两种推理方法QIP和FSI的鲁棒性结果及其比较
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摘要
基于逻辑相似度和剩余蕴涵,研究了五蕴涵推理方法(QIP)和相似度推理方法(FSI)的鲁棒性,给出了在四个常用蕴涵下QIP的鲁棒性的具体结果,以及基于修正的Kleene蕴涵的FSI的鲁棒性结论,并且对这两种推理方法的鲁棒性进行了初步的比较.
Based on logical similarity and residual implications, the paper discusses the robustness of two important reasoning methods, the five implication inference method(QIP) and the similarity inference method(FSI). The concrete results of the robustness of QIP method under four common implications are given, based on the revised Kleene implication the FSI's robustness conclusion, and a preliminary comparison of the robustness of these two inference methods.
Based on logical similarity and residual implications, the paper discusses the robustness of two important reasoning methods, the five implication inference method(QIP) and the similarity inference method(FSI). The concrete results of the robustness of QIP method under four common implications are given, based on the revised Kleene implication the FSI's robustness conclusion, and a preliminary comparison of the robustness of these two inference methods.
引文
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[6]王龙,裴道武.对称蕴涵推理方法鲁棒性分析[J].高校应用数学学报,2018, 33(2):232-242.
[7] Zhou Baokui,Xu Genqi, Li Sanjiang. The quintuple implication principle of fuzzy reasoning[J]. Information Sciences, 2015, 297:202-215.
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[9] Wang Degang, Meng Yanping, Li Hongxing. A fuzzy similarity inference method for fuzzy reasoning[J]. Computers and Mathematics with Applications, 2008, 56:2445-2454.
[10]郭方芳,陈图云,夏尊全.基于极大模糊熵原理的模糊推理三Ⅰ算法[J].模糊系统与数学,2003,17(4):56-59.
[11] Ying Mingsheng. Perturbation of fuzzy reasoning[J]. IEEE Transactions on Fuzzy Systems,1999, 7(5):625-629.
[12] Cai Kaiyuan.δ-equalities of fuzzy sets[J]. Fuzzy Sets and Systems, 1995, 76:97-112.
[13] Jin Jianhua, Li Yongming, Li Chunquan. Robustness of fuzzy reasoning via logically equivalence measure[J]. Information Sciences, 2007, 177:5103-5117.
[14] Dai Songsong, Pei Daowu, Guo Donghui. Robustness analysis of fully implication inference method[J]. International Journal of Approximate Reasoning, 2013, 54:653-666.
[15] Li Yingfang, Qin Keyun, He Xingxing. Robustness of fuzzy connectives and fuzzy reasoning with respect to general divergence measures[J]. Fuzzy Sets and Systems, 2016, 294:63-78.
[16]刘华文,王国俊.模糊推理三Ⅰ约束算法的一般表述[J].模糊系统与数学,2008, 22(3):1-7.
[17] Klement E P, Mesiar R, Pap E. Triangular Norms[M]. Dordrecht:Kluwer Academic Publishers, 2000.
[18] Kukkurainen P, Turunen E. Many-valued similarity reasoning. An Axiomatic approach[J].Multiple-Valued Logic, 2002, 8:751-760.
[19] Turuuen E. Mathematics behind Fuzzy Logic[M]. Wurzburg:Physica-verlag, 1999.
[20] Belohlavek R. Fuzzy Relational Systems:Foundations and Principles[M]. Dordrecht:Kluwer Academic Publishers, 2002.
[21]李冰荣.相似度及其在模糊推理中的应用[D].杭州:浙江理工大学,2017.
[2]王国俊.模糊推理的全蕴涵三Ⅰ算法[J].中国科学E辑,1999, 29:43-53.
[3]王国俊.非经典数量逻辑与近似推理[M].北京:科学出版社,2008.
[4]裴道武.模糊推理全蕴含算法及其还原性[J].数学研究与评论,2004,24(2):359-368.
[5] Tang Yiming, Yang Xuezhi. Symmetric implicational method of fuzzy reasoning[J]. International Journal of Approximate Reasoning, 2015, 54(8):1034-1048.
[6]王龙,裴道武.对称蕴涵推理方法鲁棒性分析[J].高校应用数学学报,2018, 33(2):232-242.
[7] Zhou Baokui,Xu Genqi, Li Sanjiang. The quintuple implication principle of fuzzy reasoning[J]. Information Sciences, 2015, 297:202-215.
[8]宋士吉,吴澄.模糊推理的反向三Ⅰ算法[J].中国科学E辑,2002, 32(2):230-246.
[9] Wang Degang, Meng Yanping, Li Hongxing. A fuzzy similarity inference method for fuzzy reasoning[J]. Computers and Mathematics with Applications, 2008, 56:2445-2454.
[10]郭方芳,陈图云,夏尊全.基于极大模糊熵原理的模糊推理三Ⅰ算法[J].模糊系统与数学,2003,17(4):56-59.
[11] Ying Mingsheng. Perturbation of fuzzy reasoning[J]. IEEE Transactions on Fuzzy Systems,1999, 7(5):625-629.
[12] Cai Kaiyuan.δ-equalities of fuzzy sets[J]. Fuzzy Sets and Systems, 1995, 76:97-112.
[13] Jin Jianhua, Li Yongming, Li Chunquan. Robustness of fuzzy reasoning via logically equivalence measure[J]. Information Sciences, 2007, 177:5103-5117.
[14] Dai Songsong, Pei Daowu, Guo Donghui. Robustness analysis of fully implication inference method[J]. International Journal of Approximate Reasoning, 2013, 54:653-666.
[15] Li Yingfang, Qin Keyun, He Xingxing. Robustness of fuzzy connectives and fuzzy reasoning with respect to general divergence measures[J]. Fuzzy Sets and Systems, 2016, 294:63-78.
[16]刘华文,王国俊.模糊推理三Ⅰ约束算法的一般表述[J].模糊系统与数学,2008, 22(3):1-7.
[17] Klement E P, Mesiar R, Pap E. Triangular Norms[M]. Dordrecht:Kluwer Academic Publishers, 2000.
[18] Kukkurainen P, Turunen E. Many-valued similarity reasoning. An Axiomatic approach[J].Multiple-Valued Logic, 2002, 8:751-760.
[19] Turuuen E. Mathematics behind Fuzzy Logic[M]. Wurzburg:Physica-verlag, 1999.
[20] Belohlavek R. Fuzzy Relational Systems:Foundations and Principles[M]. Dordrecht:Kluwer Academic Publishers, 2002.
[21]李冰荣.相似度及其在模糊推理中的应用[D].杭州:浙江理工大学,2017.