In a theoretical setting, the Representation Theorem is used to generate T-indistinguishability operators (fuzzy similarity relations) from a given set of fuzzy criteria. In applied domains, though, other ways of generation are often used which involve quasi-arithmetic means. In this paper we study when one single fuzzy subset, obtained by averaging multiple fuzzy criteria, is able to generate the same T-indistinguishability operator obtained by all of them, either exactly or approximately.

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