A new map (Λ_E) between fuzzy subsets of a universe X endowed with a T-indistinguishability operator E is introduced. The main feature of Λ_E is that it has the columns of E as fixed points, and thus it provides us with a new criterion to decide whether a generator is a column. Two well known maps (φ_E and ψ_E) are also reviewed, in order to compare them with Λ_E. Interesting properties of the fixed points of φ_E and [Formula: see text] are studied. Among others, the fixed points of Λ_E ( Fix (Λ_E)) are proved to be the maximal fuzzy points of (X, E) and the fixed points of [Formula: see text] coincide with the Image of Λ_E. An isometric embedding of X into Fix (Λ_E) is established and studied.