Ranking

RIM: Reference Ideal Method

Cables, E., Lamata, M. T., Verdegay, J. L. · 2016

Overview

Distance to user-defined reference intervals (ideal + anti-ideal). Output typically utility (higher value = preferred).

Strengths

•Method-specific: Distance to user-defined reference intervals (ideal + anti-ideal)

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)

Method assistant

Grounded explanations: it explains the method, it does not compute.

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

Common pitfalls

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

Worked example

1.Adım 1 (F1): Step 1: Compute distance d_ij^+ (distance to reference ideal interval RI_j) and d_ij^- (distance to anti-ideal, computed as furthest point in feasible range from RI_j). Formül: d_{ij}^{+} = \max\bigl(0,\,x_{ij}-RI_{j}^{high}\bigr) + \max\bigl(0,\,RI_{j}^{low}-x_{ij}\bigr);\quad d_{ij}^{-} = \max\bigl(|x_{ij}-RI_{j}^{low}|,\,|x_{ij}-RI_{j}^{high}|\bigr) Anchor: Cables et al. 2016, p.4 Eqs.(3)-(4)
2.Adım 2 (F2): Step 2: Compute weighted aggregate distances D_i^+ (to ideal) and D_i^- (to anti-ideal). Formül: D_{i}^{+} = \sqrt{\sum_{j=1}^{n}w_{j}\,(d_{ij}^{+})^{2}},\qquad D_{i}^{-} = \sqrt{\sum_{j=1}^{n}w_{j}\,(d_{ij}^{-})^{2}} Anchor: Cables et al. 2016, p.5 Eqs.(5)-(6)
3.Adım 3 (F3): Step 3: Compute closeness coefficient CC_i = D_i^- / (D_i^+ + D_i^-). Rank descending. Formül: CC_{i} = \frac{D_{i}^{-}}{D_{i}^{+} + D_{i}^{-}} Anchor: Cables et al. 2016, p.5 Eq.(7)

Commonly paired with

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

How to cite

Cables, E.; Lamata, M. T.; Verdegay, J. L. (2016). RIM-reference ideal method in multicriteria decision making. Information Sciences. https://doi.org/10.1016/j.ins.2015.12.011

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Common pitfalls

•Hatalı: 'RIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)

•Hatalı: 'RIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another

•Hatalı: 'RIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)

•Hatalı: RIM'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

•Hatalı: RIM'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1.Adım 1 (F1): Step 1: Compute distance d_ij^+ (distance to reference ideal interval RI_j) and d_ij^- (distance to anti-ideal, computed as furthest point in feasible range from RI_j). Formül: d_{ij}^{+} = \max\bigl(0,\,x_{ij}-RI_{j}^{high}\bigr) + \max\bigl(0,\,RI_{j}^{low}-x_{ij}\bigr);\quad d_{ij}^{-} = \max\bigl(|x_{ij}-RI_{j}^{low}|,\,|x_{ij}-RI_{j}^{high}|\bigr) Anchor: Cables et al. 2016, p.4 Eqs.(3)-(4)

2.Adım 2 (F2): Step 2: Compute weighted aggregate distances D_i^+ (to ideal) and D_i^- (to anti-ideal). Formül: D_{i}^{+} = \sqrt{\sum_{j=1}^{n}w_{j}\,(d_{ij}^{+})^{2}},\qquad D_{i}^{-} = \sqrt{\sum_{j=1}^{n}w_{j}\,(d_{ij}^{-})^{2}} Anchor: Cables et al. 2016, p.5 Eqs.(5)-(6)

3.Adım 3 (F3): Step 3: Compute closeness coefficient CC_i = D_i^- / (D_i^+ + D_i^-). Rank descending. Formül: CC_{i} = \frac{D_{i}^{-}}{D_{i}^{+} + D_{i}^{-}} Anchor: Cables et al. 2016, p.5 Eq.(7)