IR-CODAS - Interval Rough CODAS (Combinative Distance-based Assessment with Interval Rough Numbers for MCGDM)

Overview

IR-CODAS extends the crisp CODAS method (Keshavarz Ghorabaee 2016) to interval rough numbers (Pamucar 2018) for multi-criteria GROUP decision making. Linguistic DM evaluations are first translated to integer poles (paper Table 1), then converted to per-DM IR matrices via rough-sequence operations (Eqs.7-12), then aggregated by averaging (Eq.28). This kernel accepts the group IR matrix and performs Steps 5-12.

Output

crisp, higher is better

Data

Interval Rough, interval rough complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Risk assessment under linguistic uncertainty, Supplier selection with group DM evaluations, Sustainability ranking with rough preferences

Look elsewhere when

Assumptions to verify

• Decision matrix entries are valid IRNs (a ≤ b ≤ c ≤ d, non-negative)
• Weights pre-aggregated across DMs and sum to 1
• Threshold τ ∈ [0.01, 0.05] appropriate for problem scale

Edge cases and pitfalls

• IRN ordering constraint a ≤ b ≤ c ≤ d must hold on INPUT matrix; normalization (Eq.29) can break ordering in cost criteria because component-wise divisors are heterogeneous - kernel does not re-validate ordering post-normalization.

• Weights MUST be pre-aggregated across DMs (Eq.31 group weight); kernel does not perform DM-weight averaging.

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