ZF-CRADIS - Z-Number Fuzzy Compromise Ranking from Distance to Ideal Solution

Overview

Output is a compromise score Q_i per alternative - higher means the alternative is simultaneously closer to the ideal solution and farther from the anti-ideal. The top-ranked alternative is the best green supplier under the expert consensus. Pair this method with ZF-LMAW or any other Z-aware weighting source; the input decision matrix supports per-cell Z-number reliability. When experts are uncertain (low B-rating), the implicit √α down-scaling correctly reduces that cell's influence on the final ranking.

Data

Z-Number

Weights

Needs a weight source

Edge cases and pitfalls

• Forgetting that ideal/anti-ideal in CRADIS are scalars taken across the entire weighted matrix, not per-criterion (unlike TOPSIS which uses per-criterion ideals).

• Confusing the GMIR defuzzification weights (1, 4, 1)/6 with simple centroid (1, 1, 1)/3 - Puška Eq.(17) is strictly GMIR.

• s0+ is the SMALLEST s+ (best deviation from ideal); s0- is the LARGEST s- (best deviation from anti-ideal). Inverting these flips the ranking.

• Equation 20 in Puška reads Q_i = (K_i^+ + K_i^+)/2 due to a typesetting typo; the correct (and verified-by-Table-9-numbers) formula is Q_i = (K_i^+ + K_i^-)/2.

• If B (reliability) is identical in every cell, the sqrt(alpha) constant applied in F3 cancels exactly in F5's min-max ratio normalisation (ñ_ij = l/x_d^u etc.); the result is unchanged. This is a mathematical property, not a defect. B changes the result only when reliability differs between alternatives.

How to cite