计算机工程与应用2019，Vol.55Issue(6)：42-49,125,9.DOI:10.3778/j.issn.1002-8331.1805-0010
Lipschitz聚合算子的模糊推理鲁棒性研究
Research on Robustness of Fuzzy Reasoning on Lipschitz Operators
摘要
Abstract
In fuzzy reasoning, when the input and inference rules are perturbed, the selection of the internal connection operator is the main factor affecting the reasoning output. In this paper, the definition of fuzzy Lipschitz operator is given, the triangular-norm operators and implication operators satisfying Lipschitz condition are proved. The stable Lipschitz operators to influence the robustness of fuzzy reasoning are focused on. When the input is perturbed and the rule is per-turbed, the internal connection operators which are 1-Lipschitz operators can effectively restrain the output perturbation, especially when the internal connective operators are 1-k∞-Lipschitz and quasi-copulas, the output of fuzzy reasoning is safer and more feasible, the robustness of fuzzy reasoning can get better control. In addition, the experimental results show that the rule perturbation has great effect on output. The experimental part is not only a good verification of the theory proposed in this paper, but also a specific application of the theory in image processing and face association.关键词
Lipschitz/三角模/蕴涵/摄动/模糊推理Key words
Lipschitz/t-norm/implication/perturbation/fuzzy reasoning分类
信息技术与安全科学引用本文复制引用
陈芳,赵树宇,杨素娣,高秀梅..Lipschitz聚合算子的模糊推理鲁棒性研究[J].计算机工程与应用,2019,55(6):42-49,125,9.基金项目
国家自然科学基金面上项目(No.61772019) （No.61772019）
陕西省自然科学基础研究计面上项目(No.2017JM1036). （No.2017JM1036）
