M范数的定义,性质及生成定理

不确定性推理在故障诊断、医疗咨询等领域已经得到了广泛的应用。本文首先从代数系统角度提出了均值求解模型Ｍ范数的定义，然后研究了它的性质，最后给出并证明了生成Ｍ范数的若干定理。Ｍ范数是一簇均值求解模型，它填补了“与”、“或”运算之间的一个空白，在已有相关性准则的基础上，提出了依存相关准则和中立相关准则，从而把相关性准则扩展成比较完整的相关性准则体系，使不确定性推理理论能处理均值求解问题，均值求解模型设计具有理论依据，推理过程易于操作，推理结论更加精确

On M Norm Useful in Artificial Intelligence

In our work done on an Expert System(ES) begun in September 1993 on contract for the MineralOil and Chemical Corporation of Dalian, we reached in 1994 the point that M norm, proposed by us, was necessary for filling up the need of Uncertain Reasoning(UR) in Artificial Intelligence. The long used t norm and t conorm do not fully satisfy the need of UR. We found that they need to be supplemented with M norm. From the viewpoint of algebraic system, we defined M norm as a collection of meansolving models. We found the main properties of M norm in the form of Theorems 1 through 5 and proved these five theorems. Only Theorem 4 had been proved from the viewpoint of functions. As the logical next step, we proposed two correlation criteria: interdependent, and neutral. They are similar to three correlation criteria proposed by others for t norm and t conorm. Finally, we put forward seven generating theorems: Theorems 6 through 12. Only Theorem 6 had been proved from the viewpoint of functions. The seven generating theorms ensure that all operations satisfying our definition of M norm, which includes all averaging operators in common use, do actually exist.