Journal of Mathematical Psychology | 2021
On the correspondence between knowledge structures and attribution functions
Abstract
Abstract 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 K of all knowledge structures and the collection F of all attribution functions, where knowledge spaces and complete attribution functions are closed elements of ( f , g ) in K and 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).