NAIADE: Novel Approach to Imprecise Assessment and Decision Environments

Overview

Fuzzy pairwise equity/inequality comparison (semantic distance). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Fuzzy pairwise equity/inequality comparison (semantic distance)

Limitations

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

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)

When not to use

• •Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• •Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Edge cases

• •See F.steps and D.parameters for NAIADE-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'NAIADE bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'NAIADE bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'NAIADE bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: NAIADE'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: NAIADE'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Min-max normalise criterion values to [0,1] (direction aware). Formül: n_{ij} = \frac{x_{ij}-x_{j}^{\min}}{x_{j}^{\max}-x_{j}^{\min}} \text{ (benefit)};\quad n_{ij} = \frac{x_{j}^{\max}-x_{ij}}{x_{j}^{\max}-x_{j}^{\min}} \text{ (cost)} Anchor: Munda 1995, Ch.4
2. 2.Adım 2 (F2): Step 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. Formül: \mu_{\text{better}}(A_{i},A_{k},C_{j}) = \begin{cases}1 & n_{ij}-n_{kj} \geq \alpha \\ \frac{n_{ij}-n_{kj}}{\alpha} & 0 < n_{ij}-n_{kj} < \alpha \\ 0 & \text{otherwise}\end{cases} Anchor: Munda 1995, Ch.4 Eq.(4.3)
3. 3.Adım 3 (F3): Step 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. Formül: \varphi_{i} = \frac{1}{m-1}\sum_{k \neq i}\bigl[\mu_{\text{ineq}}(A_{i},A_{k}) - \mu_{\text{ineq}}(A_{k},A_{i})\bigr] Anchor: Munda 1995, Ch.4 Eq.(4.7)

Commonly paired with

• •AHP + NAIADE (high)
• •BWM + NAIADE (high)
• •ENTROPY + NAIADE (high)
• •CRITIC + NAIADE (high)
• •SWARA + NAIADE (high)

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