基于平均逻辑相似度的α-反向三Ⅰ算法的鲁棒性
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摘要
鲁棒性是评价算法优劣的一个重要标准。以平均逻辑相似度为衡量扰动的指标,分别讨论了α-反向三Ⅰ支持算法和α-反向三Ⅰ约束算法的鲁棒性,结论表明FMP(FMT)问题的α-反向三Ⅰ支持算法和α-反向三Ⅰ约束算法具有相同的鲁棒性。
Robustness is an important criterion for evaluating the performance of an algorithm. This paper discusses the robustness of the α-reverse triple I sustaining methods and α-reverse triple I restriction algorithm by means of the average logical similarity. It shows that the α-reverse triple I sustaining methods of FMP(FMT) has the same robustness as theα-reverse triple I restriction algorithm.
Robustness is an important criterion for evaluating the performance of an algorithm. This paper discusses the robustness of the α-reverse triple I sustaining methods and α-reverse triple I restriction algorithm by means of the average logical similarity. It shows that the α-reverse triple I sustaining methods of FMP(FMT) has the same robustness as theα-reverse triple I restriction algorithm.
引文
[1]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8(3):338-356.
[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]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.
[4]Song Shiji,Feng Chunbo,Lee E S.Triple I method of fuzzy reasoning[J].Computer and Mathematics with Applications,2002,44(12):1567-1579.
[5]宋士吉,吴澄.模糊推理的反向三I约束算法[J].自然科学进展,2002,12(1):95-100.
[6]Ying Mingsheng.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1999,7(5):625-629.
[7]Dai Songsong,Pei Daowu.Robustness analysis of full implication inference method[J].International Journal of Approximate Reasoning,2013,54(5):653-666.
[8]杨超,李得超.三I算法的鲁棒性[J].模糊系统与数学,2014,28(1):72-77.
[9]Jin Jianhua,Li Yongming,Li Chunquan.Robustness of fuzzy reasoning via logically equivalence measure[J].Information Sciences,2007,177(22):5103-5117.
[10]Dai Songsong,Pei Daowu,Wang Sanmin.Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distances[J].Fuzzy Sets and Systems,2011,189:63-73.
[11]罗敏霞,程泽.区间值三I算法的鲁棒性[J].计算机科学,2016,43(10):277-281.
[12]Dai Songsong,Pei Daowu.Robustness analysis of full implication inference method[J].International Journal of Approximate Reasoning,2013,54(5):653-666.
[13]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(3):787-796.
[14]王国俊.数理逻辑引论与归结原理[M].2版:北京:科学出版社,2006.
[15]Li Y F,Qin K Y,He X X.Robustness of fuzzy connectivesand fuzzy reasoning[J].Fuzzy Sets and Systems,2013,225:93-105.
[16]Klement E P,Mesiar R,Pap E.Triangular norms[M].Dordrecht:Kluwer Academic Publishers,2000.
[17]段景瑶,王国俊,李永明.逻辑等价算子在模糊推理中的应用[D].西安:陕西师范大学,2015:1-97.
[18]谷焕春,宋颖,张兴芳.模糊推理α-反向三I支持度算法的一般表示[J].模糊系统与数学,2014,28(1):80-82.
[19]谷焕春,宋颖,张兴芳.模糊推理α-反向三I约束算法的一般表示[J].河北师范大学学报:自然科学版,2013,37(3):223-225.
[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]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.
[4]Song Shiji,Feng Chunbo,Lee E S.Triple I method of fuzzy reasoning[J].Computer and Mathematics with Applications,2002,44(12):1567-1579.
[5]宋士吉,吴澄.模糊推理的反向三I约束算法[J].自然科学进展,2002,12(1):95-100.
[6]Ying Mingsheng.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1999,7(5):625-629.
[7]Dai Songsong,Pei Daowu.Robustness analysis of full implication inference method[J].International Journal of Approximate Reasoning,2013,54(5):653-666.
[8]杨超,李得超.三I算法的鲁棒性[J].模糊系统与数学,2014,28(1):72-77.
[9]Jin Jianhua,Li Yongming,Li Chunquan.Robustness of fuzzy reasoning via logically equivalence measure[J].Information Sciences,2007,177(22):5103-5117.
[10]Dai Songsong,Pei Daowu,Wang Sanmin.Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distances[J].Fuzzy Sets and Systems,2011,189:63-73.
[11]罗敏霞,程泽.区间值三I算法的鲁棒性[J].计算机科学,2016,43(10):277-281.
[12]Dai Songsong,Pei Daowu.Robustness analysis of full implication inference method[J].International Journal of Approximate Reasoning,2013,54(5):653-666.
[13]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(3):787-796.
[14]王国俊.数理逻辑引论与归结原理[M].2版:北京:科学出版社,2006.
[15]Li Y F,Qin K Y,He X X.Robustness of fuzzy connectivesand fuzzy reasoning[J].Fuzzy Sets and Systems,2013,225:93-105.
[16]Klement E P,Mesiar R,Pap E.Triangular norms[M].Dordrecht:Kluwer Academic Publishers,2000.
[17]段景瑶,王国俊,李永明.逻辑等价算子在模糊推理中的应用[D].西安:陕西师范大学,2015:1-97.
[18]谷焕春,宋颖,张兴芳.模糊推理α-反向三I支持度算法的一般表示[J].模糊系统与数学,2014,28(1):80-82.
[19]谷焕春,宋颖,张兴芳.模糊推理α-反向三I约束算法的一般表示[J].河北师范大学学报:自然科学版,2013,37(3):223-225.