Strict Fuzzy Orderings in a Similarity-Based Setting

This paper introduces and justifies a similaritybased concept of strict fuzzy orderings and provides constructions how fuzzy orderings can be transformed into strict fuzzy orderings and vice versa. We demonstrate that there is a meaningful correspondence between fuzzy orderings and strict fuzzy orderings. Unlike the classical case, however, we do not obtain a general one-to-one correspondence. We observe that the strongest results are achieved if the underlying t-norm induces a strong negation, which, in particular, includes nilpotent t-norms and the nilpotent minimum.