Rough-TOPSIS - Rough extension of TOPSIS

Overview

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.

Output

utility, higher is better

Data

Rough Number, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Rough MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

Look elsewhere when

Assumptions to verify

• Decision matrix entries are valid Rough numbers/tuples
• Underlying crisp method's compensation assumption holds in uncertain space
• All decision-maker(s) and experts use the same linguistic/uncertainty scale

Edge cases and pitfalls

• Value-space violation: ensure all entries satisfy Rough: L ≤ U; approximations defined by equivalence classes before computation.

• α parameter affects ranking: S⁺*=(1−α)S⁺L+αS⁺U and S⁻*=αS⁻L+(1−α)S⁻U - note asymmetry (α applies to upper for S⁺ but lower for S⁻). Default α=0.5 (moderate risk propensity); α>0.5 = optimistic, α<0.5 = pessimistic.

Works with

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