Steinhaus Transforms of Fuzzy String Distances in Computational Linguistics

In this paper we deal with distances for fuzzy strings in \([0,1]^n\), to be used in distance-based linguistic classification. We start from the fuzzy Hamming distance, anticipated by the linguist Muljacic back in 1967, and the taxicab distance, which both generalize the usual crisp Hamming distance, using in the first case the standard logical operations of minimum for conjunctions and maximum for disjunctions, while in the second case one uses Łukasiewicz’ T-norms and T-conorms. We resort to the Steinhaus transform, a powerful tool which allows one to deal with linguistic data which are not only fuzzy, but possibly also irrelevant or logically inconsistent. Experimental results on actual data are shown and preliminarily commented upon.