NAIADE - Novel Approach to Imprecise Assessment and Decision Environments

Overview

φ_i ∈ [−1, 1]. Higher φ means greater net pairwise inequality advantage. NAIADE is weight-free by design. The α parameter controls what counts as 'similar' vs 'different' performance. α=0 → crisp sign comparison (like REGIME); α=1 → all differences ignored (all φ=0). NAIADE also supports equity analysis across stakeholder groups.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Alternative selection, Supplier evaluation

How it works

1. 1

   Min-max normalise criterion values to [0,1] (direction aware).

   $$n_{ij}=\frac{x_{ij}-x_j^{\min }}{x_j^{\max }-x_j^{\min }}\text{ (benefit)};n_{ij}=\frac{x_j^{\max }-x_{ij}}{x_j^{\max }-x_j^{\min }}\text{ (cost)}$$

   Munda 1995, Ch.4

2. 2

   Compute fuzzy pairwise comparison for each pair (A_i, A_k): degree of 'much better', 'similar', 'much worse' using semantic distance |n_ij − n_kj| relative to α.

   $${\mu }_{\text{better}}(A_i,A_k,C_j)=\{\begin{array}{ll}1& n_{ij}-n_{kj}\ge \alpha \\ \frac{n_{ij}-n_{kj}}{\alpha }& 0<n_{ij}-n_{kj}<\alpha \\ 0& \text{otherwise}\end{array}$$

   Munda 1995, Ch.4 Eq.(4.3)

3. 3

   Aggregate across criteria to produce equity and inequality indices μ_eq(A_i, A_k) and μ_ineq(A_i, A_k). Compute net flow φ_i = Σ_k [μ_ineq(A_i,A_k) − μ_ineq(A_k,A_i)] / (m−1). Rank descending.

   $${\phi }_i=\frac{1}{m-1}\sum _{k\ne i}[{\mu }_{\text{ineq}}(A_i,A_k)-{\mu }_{\text{ineq}}(A_k,A_i)]$$

   Munda 1995, Ch.4 Eq.(4.7)

Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Edge cases and pitfalls

• α sensitivity: results can vary significantly with α - always test multiple values.

Works with

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