A T-indistinguishability operator (or fuzzy similarity relation) E is called unidimensional when it may be obtained from one single fuzzy subset (or fuzzy criterion). In this paper, we study when a T-indistinguishability operator that has been obtained as an average of many unidimensional ones is unidimensional too. In this case, the single fuzzy subset used to generate E is explicitly obtained as the quasi-arithmetic mean of all the fuzzy criteria primarily involved in the construction of E.
Boixader, D., Recasens, J. Characterization of unidimensional averaged similarities. "Journal of applied logic", 1 Setembre 2017, vol. 23, p. 16-26.