Rough-COPRAS - Rough extension of COPRAS

Overview

ROUGH-COPRAS extends COPRAS to Interval Rough Number (IRN) uncertainty. Steps: (1) column-sum IRN normalization, (2) scalar weighting (w_j ⊗ IRN), (3) separate benefit S+^IRN and cost S-^IRN sums in rough domain, (4) defuzzify S+ and S- via midpoint then compute crisp COPRAS Q_i, (5) normalize to N_i(%). Note: the seminal paper (Pamučar 2018) uses full 4-tuple IRNWGBM arithmetic throughout - our implementation uses simplified 2-tuple [L,U] outer-bound IRN with scalar weights, producing different rankings.

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.

• Defuzzification method affects ranking: midpoint (L+U)/2 is the canonical choice but alternatives exist.

Works with

How to cite