广义摄动度及BKS推理方法的鲁棒性
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摘要
针对用于研究模糊推理鲁棒性的模糊集摄动程度概念不统一的状况,提出了广义摄动度的概念,使文献中出现的多个概念成为新概念的特殊情形。基于提出的广义摄动度概念,系统研究了一些常用蕴涵和模糊连接词的摄动程度,给出了常用蕴涵和模糊连接词的广义摄动度,并且得到基于五个模糊蕴涵的Bandler-Kohout Subproduct(BKS)推理方法的鲁棒性结果。
Aiming at the situation that the concept of fuzzy set perturbation degree used to study the robustness of fuzzy reasoning is not uniform, the concept of generalized perturbation is proposed, which makes the multiple concepts appearing in the literature become special cases of the new concept. Based on the proposed concept of generalized perturbation degree, the perturbation degree of some commonly used implications and fuzzy connection words are systematically studied. The generalized perturbation of common implications and fuzzy connection words are given, and the robustness of the Bandler-Kohout Subproduct(BKS) reasoning method based on five fuzzy implications is obtained.
Aiming at the situation that the concept of fuzzy set perturbation degree used to study the robustness of fuzzy reasoning is not uniform, the concept of generalized perturbation is proposed, which makes the multiple concepts appearing in the literature become special cases of the new concept. Based on the proposed concept of generalized perturbation degree, the perturbation degree of some commonly used implications and fuzzy connection words are systematically studied. The generalized perturbation of common implications and fuzzy connection words are given, and the robustness of the Bandler-Kohout Subproduct(BKS) reasoning method based on five fuzzy implications is obtained.
引文
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[2] Ying M S. Perturbation of fuzzy reasoning [J]. IEEE Transactions on Fuzzy Systems, 1999, 7(5): 625-629.
[3] Hong D H, Hwang S Y. A note on the value similarity of fuzzy systems variables[J]. Fuzzy Sets and Systems, 1994, 66(3): 383-386.
[4] Dai S S, Pei D W, Wang S M. Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distances[J]. Fuzzy Sets and Systems, 2011, 189(1): 63-73.
[5] Montes S, Couso I, Gil P, et al. Divergence measures between fuzzy sets[J]. International Journal of Approximate Reasoning, 2002, 30(2): 91-105.
[6] Wang G J, Duan J Y. On robustness of the full implication triple I inference method with respect to finer measurements[J]. International Journal of Approximate Reasoning, 2014, 55(3): 787-796.
[7] 王国俊,段景瑶.适宜于展开模糊推理的两类模糊度量空间[J].中国科学:信息科学,2014,44(5):623-632.
[8] Li Y F, Qin K Y, He X, et al. Robustness of fuzzy connectives and fuzzy reasoning with respect to general divergence measures[J]. Fuzzy Sets and Systems, 2016, 294: 63-78.
[9] 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,2013:7-15.
[10] Cai K Y. qualities of fuzzy sets [J]. Fuzzy Sets and Systems, 1995, 76(1): 97-112.
[11] Duan J Y, Li Y M. Robustness analysis of logic metrics on F(X) F(X) math container loading mathjax [J]. International Journal of Approximate Reasoning, 2015, 61: 33-42.
[12] Zadeh L A. Outline of new approach to the analysis of complex systems and decision processes[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1973, 3(1): 28-44.
[13] Pedrycz W. Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data[J]. Fuzzy Sets and Systems, 1985, 16(2): 163-175.