A map characterizing the fuzzy points and columns of a T-indistinguishability operator
A new map (Lambda(E)) between fuzzy subsets of a universe X endowed with a T-indistinguishability operator E is introduced. The main feature of Lambda(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 (phi(E) and psi(E)) are also reviewed, in order to compare them with Lambda(E). Interesting properties of the fixed points of Lambda(E) and Lambda(E) are studied. Among others, the fixed points of Lambda(E) (Fix(Lambda(E))) are proved to be the E maximal fuzzy points of (X, E) and the fixed points of Lambda(2)(E) coincide with the Image of E Lambda(E). An isometric embedding of X into Fix(Lambda(E)) is established and studied.
fuzzy point t-indistinguishability operator generator fuzzy relation column of a fuzzy relation t-norm