Rough-TOPSIS — Rough extension of TOPSIS

ROUGH-TOPSIS (Song, Ming & Wu 2013) is NOT standard TOPSIS adapted to rough numbers. It uses a deviation-coefficient approach: (1) PIS/NIS are crisp scalars from raw matrix bound extremes (no normalization); (2) rough deviation coefficients d+/d− are linear distances (not Euclidean); (3) deviations are normalized per criterion by column max upper bound; (4) separation measures S+/S− are rough intervals from weighted normalized deviations; (5) final CC uses α-defuzzification: S+*=(1-α)S+L+αS+U, S−*=αS−L+(1-α)S−U; CC=S−*/(S−*+S+*); rank descending. α=0.5 = moderate risk propensity.