Classification by means of fuzzy analogy-related proportions — A preliminary report

Boolean logic interpretations, as well as multiple-valued logic extensions, have been recently proposed for analogical proportions (i.e. statements of the form “a is to b as c is to d”), and for two other related formal proportions named reverse analogy (“what a is to b is the reverse of what c is to d”), and paralogy (“what a and b have in common c and d have it also”). These proportions relate items a, b, c, and d on the basis of their differences, or of their similarities. This may provide a basis for proposing a plausible classification for an object d described in terms of a set of features, on the basis of three other already classified objects described on the same features, considering that if some proportion holds for a sufficiently large number of features, it may hold on the allocation of the classes as well. This is the basis of a classification method which is tested on machine learning benchmarks for binary or multiple class problems with objects that have numerical features.