IV-TOPSIS: Interval extension of TOPSIS

Overview

Interval outranking/ranking: Interval Number (IN: [a, b]). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Interval outranking/ranking: Interval Number (IN: [a, b])
• •Preserves interval uncertainty through the pipeline rather than premature crispification at elicitation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Rank reversal known on alternative-set changes (ref: inherited from crisp base; cf. Belton-Gear 1983, Wang-Luo 2009)
• •Assumes: Decision matrix entries are valid Interval numbers/tuples
• •Assumes: Underlying crisp method's compensation assumption holds in uncertain space
• •Assumes: All decision-maker(s) and experts use the same linguistic/uncertainty scale

Assumptions to verify

• •Decision matrix entries are valid Interval numbers/tuples
• •Underlying crisp method's compensation assumption holds in uncertain space
• •All decision-maker(s) and experts use the same linguistic/uncertainty scale

When not to use

• •Crisp data sufficient: use base TOPSIS directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

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

Common pitfalls

• •Hatalı: 'IV-TOPSIS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Interval numbers/tuples
• •Hatalı: 'IV-TOPSIS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'IV-TOPSIS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: IV-TOPSIS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: IV-TOPSIS'yi 'Aggregation operator (PFWA/PFOWA/etc.) not specified' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Formül: \tilde{a}_{ij}^c=([\nu^L_{ij},\nu^U_{ij}],[\mu^L_{ij},\mu^U_{ij}])\quad\text{for cost criteria} Anchor: IV-TOPSIS-base
2. 2.Adım 2 (F2): Formül: \tilde{v}_{ij}=w_j\otimes\hat{a}_{ij}=\Bigl([1-(1-\mu^L_{ij})^{w_j},\;1-(1-\mu^U_{ij})^{w_j}],\;[\nu^L_{ij}{}^{w_j},\nu^U_{ij}{}^{w_j}]\Bigr) Anchor: IV-TOPSIS-base
3. 3.Adım 3 (F3): Formül: A^+_j=\bigl([\max_i\mu^L_{ij},\max_i\mu^U_{ij}],[\min_i\nu^L_{ij},\min_i\nu^U_{ij}]\bigr),\quad A^-_j=\bigl([\min_i\mu^L_{ij},\min_i\mu^U_{ij}],[\max_i\nu^L_{ij},\max_i\nu^U_{ij}]\bigr) Anchor: IV-TOPSIS-base
4. 4.Adım 4 (F4): Formül: d_i^{\pm}=\sqrt{\frac{1}{4}\sum_{j=1}^n\bigl[(\mu^L_{ij}-\mu^{L\pm}_j)^2+(\mu^U_{ij}-\mu^{U\pm}_j)^2+(\nu^L_{ij}-\nu^{L\pm}_j)^2+(\nu^U_{ij}-\nu^{U\pm}_j)^2\bigr]} Anchor: IV-TOPSIS-base
5. 5.Adım 5 (F5): Formül: CC_i=\frac{d_i^-}{d_i^++d_i^-},\quad\text{rank descending} Anchor: IV-TOPSIS-base

Commonly paired with

• •n_a + IV-TOPSIS (common)

How to cite