qR-PROMETHEE - q-Rung Orthopair extension of PROMETHEE

Overview

QR-PROMETHEE runs PROMETHEE II on q-rung orthopair ratings. Each (mu, nu) cell is turned into a crisp score s = (1 + mu^q - nu^q)/2, the usual criterion preference function compares alternatives pairwise on those scores, and the weighted preference index feeds the outgoing, incoming and net outranking flows. Rank by net flow, larger is better.

Output

preference flow, higher is better

Data

Q-Rung Orthopair Fuzzy, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Q-Rung Orthopair Fuzzy MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

Look elsewhere when

Assumptions to verify

• Thresholds (q, p, v) can be expressed in q-Rung Orthopair Fuzzy scale
• Veto + concordance semantics adapted to fuzzy arithmetic

Edge cases and pitfalls

• Every cell must satisfy mu^q + nu^q <= 1 for the rung q you declare; a matrix that is valid at q=3 can be invalid at q=1.

• The usual criterion is a step function: any positive deviation, however small, counts as full preference. Rounded input can flip a cell from 0 to 1.

Works with

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