This paper generalizes (fuzzifies) actions of a monoid or group on a set to deal with situations where imprecision and uncertainty are present. Fuzzy actions can handle the granularity of a set or even create it by defining a fuzzy equivalence relation on it.
Boixader, D., Recasens, J. Fuzzy actions. "Fuzzy sets and systems", 1 Gener 2017, p. 1-14.