Fuzzy测度的扩张

本文首先给出反例,说明普通测度论中的测度扩张定理对fuzzy测度是不成立的。然后引进泛σ-可加性的概念,给出了一类可被构造的余范,使得对于这类余范是泛σ-可加的fuzzy测度,测度扩张定理是成立的。

The ExtenSion of Fuzzy Measure

This paper gives first a couter example, it illust■tes tlat the extension theorem of n■ ea ure i ■ o di ■a mea■ure theory does not hold. Then, we introduce■ the notion of "σ-pan■dditivity" and giva a class of conorm which can be constructed. For those fuzzy measures which are σ-pa■additive about afore-nentioned conorm the exten ion the rem of measure hold.