基于直觉模糊推理(1,2,2)-a型泛三Ⅰ算法的鲁棒性
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摘要
本文基于直觉模糊集,研究了直觉模糊推理(1,2,2)-a型泛三Ⅰ算法,给出了IFMP、IFMT问题的直觉模糊推理(1,2,2)-a型泛三Ⅰ算法解的表达形式和分解形式.其次,利用直觉模糊集间的自然距离定义了直觉模糊连接词和直觉模糊集的灵敏度,给出了直觉?ukasiewicz蕴涵、直觉G?del蕴涵以及它们各自对应三角模的灵敏度,在此基础上,证明了直觉?ukasiewicz蕴涵是直觉模糊集上最鲁棒剩余型蕴涵算子.最后,讨论了直觉模糊推理(1,2,2)-a型泛三Ⅰ算法的鲁棒性,并且针对以上两种具体蕴涵算子,相应地获得了直觉模糊推理(1,2,2)-a型泛三Ⅰ算法解的灵敏度.结论表明,直觉模糊推理算法的鲁棒性完全取决所选择的直觉模糊连接词.
The intuitionistic fuzzy inference( 1,2,2)-a type universal triple Ⅰ methods based on intuitionistic fuzzy set are discussed, the expression form and decomposition form of solutions of intuitionistic fuzzy inference( 1,2,2)-a type universal triple methods based on IFMP and IFMT problems are given. Then,based on the natural distances between intuitionistic fuzzy sets, the sensitivity of intuitionistic fuzzy connectives and intuitionistic fuzzy sets are defined, the sensitivity of intuitionistic ?ukasiewicz implication, intuitionistic G9 del implication and their corresponding triangular norm are provided.On this basis, it is proved that intuitionistic ?ukasiewicz implication is the most robust residual implication on intuitionistic fuzzy sets. Finally, robustness of intuitionistic fuzzy inference( 1,2,2)-a type universal triple Ⅰ methods are investigated,corresponding sensitivity of solutions of intuitionistic fuzzy inference type universal triple methods are obtained for two kinds of specific implications. These results indicated that the robustness of intuitionistic fuzzy inference methods directly depended on the selection of intuitionistic fuzzy connectives.
The intuitionistic fuzzy inference( 1,2,2)-a type universal triple Ⅰ methods based on intuitionistic fuzzy set are discussed, the expression form and decomposition form of solutions of intuitionistic fuzzy inference( 1,2,2)-a type universal triple methods based on IFMP and IFMT problems are given. Then,based on the natural distances between intuitionistic fuzzy sets, the sensitivity of intuitionistic fuzzy connectives and intuitionistic fuzzy sets are defined, the sensitivity of intuitionistic ?ukasiewicz implication, intuitionistic G9 del implication and their corresponding triangular norm are provided.On this basis, it is proved that intuitionistic ?ukasiewicz implication is the most robust residual implication on intuitionistic fuzzy sets. Finally, robustness of intuitionistic fuzzy inference( 1,2,2)-a type universal triple Ⅰ methods are investigated,corresponding sensitivity of solutions of intuitionistic fuzzy inference type universal triple methods are obtained for two kinds of specific implications. These results indicated that the robustness of intuitionistic fuzzy inference methods directly depended on the selection of intuitionistic fuzzy connectives.
引文
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[17]井美,惠小静,王蓉.直觉模糊推理的三I约束算法[J].计算机工程与应用,2018,54(15):53-56.Jing M,Hui X J,Wang R. Triple I restriction methods ofintuitionistic fuzzy inference[J]. Computer Engineeringand Application,2018,54(15):53-56.(in Chinese)
[18]于祥雨,李得超.直觉模糊推理系统的鲁棒性[J].模糊系统与数学,2014,28(2):111-119.Yu X Y,Li D C. Robustness of atanassov’s intuitionisticfuzzy reasoning system[J]. Fuzzy Systems and M athe-matics,2014,28(2):111-119.(in Chinese)
[19]刘岩.几种度量下ukasiewicz型直觉模糊推理三I算法的性质分析[D].兰州理工大学,2017.Lui Y. Property analysis of the triple I method forukasiew icz intuitionistic fuzzy reasoning based on sever-al distances[D]. Lanzhou University of Technology,2017.(in Chinese)
[20]段景瑶.基于模糊逻辑等价的直觉相似度[J].模糊系统与数学,. 2017,31(1):110-122.Duan J Y. Intuitionistic similarities based on the fuzzylogical equivalence operators[J]. Fuzzy Systems andM athematics,2017,31(1):110-122.(in Chinese)
[21]许小芾.直觉模糊推理SIS算法的统一形式及其性质研究[D].兰州理工大学,2017.Xu X F. Research on the unified form and property of theSIS methods for intuitionistic fuzzy reasoning[D].Lanzhou University of Technology,2017.(in Chinese)
[22]Klement E P,Mesiar R,Pap E. Triangular Norms[M].Dordrecht:Kluw er Academic Publishers,2000.
[2] Dubois D,Prade H. Fuzzy Sets in approximate reasoning[J]. Fuzzy Sets and Systems,1991,40(1):143-244.
[3]Zadeh L A. Toward extended fuzzy logic-A first step[J].Fuzzy Sets and Systems,2009,160(21):3175-3181.
[4] Zadeh L A. Outline of a new approach to the analysis ofcomplex systems and decision and process[J]. IEEETransaction on Systems,M an,and Cybernetics,1973,3(1):28-44.
[5]Wang G J. Full implicational triple I methods for fuzzy rea-soning[J]. Science in China(Series E),1999,29(1):43-53.
[6]李洪兴. Fuzzy系统的概率表示[J].中国科学(E辑),2006,36(4):359-366.Li H X. Probability representation of Fuzzy systems[J].Science in China(Series E),2006,36(4):359-366.(inChinese)
[7]唐益明.(1,2,2)型异蕴涵泛三I算法及其应用研究[D].合肥工业大学,2011.Tang Y M. Research on differently implicational universaltriple I method of(1,2,2)type and its applications[D].Hefei University of Technology,2011.(in Chinese)
[8] Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Sets andSystems,1986,20(1):87-96.
[9]Das S,Dutta B,Guha D. Weight computation of criteria ina decision-making problem by know ledge measure w ithintuitionistic fuzzy set and interval-valued intuitionisticfuzzy set[J]. Soft Computing,2016,20(9):3421-3442.
[10]王毅,刘三阳,张文.属性权重不确定的直觉模糊多属性决策的威胁评估方法.[J]电子学报,2014,42(12):2510-2514.Wang Y Y,Liu S Y,Zhang W. Threat assessment methodw ith uncertain attribute w eight based on intuitionistic fuzz-y multi-Attribute decision[J]. Acta Electronica Sinica,2014,42(12):2510-2514.(in Chinese)
[11]Deschrijver G,Cornelis C,Kerre E E. On the representa-tion of intuitionistic fuzzy t-norms and t-conorms[J].IEEE Transaction on Fuzzy Systems,2004,12(1):45-61.
[12]Cornelis C,Deschrijver G,Keer E E. Implication in intu-itionistic fuzzy and interval-valued fuzzy set theory:con-struction,classsification,application[J]. Internal Journalof Approximate Reasoning,2004,35(1):55-95.
[13]Liu H W,Wang G J. Multi-criteria decision-makingmethods based on intuitionistic fuzzy sets[J]. EuropeanJournal of Operational Research,2007,179(1):220-233.
[14]郑慕聪.剩余型直觉蕴涵算子的统一形式[J].模糊系统与数学,2013,27(2):15-22.Zheng M C. Unified form of residual intuitionistic fuzzyimplicators[J]. Fuzzy Systems and M athematics,2013,27(2):15-22.(in Chinese)
[15]郑慕聪.剩余型直觉模糊推理的三I方法[J].中国科学(信息科学),2013,43(6):810-820.Zheng M C. Triple I M ethod of intuitionistic fuzzy reason-ing based on residual implicator[J]. Science in China(In-formation Science),2013,43(6):810-820.(in Chi-nese)
[16]Zheng M C,Shi Z K,Liu Y. Triple I methods of approx-imate reasoning on Atanassov’s intuitionistic fuzzy sets[J]. International Journal of Approximate Reasoning,2014,55(6):1369-1382.
[17]井美,惠小静,王蓉.直觉模糊推理的三I约束算法[J].计算机工程与应用,2018,54(15):53-56.Jing M,Hui X J,Wang R. Triple I restriction methods ofintuitionistic fuzzy inference[J]. Computer Engineeringand Application,2018,54(15):53-56.(in Chinese)
[18]于祥雨,李得超.直觉模糊推理系统的鲁棒性[J].模糊系统与数学,2014,28(2):111-119.Yu X Y,Li D C. Robustness of atanassov’s intuitionisticfuzzy reasoning system[J]. Fuzzy Systems and M athe-matics,2014,28(2):111-119.(in Chinese)
[19]刘岩.几种度量下ukasiewicz型直觉模糊推理三I算法的性质分析[D].兰州理工大学,2017.Lui Y. Property analysis of the triple I method forukasiew icz intuitionistic fuzzy reasoning based on sever-al distances[D]. Lanzhou University of Technology,2017.(in Chinese)
[20]段景瑶.基于模糊逻辑等价的直觉相似度[J].模糊系统与数学,. 2017,31(1):110-122.Duan J Y. Intuitionistic similarities based on the fuzzylogical equivalence operators[J]. Fuzzy Systems andM athematics,2017,31(1):110-122.(in Chinese)
[21]许小芾.直觉模糊推理SIS算法的统一形式及其性质研究[D].兰州理工大学,2017.Xu X F. Research on the unified form and property of theSIS methods for intuitionistic fuzzy reasoning[D].Lanzhou University of Technology,2017.(in Chinese)
[22]Klement E P,Mesiar R,Pap E. Triangular Norms[M].Dordrecht:Kluw er Academic Publishers,2000.