Abstract: As a tool of composing states of factors，multifactorial function which has been successfully applied in fuzzy decision-making and comprehensive degree evaluation.In the paper proposed by Li Hong-xing，the additive standard multifactorial function has been studied in detail.As a series of the paper proposed by Li Hong-xing，the axiomatic definition of the nonadditive standard multifactorial function is given.The construction and the properties of it are also researched.

摘要： 综合函数作为因素状态合成的工具，在多准则Fuzzy决策、综合程度估计以及多因素Fuzzy决策当中都得到了成功的应用。李洪兴详细研究了可加型标准综合函数，在此基础上，研究了非可加型标准综合函数，即突变型标准综合函数的公理化定义，以及性质和构造。