Construction of implicational quantifiers from fuzzy implications

Relations between two Boolean attributes derived from data can be quantified by [0,1]-valued functions defined on four-fold tables corresponding to pairs of the attributes. The most important of such quantifiers are implicational ones widely used in data-mining procedures. On the other hand, there are operators of fuzzy implication introduced and studied in fuzzy logic. In the paper, two methods of construction of implicational quantifiers from fuzzy implications are described and formally justified.