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 Lukasiewicz implication, intuitionistic Godel implication and their corresponding triangular norm are provided.On this basis, it is proved that intuitionistic Lukasiewicz 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.
作者
惠小静
井美
王蓉
HUI Xiao-jing;JING-mei;WANG-rong(College of Mathematics and Computer Science,Yan’an University,Yan’an,Shaanxi 716000,China)
出处
《电子学报》
EI
CAS
CSCD
北大核心
2019年第2期410-416,共7页
Acta Electronica Sinica
基金
国家自然科学基金(No.11471007
No.61763045)
关键词
鲁棒性
直觉模糊推理
泛三Ⅰ算法
解的灵敏度
robustness
intuitionistic fuzzy inference
universal triple Ⅰ methods
sensitivity of solutions
