基于Schweizer-Sklar三角范数簇的反向三I算法的鲁棒性

摘要

Schweizer-Sklar三角范数具有很好的柔性，使得基于柔性化算子的模糊推理算法有良好的属性。本文基于Minkowski距离标准研究Schweizer-Sklar算子簇的性质及模糊推理算法的鲁棒性。证明了Schweizer-Sklar三角范数簇关于参数m是单调递减的；Schweizer-Sklar三角余范簇关于参数m是单调递增的；并且给出了Schweizer-Sklar三角余范簇、三角范数簇及其诱导的剩余蕴涵簇的扰动；证明了 m∈（0，∞）时，Schweizer-Sklar 剩余蕴涵簇（包含Lukasiewizc蕴涵）均适合用于模糊推理。进一步证明了：当m∈（0，∞）时，基于Schweizer-Sklar剩余蕴涵簇的FMP-反向三I算法具有鲁棒性；当m∈（0，∞）时，基于Schweizer-Sklar剩余蕴涵簇的FMT-反向三I算法具有鲁棒性。%Since the family of Schweizer-Sklar t-norm is flexible,they have good characteristics for fuzzy reasoning based on these flexible operators.In this paper,the properties of the Schweizer-Sklar operators family and the robustness of fuzzy reasoning algorithms are studied.The family of Schweizer-Sklar t-norms are decreasing for the variable m.The family of Schweizer-Sklar t-conorms are increasing for the variable m.These perturbations of Schweizer-Sklar t-conorms,Schwei-zer-Sklar t-norms and its residual implications are given.We proved that Schweizer-Sklar residual implication operators (in-clude Lukasiewizc implication operator)are more suitable in fuzzy reasoning for m∈(0,∞).Moreover,we showed that the FMP reverse triple I algorithms based on the Schweizer-Sklar residual implications are robust for m∈(0,∞),and the FMT reverse triple I algorithms based on the Schweizer-Sklar residual implications are robust for m∈(0,∞).