The document contains mathematical formulas and definitions related to fuzzy sets and systems classification. It defines μPX(F) as the infimum of taking the maximum of 1 minus the membership of F at x and the membership of X at x, summed over all x. It also defines μPX(x) as the supremum of taking the minimum of the membership of F at x and μPX(F), summed over all F in U/P and x in U. Finally, it defines γP(Q) as the membership of POSP(Q) at x, which is the supremum of the memberships of PX at x, summed over all X in U/Q.