In this paper, the completeness (completion) of attribution functions is introduced and a general way is given to derive an attribution function from a knowledge structure on an arbitrary domain. With the help of these, this paper establishes a Galois connection $(f,g)$ between the collection $\mathfrak{K}$ of all knowledge structures and the collection $\mathfrak{F}$ of all attribution functions, where knowledge spaces and complete attribution functions are closed elements of $(f,g)$ in $\mathfrak{K}$ and $\mathfrak{F}$, respectively. In addition, this paper introduces the reduct of attribution functions to give a direct characterization of granular attribution functions, which answers an open problem posed by Falmagne and Doignon (2011).

本文介绍了归因函数的完备性（完备性），并给出了从任意域上的知识结构推导出归因函数的一般方法。借助这些，本文建立了伽罗瓦连接$(F,G)$ 集合之间 $\mathfrak{钾}$ 所有知识结构和集合 $\mathfrak{F}$ 在所有归因函数中，知识空间和完全归因函数是 $(F,G)$ 在 $\mathfrak{钾}$ 和 $\mathfrak{F}$， 分别。此外，本文介绍了归因函数的约简，以直接表征粒度归因函数，回答了 Falmagne 和 Doignon (2011) 提出的一个开放问题。