ERVD: Election based on Relative Value Distances

Overview

Prospect-theory value function with reference-point separation. Output typically ranking.

Strengths

• •Method-specific: Prospect-theory value function with reference-point separation

Edge cases

• •if r_ij > φ_j, else −λ(φ_j − r_ij)^α. For cost (type=min): v_ij = (φ_j − r_ij)^α if r_ij < φ_j, else −λ(r_ij − φ_j)^α.

Common pitfalls

• •Bkz. ERVD F.steps citation_anchor'lar ve P.verification_status.

Worked example

1. 1.Adım 1 (F1): Step 1: Sum normalization (direction-unaware): r_ij = x_ij / Σ_k x_kj. Reference point also normalized: φ_j = μ_j / Σ_k x_kj. Formül: r_{ij} = \frac{x_{ij}}{\sum_k x_{kj}};\quad \varphi_j = \frac{\mu_j}{\sum_k x_{kj}} Anchor: Shyur et al. 2015 §3
2. 2.Adım 2 (F2): Step 2: Prospect-theory value function v_ij relative to normalized reference φ_j. For benefit (type=max): v_ij = (r_ij − φ_j)^α if r_ij > φ_j, else −λ(φ_j − r_ij)^α. For cost (type=min): v_ij = (φ_j − r_ij)^α if r_ij < φ_j, else −λ(r_ij − φ_j)^α. Formül: v_{ij} = \begin{cases} (r_{ij}-\varphi_j)^{\alpha} & \text{benefit, } r_{ij}>\varphi_j \\ -\lambda(\varphi_j-r_{ij})^{\alpha} & \text{benefit, } r_{ij}\le\varphi_j \\ (\varphi_j-r_{ij})^{\alpha} & \text{cost, } r_{ij}<\varphi_j \\ -\lambda(r_{ij}-\varphi_j)^{\alpha} & \text{cost, } r_{ij}\ge\varphi_j \end{cases} Anchor: Shyur et al. 2015 §3
3. 3.Adım 3 (F3): Step 3: Positive ideal A+_j = max_i v_ij; negative ideal A-_j = min_i v_ij per criterion. Separation measures S+_i = Σ w_j |v_ij − A+_j|; S-_i = Σ w_j |v_ij − A-_j|. Formül: A^{+}_j = \max_i v_{ij};\quad A^{-}_j = \min_i v_{ij};\quad S^{+}_i = \sum_j w_j|v_{ij}-A^{+}_j|;\quad S^{-}_i = \sum_j w_j|v_{ij}-A^{-}_j| Anchor: Shyur et al. 2015 §3
4. 4.Adım 4 (F4): Step 4: Relative closeness φ_i = S-_i / (S+_i + S-_i). Rank descending (higher = better). Formül: \phi_i = \frac{S^{-}_i}{S^{+}_i + S^{-}_i},\quad \text{rank descending} Anchor: Shyur et al. 2015 §3

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