均衡度公理化定义的改进

The Improvement on the Axiomatic Definition of Balance Degree

研究均衡度概念的公理化定义及其构造问题。首先,借助实例说明现有均衡度定义存在的问题;随后,在分析均衡度概念的特点和典型均衡度函数的图形的基础上,给出一种新的均衡度公理化定义。接着,讨论均衡度函数的构造问题,给出四类常用的均衡度函数,证明了均衡度函数与一类单调函数的复合仍是均衡度。最后,讨论了新的均衡度定义与原定义之间的关系以及四类常见均衡度函数之间的关系。

The axiomatic definition and construction of balance degree function are discussed. Firstly, by using an example, it is shown that the definition of balance degree introduced in the literature has some imperfect aspects. A new approach of balance degree axiomatic definition is given based on the analysis of the character and the graph of a normal balance degree function. Then, the construction of balance degree functions are discussed, four kinds of balance degree functions are obtained. It is proved that the composite functions obtained by balance degree function and a kind of Monotone Function are balance degree function. At last, the relations between the new definition of balance degree and the original one as well as the relations of four kinds of balance degree functions are studied.