AHPSort: AHP-based classification of alternatives into ordered categories

Overview

AHP-based sorting with limiting or central profiles. Output typically class_label (higher value = preferred).

Strengths

• •Method-specific: AHP-based sorting with limiting or central profiles

Limitations

• •Rank reversal known on alternative-set changes (ref: Belton-Gear-1983; Wang-Luo-Hua-2008 (AHP-inherited))
• •Assumes: Pre-defined ordered classes/categories exist
• •Assumes: Reference profiles or examples are available

Assumptions to verify

• •Pre-defined ordered classes/categories exist
• •Reference profiles or examples are available

When not to use

• •No predefined classes → use a ranking method first

Edge cases

• •ties p_kj and p_ij via Eq.(1).
• •ties: P_k = Σ_j p_kj · w_j (alternatives) and P_i (lp or cp) = Σ_j p_ij · w_j (profiles).
• •If profile_type='limiting': a_k ∈ C_i ⟺ P_i ≤ P_k < P_{i-1}. If profile_type='central': a_k assigned to class with minimum |P_k − P_i^{cp}|.

Common pitfalls

• •Hatalı: 'AHPSORT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Pre-defined ordered classes/categories exist
• •Hatalı: 'AHPSORT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Reference profiles or examples are available
• •Hatalı: AHPSORT'yi 'No predefined classes → use a ranking method first' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Phase 1.1-1.2: Define criteria c_j, alternatives a_k, goal, and ordered classes C_i with linguistic descriptors. Anchor: Ishizaka 2012; recap in Ishizaka 2020 §3.1 Phase 1 steps 1-2
2. 2.Adım 2 (F2): Phase 1.3: Define limiting profiles lp_ij OR central profiles cp_ij per class i × criterion j. Anchor: Ishizaka 2020 §3.1 Phase 1 step 3
3. 3.Adım 3 (F3): Phase 2.4: Compute criterion weights w_j via AHP eigenvalue method on the criteria pairwise matrix A: A·p = λ_max·p. Check CR ≤ cr_threshold. Formül: A \cdot p = \lambda_{\max} \cdot p,\quad CI = (\lambda_{\max} - n) / (n-1),\quad CR = CI / RI Anchor: Ishizaka 2020 §3.1 Phase 2 step 4, Eq.(1)-(3)
4. 4.Adım 4 (F4): Phase 2.5-2.6: For each criterion j, pairwise compare each alternative a_k against the profiles (lp_ij or cp_ij), build matrix, compute local priorities p_kj and p_ij via Eq.(1). Formül: p_{kj}, p_{ij} \text{ from AHP eigenvalue of profile-vs-alternative matrix per criterion} Anchor: Ishizaka 2020 §3.1 Phase 2 steps 5-6, Eq.(1)
5. 5.Adım 5 (F5): Phase 3.7: Aggregate global priorities: P_k = Σ_j p_kj · w_j (alternatives) and P_i (lp or cp) = Σ_j p_ij · w_j (profiles). Formül: P_k = \sum_{j=1}^{m} p_{kj} \cdot w_j,\quad P_i^{(lp \,|\, cp)} = \sum_{j=1}^{m} p_{ij} \cdot w_j Anchor: Ishizaka 2020 §3.1 Phase 3 step 7, Eq.(4)-(5)
6. 6.Adım 6 (F6): Phase 3.8: Assignment. If profile_type='limiting': a_k ∈ C_i ⟺ P_i ≤ P_k < P_{i-1}. If profile_type='central': a_k assigned to class with minimum |P_k − P_i^{cp}|. Formül: limiting:\, a_k \in C_i \iff P_i \le P_k < P_{i-1};\;\; central:\, a_k \in C_{\arg\min_i |P_k - P_i^{cp}|} Anchor: Ishizaka 2020 §3.1 Phase 3 step 8

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