Balanced SPOTIS: Balanced Stable Preference Ordering Towards Ideal Solution

Overview

Distance-to-ideal with blended ISP/ESP reference. Output typically ranking.

Strengths

• •Blends Ideal Solution Point (ISP, objective) and Expected Solution Point (ESP, subjective) via tunable trust parameter α ∈ [0,1] (Shekhovtsov et al. 2025 §3.3).
• •Special cases recover known methods: α=0 → standard ISP-SPOTIS (Dezert 2020 rank-reversal-free); α=1 → ESP-SPOTIS (Shekhovtsov 2022). (§4.1 line 365-368)
• •Inherits SPOTIS rank-reversal-free property by design (user-defined bounds; §3.1 + Dezert 2020 §III).
• •Enables α-sensitivity analysis (§4.2) to investigate how decision-maker trust in ESP affects ranking: provides deeper insight than single-α methods.
• •More flexible than ESP-COMET (§4.3): supports criteria weights (ESP-COMET treats all criteria equally) and avoids the curse of dimensionality (ESP-COMET needs pairwise comparison matrices).

Limitations

• •α=0.5 indifference Theorem (§4.1 Eqs.7-8): alternatives strictly between ISP and ESP receive identical P_i at α=0.5, leading to forced ties. Mitigation: vary α (paper recommends sweep with Δα=0.1).
• •ESP must lie within user-defined bounds (S+_j ∈ [Smin_j, Smax_j]); out-of-bounds ESP breaks the normalization assumption (§3.1 line 147-150).
• •Inherits SPOTIS requirement that decision-maker provide bounds Smin_j, Smax_j (not derivable from data alone without losing rank-reversal-free guarantee).
• •Method validated for crisp data only; paper §5 notes 'imprecise data' extension as future work.

Edge cases

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

Common pitfalls

• •Bkz. BALANCED-SPOTIS F.steps citation_anchor'lar ve P.verification_status.

Worked example

1. 1.Adım 1 (F1): Step 1: Determine ISP (Ideal Solution Point) from bounds based on criterion direction; load user-provided ESP. Formül: S^{*}_{j} = \begin{cases} \max\text{-bound}_j & j \in J^{+} \\ \min\text{-bound}_j & j \in J^{-} \end{cases} Anchor: Shekhovtsov et al. 2025 §2
2. 2.Adım 2 (F2): Step 2: Normalised distance from ESP and ISP: d_ij = |x_ij − ref_j| / |bounds_min_j − bounds_max_j|. Formül: d_{ij}(S^{+}) = \frac{|x_{ij} - S^{+}_j|}{|b^{\min}_j - b^{\max}_j|};\quad d_{ij}(S^{*}) = \frac{|x_{ij} - S^{*}_j|}{|b^{\min}_j - b^{\max}_j|} Anchor: Shekhovtsov et al. 2025 §2
3. 3.Adım 3 (F3): Step 3: Weighted aggregated distances D_i(ESP) and D_i(ISP). Formül: D_{i}(S^{+}) = \sum_{j} w_j\, d_{ij}(S^{+});\quad D_{i}(S^{*}) = \sum_{j} w_j\, d_{ij}(S^{*}) Anchor: Shekhovtsov et al. 2025 §2
4. 4.Adım 4 (F4): Step 4: Balanced score P_i = (1−α)·D_i(ISP) + α·D_i(ESP). Rank ascending (lower P = better). Formül: P_i = (1-\alpha)\,D_i(S^{*}) + \alpha\,D_i(S^{+}),\quad \text{rank ascending} Anchor: Shekhovtsov et al. 2025 §2 Eq.(main)

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