CFZN-WASPAS - Complex Fuzzy Z-Number Weighted Aggregated Sum Product Assessment

Overview

CFZN-WASPAS ranks alternatives based on performance scores. Higher score = better rank.

Data

Complex Fuzzy Z-Number

Weights

Needs a weight source

Edge cases and pitfalls

• Shahid 2026 paper text OMITS explicit criterion weight values W_ℛ - engine MUST require user-supplied weights and surface a paper-incompleteness warning.

• Paper §4 Step 6 sets ϒ=1, reducing WASPAS to pure WSM. Standard WASPAS convention uses ϒ=0.5; document this paper-specific choice and expose ϒ as user parameter.

• WSM Table 5 phase values (τ_WSM up to 1.35) exceed paper's own §2.6 constraint τ ∈ [0,1]. This is the natural consequence of summing weighted phases without normalization - paper does not address this constraint violation; engine should warn when post-aggregation τ or R > 1.

• WSM scalar component-wise weighting (T'·W applied independently on σ, τ, ϖ, R) is methodologically simplified vs full CFZN ⊗ operator from §3 eq 7 (which would couple σ and τ through complex multiplication). Paper choice is the simpler 4-real-scalar approach; engine should mirror this.

• Normalization in Step 3 (eq 5-6) divides each CFZN component (σ, τ, ϖ, R) by per-column max (benefit) or min (cost) independently. This does NOT preserve CFZN constraint τ ∈ [0,1] when original values already at boundary; engine should clip post-normalization to [0,1] with warning.

• Score function μ = (σϖ + τR)/2 (Shahid §3 eq 3) couples amplitude pair and phase pair multiplicatively. This is the load-bearing scalarization - μ(Ě^WSM) reproduces Table 7 scores exactly even when phase values > 1.

• Both WASPAS (this manifest) and MARCOS (CFZN-MARCOS) share Table 1 input but produce different rankings: WASPAS U2≻U4≻U3≻U1 vs MARCOS U2≻U1≻U4≻U3. U2 is consistently top; ranks 2-4 differ between methods.

• Ranking criterion: largest S_i wins. Engine must descending-sort.

• Engine should NOT scalarize prematurely - all WSM/WPM aggregations stay in CFZN space (4-tuple) until final μ-scoring.

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