Fuzzy WASPAS: Fuzzy extension of WASPAS

Overview

Fuzzy outranking/ranking: Triangular Fuzzy Number (TFN: l, m, u). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Fuzzy outranking/ranking: Triangular Fuzzy Number (TFN: l, m, u)
• •Preserves fuzzy_TFN uncertainty through the pipeline rather than premature crispification at elicitation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Rank reversal known on alternative-set changes (ref: inherited from crisp base; cf. Belton-Gear 1983, Wang-Luo 2009)
• •Assumes: Decision matrix entries are valid Fuzzy (Triangular) numbers/tuples
• •Assumes: Underlying crisp method's compensation assumption holds in uncertain space
• •Assumes: All decision-maker(s) and experts use the same linguistic/uncertainty scale

Assumptions to verify

• •Decision matrix entries are valid Fuzzy (Triangular) 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

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

Common pitfalls

• •Hatalı: 'FUZZY-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Fuzzy (Triangular) numbers/tuples
• •Hatalı: 'FUZZY-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'FUZZY-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: FUZZY-WASPAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: FUZZY-WASPAS'yi 'Aggregation operator (PFWA/PFOWA/etc.) not specified' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Form fuzzy decision-making matrix (FDMM). Performance values x̃ij = (xijα, xijβ, xijγ) and fuzzy weights w̃j = (wjα, wjβ, wjγ) are TFNs. Formül: X̃ = [x̃ij]_{m×n}, x̃ij = (xijα, xijβ, xijγ); W̃ = [w̃j], w̃j = (wjα, wjβ, wjγ) Anchor: Turskis 2015, Eq.(15)
2. 2.Adım 2 (F2): Step 2: Normalize FDMM. Benefit: divide each TFN component by scalar max_i(xijγ). Cost: multiply by scalar min_i(xijα), divide TFN components. Formül: Benefit: x̄̃ij = (xijα/max_i(xijγ), xijβ/max_i(xijγ), xijγ/max_i(xijγ)) Cost: x̄̃ij = (min_i(xijα)/xijγ, min_i(xijα)/xijβ, min_i(xijα)/xijα) Anchor: Turskis 2015, Eq.(16)
3. 3.Adım 3 (F3): Step 3a: WSM weighted matrix: x̂̃ij = x̄̃ij ⊗ w̃j (component-wise TFN multiplication). Step 3b: WPM weighted matrix: x̄̄̃ij = x̄̃ij^w̃j (TFN power, Eq.13: (α^γ, β^β, γ^α) for values in [0,1]). Formül: WSM: x̂̃ij = (x̄̃ijα·w̃jα, x̄̃ijβ·w̃jβ, x̄̃ijγ·w̃jγ) [Eq.17] WPM: x̄̄̃ij = (x̄̃ijα^w̃jγ, x̄̃ijβ^w̃jβ, x̄̃ijγ^w̃jα) [Eq.18, Eq.13] Anchor: Turskis 2015, Eq.(17-18)
4. 4.Adım 4 (F4): Step 4: Compute Q̃i (WSM) and P̃i (WPM) as TFN sums/products, then defuzzify via centroid COA. Formül: Q̃i = Σj x̂̃ij = (Σj x̂̃ijα, Σj x̂̃ijβ, Σj x̂̃ijγ) [Eq.19] P̃i = Πj x̄̄̃ij = (Πj x̄̄̃ijα, Πj x̄̄̃ijβ, Πj x̄̄̃ijγ) [Eq.20] Qi = (Qiα+Qiβ+Qiγ)/3 [Eq.21] Pi = (Piα+Piβ+Piγ)/3 [Eq.22] Anchor: Turskis 2015, Eq.(19-22)
5. 5.Adım 5 (F5): Step 5: Compute adaptive λ from defuzzified scores, then integrated utility Ki = λ·Qi + (1−λ)·Pi. Formül: λ = Σi Pi / (Σi Qi + Σi Pi) [Eq.24] Ki = λ·Qi + (1−λ)·Pi, λ∈[0,1] [Eq.23] Anchor: Turskis 2015, Eq.(23-24)
6. 6.Adım 6 (F6): Step 6: Rank alternatives by Ki descending. Highest Ki = best alternative. Formül: rank = argsort(K, descending=True) Anchor: Turskis 2015, Section 2.3

Commonly paired with

• •FUZZY-AHP + FUZZY-WASPAS (common)

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