Fuzzy测度的绝对连续性及扩张

Absolute Continuity and Extension of Fuzzy Measures

要建立定义在环上的Fuzzy测度(或更广泛一些的非可加测度)的一般扩张理论是困难的。迄今为止,有关的讨论都局限于某些特殊类型的Fuzzy测度(非可加测度)。在本文中,我们也仅研究一类特殊的Fuzzy测度的扩张,给出它们能从一个代数扩张到包含这个代数的σ-代数上去的条件。

It is difficult to establish a general extension theory for fuzzy measures defined on a ring. In this paper, we shall discuss the extension problem for a special class of fuzzy measures, and give a condition that they can be extended from an algebra onto a 6-algebra containing it.