量化Domain理论的L-Fuzzy式处理(II) L-Fuzzy拟序集的表示

A Fuzzy Approach to Quantitative Domain Theory (II) Representation of L-Fuzzy Quasi-Posets

本文是文献[4]的续。对于固定的FrameL,本文证明了每个LF-拟序集可以等价地表示为拟序的层,该结果与L-Fuzzy集的分解和表示定理类似。由这此定理可得出以下结论:一类量化Domain(例如,广义超度量Domain)实际上是将满足一定条件的拟序族进行"粘贴"的结果(按照层论的语言叙述,就是拟序的层),而通常的拟序则是常值拟序层的特例。

<Abstrcat> This paper is a continuation of paper [4]. In this paper we prove that every LF-quasiposet can be represented as a sheaf of quasi-posets, a result that is very similar to the decomposition and (representation) theorems of L-fuzzy set. From the result we know that a certain class of quantitative (domains) such as generalized ultrametric domains can be seen as the results of (patching) a certain (quasi-posets,) that is, a sheaf of quasi-posets in terms of language of sheaf theory. In particular, a (quasi-poset) itself is just the constant sheaf.