slightly and propose robustness concepts of general fuzzy reasoning methods with perturbations of rules; investigate mainly impacts of general fuzzy implication operators on such robustness of various important methods, respectively for multifold fuzzy reasoning, multidimensional fuzzy reasoning as well as a chain of fuzzy reasoning, further present corresponding necessary and sufficient conditions; in addition, do a certain attempt to improve the robustness by means of perturbation restriction of rules; also point out that many fuzzy implication operators make the discussed fuzzy reasoning methods hold good robustness, therefore under such condition, the discussed fuzzy reasoning is still secure and feasible even if there are some roughness or perturbations of membership degrees of rules. The work in the paper is useful for analysis of fuzzy systems, choice of fuzzy implication operators, and guidance to fuzzy rule acquisition.
出处
《计算机学报》
EI
CSCD
北大核心
2005年第10期1700-1707,共8页
Chinese Journal of Computers
基金
国家自然科学基金(60472060)
湖南省自然科学基金(05JJ40004)
湖南省教育厅科研基金(04C509)资助.~~
关键词
模糊系统
模糊蕴涵
模糊逻辑
模糊推理
鲁棒性
摄动
fuzzy system
fuzzy implication
fuzzy logic
fuzzy reasoning
robustness
perturbation
