Linguistic classification: T-norms, fuzzy distances and fuzzy distinguishabilities

摘要

Back in 1967 the linguist ?. Mulja?i? used an additive distance between ill-defined linguistic features which is a forerunner of the fuzzy Hamming distance between strings of truth values in standard fuzzy logic. Here we show that if the logical frame is changed one obtains additive distances which are either sorely inadequate, as in the ?ukasiewicz or probabilistic case, or coincide with the distance originally envisaged by Mulja?i?, as happens with a whole class of T-norms (abstract logical conjunctions) which includes the nilpotent minimum. All this strengthens the role of Mulja?i? distances in linguistic clustering and of Mulja?i? distinguishabilities (a notion subtly different from distances, but quite inalienable) in linguistic evolution. As a preliminary example we re-take and re-examine Mulja?i? original data.