Ranking
SF-WASPAS: Spherical extension of WASPAS
Boltürk, E., Kutlu Gündoğdu, F. · 2021
Overview
SF-WASPAS (Spherical Fuzzy Weighted Aggregated Sum Product ASsessment), Zavadskas-Turskis 2012'nin "WSM + WPM hibridi" mantığını SF'ye taşır. Felsefe: ne SAW (her şey toplama, μ→0 cell'i affeder) ne WPM (her şey çarpma, μ→0 cell'i ezer) tek başına ideal: λ ile karıştır. Akış: SWAM (Eq.11) veya SWGM (Eq.12) ile DM judgments'i agrege; modified Score (Eq.14) ile ağırlıkları defuzz + normalize (Eq.15); WSM partı Q̃_i^(1)=Σ_j x̃_ij·w̄^s_j (Eqs.16-18, SF scalar mult + add); WPM partı Q̃_i^(2)=Π_j x̃_ij^(w̄^s_j) (Eqs.19-21, SF λ-power + mult); λ-hybrid Eqs.22-23 her parta uygula; final Q̃_i = λ·Q̃^(1) + (1−λ)·Q̃^(2) (Eq.24). Score Eq.9 ile defuzzify → ranking. λ=0 ⇒ pure WPM; λ=1 ⇒ pure WSM; λ=0.5 book default. Robustness: λ∈{0, 0.5, 1} sensitivity check standart.
Strengths
- •λ-tunable mix of WSM/WPM captures both decision-aggregation philosophies.
- •Eq.24 SF-aggregation preserves hesitancy through both branches.
- •Default λ=0.5 (equal mix) is decisional-neutral and matches Zavadskas-Turskis 2012 crisp WASPAS.
Limitations
- •λ-choice is a meta-decision that can dominate ranking if S/R measures differ widely.
- •Two aggregation passes (WSM+WPM) double the computational/notation burden.
- •No formal rule for choosing λ: book Recommends 0.5 but offers no optimization.
Method assistant
Grounded explanations: it explains the method, it does not compute.
Assumptions to verify
- •Decision matrix entries are valid Spherical Fuzzy 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 WASPAS directly (avoid unnecessary uncertainty layer)
- •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous
Edge cases
- •λ=1 pure WSM (SF-SAW eşdeğeri); λ=0 pure WPM (SF-WPM eşdeğeri); λ=0.5 book default consensus. Bir alt çok düşük μ'lu cell'e sahipse: WPM partı (Q̃^(2)) sert cezalandırır, WSM partı (Q̃^(1)) yumuşatır: λ=0.5'te ikisi karışır. SWAM vs SWGM seçimi: SWAM additive-mean (DM görüşleri toplamsal), SWGM geometric-mean (DM görüşleri multiplicative). Book Section 4 SWGM kullanır ağırlık için (Tablo 6). λ-power Eq.20 (w̄^s_j üs): w̄^s_j fraksiyonel olduğunda Eq.6 dikkatli: π=0 edge case test. Modified Score Eq.14 negatif (yüksek v + yüksek π) durumunda Eq.15 normalize problem.
Common pitfalls
- •(1) λ tek başına ranking'i değiştirir: sensitivity ANALİZİ ZORUNLU. (2) SWAM (Eq.11) vs SWGM (Eq.12) seçimi: book hem agg hem defuzz adımında kullanır, karıştırma; SWAM additive-DM-agg + SWGM multiplicative-DM-agg = farklı sonuçlar. (3) WSM partı Eqs.17-18: ⊕ SF addition non-trivial (μ_R²=μ_A²+μ_B²−μ_A²·μ_B²): skalar toplam YAPMA. (4) WPM partı Eq.20: SF λ-power Eq.6: π=0 ve μ→0 edge case kontrol et. (5) Eq.24 final: λ·Q̃^(1) + (1−λ)·Q̃^(2): burada λ ve (1−λ) SCALAR çarpan (SF değil), Q̃'lar SF triple. (6) Eq.9 score (μ−π)²−(v−π)² formu klasik, Eq.14 modified (2μ−π/2)²−(v−π/2)² ağırlık-defuzz için: karıştırma. (7) λ optimize edilmez book'ta; 0.5 default ama açıkça sensitivity raporla.
Commonly paired with
- •n_a + SF-WASPAS (common)
How to cite
Boltürk, E.; Kutlu Gündoğdu, F. (2021). Prioritizing Manufacturing Challenges of a Contract Manufacturing Company for Personal Auto by Using Spherical WASPAS Method. In: Kahraman C., Kutlu Gündoğdu F. (eds.) Decision Making with Spherical Fuzzy Sets: Theory and Applications. Studies in Fuzziness and Soft Computing vol. 392. Springer. https://doi.org/10.1007/978-3-030-45461-6_11