Fuzzy Hamming distinguishability

Back in 1967 the Croat linguist Ž. Muljacic had used a fuzzy generalization of the Hamming distance between binary strings to classify Romance languages. In 1956 Cl. Shannon had introduced the notion of codeword distinguishability in zero-error information theory. Distance and distinguishability are subtly different notions, even if, with distances as those usually met in coding theory (ruling out zero-error information theory, which is definitely non-metric), the need for string distinguishabilities evaporates, since the distinguishability turns out to be an obvious and trivial function of the distance. Fuzzy Hamming distinguishabilities derived from Muljacic distances, instead, are quite relevant and must be considered explicitly. They are very easy to compute, however, and we show how they could be applied in coding theory to channels with erasures and blurs. Fuzzy Hamming distinguishabilities appear to be quite a promising tool to extend Muljacic approach from linguistic classification to linguistic evolution.