Implications from data with fuzzy attributes vs. scaled binary attributes

The paper studies if and to what extent it is possible to reduce notions related to attribute implications from data with fuzzy attributes to corresponding notions related to attribute implications from data with crisp attributes. We provide a reduction (transformation) theorem. Still, working directly in fuzzy setting is beneficial. Namely, we prove that we can compute a complete and non-redundant basis of fuzzy attribute implications of data with fuzzy attributes such that the basis is at most as large as (and can be smaller than) any basis of implications of the corresponding data table with crisp attributes