对称蕴涵推理方法的鲁棒性分析
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摘要
模糊推理方法已经被成功地应用于模糊控制器设计,模糊专家系统集成等诸多领域.作为对传统模糊推理方法的改进,我国学者提出了基于三Ⅰ方法的对称蕴涵推理方法.对于模糊推理方法性质的研究,尤其是对推理方法鲁棒性的研究是模糊逻辑领域的一个重要的研究方向.基于规范的Minkowski距离讨论对称蕴涵方法的鲁棒性,给出了针对不同蕴涵算子的四个算法的鲁棒性结论,为模糊推理方法的选择与应用提供科学依据.
Fuzzy reasoning method has been successfully applied to fuzzy controller design, fuzzy expert system integration and many other fields. As an improvement of the traditional fuzzy reasoning method, Chinese scholars have proposed a symmetric inference method based on the triple Ⅰ method.The research on the nature, such as robustness of fuzzy reasoning method is an important direction in the field of fuzzy logic. This paper discusses the robustness of the symmetric implication methods based on the normalized Minkowski distance, the robustness of the four algorithms for several important implication operators are given. Thus it provides a scientific basis for the selection and applications of fuzzy reasoning methods.
Fuzzy reasoning method has been successfully applied to fuzzy controller design, fuzzy expert system integration and many other fields. As an improvement of the traditional fuzzy reasoning method, Chinese scholars have proposed a symmetric inference method based on the triple Ⅰ method.The research on the nature, such as robustness of fuzzy reasoning method is an important direction in the field of fuzzy logic. This paper discusses the robustness of the symmetric implication methods based on the normalized Minkowski distance, the robustness of the four algorithms for several important implication operators are given. Thus it provides a scientific basis for the selection and applications of fuzzy reasoning methods.
引文
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[5]Tang Yiming,Yang Xuezhi.Symmetric implicational method of fuzzy reasoning[J].International Journal of Approximate Reasoning,2013,54:1034-1048.
[6]Ying Mingsheng.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1999,7:625-629.
[7]Dai Songsong,Pei Daowu,Wang Sanmin.Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distance[J].Fuzzy Sets and Systems,2011,189:63-73.
[8]Dai Songsong,Pei Daowu,Guo Donghui.Robustness analysis of full implication inference method[J].International Journal of Approximate Reasoning,2013,54:653-666.
[9]Wang Guojun,Duan Jingyao.On robustness of the full implication triple I inference method with respect to finer measurements[J].International Journal of Approximate Reasoning,2014,55:787-796.
[10]裴道武.基于三角模的模糊逻辑理论及其应用[M].北京:科学出版社,2013.
[11]Baczynski M,Jayaram B.Fuzzy Implications[M].Berlin:Springer,2008.
[12]Chen Fang,Xu Weihong,Bai Chuanzhi,et al.A novel approach to guarantee good robustness of fuzzy reasoning[J].Applied Soft Computing,2016,41:224-234.
[13]王国俊.非经典数理逻辑与近似推理(第二版)[M].北京:科学出版社,2008.
[2]王国俊.模糊推理的全蕴涵三I算法[J].中国科学(E辑),1999,29(1):43-53.
[3]侯健,尤飞,李洪兴.由三I算法构造的一些模糊控制器及其响应能力[J].自然科学进展,2005,15(1):29-37.
[4]潘海玉,裴道武,陈仪香.基于三I算法的模糊系统的响应能力[J].控制理论与应用,2011,28(1):24-30.
[5]Tang Yiming,Yang Xuezhi.Symmetric implicational method of fuzzy reasoning[J].International Journal of Approximate Reasoning,2013,54:1034-1048.
[6]Ying Mingsheng.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1999,7:625-629.
[7]Dai Songsong,Pei Daowu,Wang Sanmin.Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distance[J].Fuzzy Sets and Systems,2011,189:63-73.
[8]Dai Songsong,Pei Daowu,Guo Donghui.Robustness analysis of full implication inference method[J].International Journal of Approximate Reasoning,2013,54:653-666.
[9]Wang Guojun,Duan Jingyao.On robustness of the full implication triple I inference method with respect to finer measurements[J].International Journal of Approximate Reasoning,2014,55:787-796.
[10]裴道武.基于三角模的模糊逻辑理论及其应用[M].北京:科学出版社,2013.
[11]Baczynski M,Jayaram B.Fuzzy Implications[M].Berlin:Springer,2008.
[12]Chen Fang,Xu Weihong,Bai Chuanzhi,et al.A novel approach to guarantee good robustness of fuzzy reasoning[J].Applied Soft Computing,2016,41:224-234.
[13]王国俊.非经典数理逻辑与近似推理(第二版)[M].北京:科学出版社,2008.