QUALIFLEX: QUALItative FLEXible multiple criteria method

Overview

Permutation concordance (all ranking permutations tested). Output typically preference_flow (higher value = preferred).

Strengths

• •Method-specific: Permutation concordance (all ranking permutations tested)

Limitations

• •Assumes: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Assumes: Non-compensatory preference structure

Assumptions to verify

• •Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Non-compensatory preference structure

When not to use

• •Small dataset (m<3) → outranking benefit minimal
• •Compensatory preferences acceptable → simpler ranking method

Edge cases

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

Common pitfalls

• •Hatalı: 'QUALIFLEX bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Hatalı: 'QUALIFLEX bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Non-compensatory preference structure
• •Hatalı: QUALIFLEX'yi 'Small dataset (m<3) → outranking benefit minimal' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: QUALIFLEX'yi 'Compensatory preferences acceptable → simpler ranking method' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Enumerate all m! permutations π of alternatives. For each permutation and each ordered pair (A_i, A_k) where π ranks A_i above A_k, compute concordance index c_jik = sign(x_ij − x_kj) adjusted for criterion direction. Formül: c_{jik}(\pi) = \begin{cases}+1 & \text{if }(x_{ij}>x_{kj}\text{ and benefit}) \text{ or } (x_{ij}<x_{kj}\text{ and cost}) \\ -1 & \text{otherwise}\end{cases} Anchor: Paelinck 1978, p.194 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Compute comprehensive concordance index I(π) = Σ_j Σ_{i≻k in π} w_j · c_jik(π). Select the permutation π* with maximum I(π) as the optimal ranking. Formül: I(\pi) = \sum_{j=1}^{n}\sum_{(i,k):\pi(i)<\pi(k)}w_{j}\,c_{jik}(\pi);\quad \pi^{*} = \arg\max_{\pi}\,I(\pi) Anchor: Paelinck 1978, p.194-195 Eq.(2)

Commonly paired with

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

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