BF-WASPAS: Bipolar extension of WASPAS

Overview

Bipolar outranking/ranking: Bipolar Fuzzy Set (BFS: positive membership μ⁺ ∈ [0,1], negative μ⁻ ∈ [-1,0]). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Bipolar outranking/ranking: Bipolar Fuzzy Set (BFS: positive membership μ⁺ ∈ [0,1], negative μ⁻ ∈ [-1,0])
• •Preserves bipolar_fuzzy 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 Bipolar Fuzzy 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 Bipolar 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

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

Common pitfalls

• •Hatalı: 'BF-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Bipolar Fuzzy numbers/tuples
• •Hatalı: 'BF-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'BF-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: BF-WASPAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: BF-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: Construct the bipolar fuzzy decision matrix. Each cell B_{ij} = (μ⁺_{ij}, ν⁻_{ij}) is a BFN with μ⁺ ∈ [0,1] and ν⁻ ∈ [-1,0]. Formül: X = [B_{ij}]_{m \times n} = [(\mu^+_{ij}, \nu^-_{ij})]_{m \times n} Anchor: Wei et al. 2018b: BFN definition; Zavadskas et al. 2012: WASPAS structure
2. 2.Adım 2 (F2): Step 2: Normalize for criterion type. Benefit criteria unchanged; cost criteria complemented: (1 − μ⁺, |ν⁻| − 1). Formül: B^*_{ij} = \begin{cases} (\mu^+_{ij},\, \nu^-_{ij}) & j \in J^+ \text{ (benefit)} \\ (1-\mu^+_{ij},\; |\nu^-_{ij}|-1) & j \in J^- \text{ (cost)} \end{cases} Anchor: Jana & Pal 2021, p.5 Eq.(7): BF cost normalization
3. 3.Adım 3 (F3): Step 3: Weighted Sum Model (WSM) component using BFWA operator. BFWA yields a BFN for each alternative across all criteria. Formül: Q^{(1)}_i = \text{BFWA}_{\boldsymbol{w}}(B^*_{i1},\ldots,B^*_{in}) = \Bigl(1 - \prod_{j=1}^n (1-\mu^+_{ij})^{w_j},\;-\prod_{j=1}^n |\nu^-_{ij}|^{w_j}\Bigr) Anchor: Wei et al. 2018b, Eq.(4) BFWA; analogue of Zavadskas 2012 Eq.(2)
4. 4.Adım 4 (F4): Step 4: Weighted Product Model (WPM) component using BFWG operator. BFWG uses BFN geometric aggregation. Formül: Q^{(2)}_i = \text{BFWG}_{\boldsymbol{w}}(B^*_{i1},\ldots,B^*_{in}) = \Bigl(\prod_{j=1}^n (\mu^+_{ij})^{w_j},\;-1 + \prod_{j=1}^n (1+\nu^-_{ij})^{w_j}\Bigr) Anchor: Wei et al. 2018b, Eq.(5) BFWG; analogue of Zavadskas 2012 Eq.(3)
5. 5.Adım 5 (F5): Step 5: Combine WSM and WPM components via BFN arithmetic. Scale each by λ and (1−λ), then add using BFN ⊕. Convert final BFN to crisp score Δ(Q_i)=(1+μ⁺+ν⁻)/2. Rank descending. Formül: \lambda B = \bigl(1-(1-\mu^+)^\lambda,\;-|\nu^-|^\lambda\bigr) \\[4pt] B_1 \oplus B_2 = \bigl(\mu^+_1 + \mu^+_2 - \mu^+_1\mu^+_2,\;-|\nu^-_1||\nu^-_2|\bigr) \\[4pt] Q_i = \lambda Q^{(1)}_i \oplus (1-\lambda) Q^{(2)}_i \\[4pt] \Delta(Q_i) = \dfrac{1 + \mu^+_{Q_i} + \nu^-_{Q_i}}{2} \\[4pt] B_\alpha \succ B_\beta \iff \Delta(Q_\alpha) > \Delta(Q_\beta) Anchor: Wei et al. 2018b: BFN scalar mult Eq.(9), BFN addition Eq.(7), score Eq.(2); Zavadskas 2012: WASPAS Eq.(5) structure

Commonly paired with

• •n_a + BF-WASPAS (common)

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