CRADIS: Compromise Ranking of Alternatives from Distance to Ideal Solution

Overview

Distance from ideal and anti-ideal (geometric mean compromise). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Distance from ideal and anti-ideal (geometric mean compromise)

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 CRADIS-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'CRADIS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'CRADIS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'CRADIS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: CRADIS'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: CRADIS'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: Linear max normalisation per criterion direction. Formül: n_{ij} = \begin{cases} x_{ij}/\max_{i} x_{ij} & j\in J^{+} \\ \min_{i} x_{ij}/x_{ij} & j\in J^{-} \end{cases} Anchor: Puška 2022, p.4 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Weighted normalised matrix v_ij = w_j n_ij. Formül: v_{ij} = w_{j}\,n_{ij} Anchor: Puška 2022, p.4 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Deviations from ideal v_j^I = max v_ij and anti-ideal v_j^A = min v_ij. Formül: d^{+}_{i} = \sum_{j=1}^{n}(v^{I}_{j} - v_{ij}),\quad d^{-}_{i} = \sum_{j=1}^{n}(v_{ij} - v^{A}_{j}) Anchor: Puška 2022, p.4 Eqs.(3)-(4)
4. 4.Adım 4 (F4): Step 4: Utility ratios: s^+_i = min_k(d^+_k) / d^+_i (closeness to ideal, best alternative gets 1) and s^-_i = d^-_i / max_k(d^-_k) (closeness to anti-ideal, best alternative gets 1). Formül: s^{+}_{i} = \dfrac{\min_{k} d^{+}_{k}}{d^{+}_{i}},\quad s^{-}_{i} = \dfrac{d^{-}_{i}}{\max_{k} d^{-}_{k}} Anchor: Puška et al. 2022 (DOI 10.1007/s10668-021-01902-2), Eqs.(5)-(6): K_o = T_o^{opt}/T_o^i (= min/d^+), K_a = T_a^i/T_a^{opt} (= d^-/max)
5. 5.Adım 5 (F5): Step 5: CRADIS final score Q_i = (s^+_i + s^−_i)/2 and descending ranking. Formül: Q_{i} = \dfrac{s^{+}_{i} + s^{-}_{i}}{2} Anchor: Puška 2022, p.5 Eq.(7)

Commonly paired with

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

How to cite