Mcda suitability analysis

MCDA & Suitability Analysis

Purpose: produce suitability maps whose weights, scales, and assumptions are explicit, consistent, and stress-tested. A suitability map without a sensitivity analysis is an opinion with a legend.

Workflow

1. Structure: goal → criteria (factors) → constraints. Constraints are binary masks (legal exclusions, water bodies, slope > threshold) applied at the END by multiplication; factors are continuous and weighted. Keep them apart — encoding a constraint as a heavily-weighted factor is a classic error that lets forbidden areas score "acceptable".
2. Criteria layers: each factor as a raster on a COMMON grid (same CRS, extent, cell size, snap). Resample categorical layers with nearest, continuous with bilinear; document each.
3. Standardization to a common suitability scale (0-1 or 0-255):
   • Linear min-max for monotonic "more is better/worse".
   • Fuzzy membership (sigmoid/linear with control points) when suitability saturates — justify control points from domain knowledge.
   • Categorical layers: explicit reclass table, shown to the user. Direction check: confirm for EVERY layer whether high raw value means high or low suitability (slope: low=good; distance-to-road: usually low=good). Direction bugs survive to the final map invisibly.
4. Weights (AHP below, or direct/ranked methods with rationale).
5. Aggregation: weighted linear combination (WLC) default; OWA when the decision-maker's risk attitude (AND-like vs OR-like) matters.
6. Constraint mask multiply; classify the result (equal interval or quantiles — say which and why); sensitivity analysis; validate against known good/bad sites if any exist.

AHP with consistency enforcement

Pairwise comparisons on Saaty's 1-9 scale; weights from the principal eigenvector; consistency ratio (CR) must be < 0.10 or the matrix goes back for revision. Run scripts/ahp_weights.py to compute weights + CR from a reciprocal comparison matrix (it validates reciprocity and reports λ_max).

Practices: elicit comparisons pair by pair with verbal anchors ("moderately more important" = 3); with multiple experts, aggregate judgments by geometric mean BEFORE computing weights; report the full matrix, weights, λ_max and CR in the deliverable. If CR ≥ 0.10, identify the most inconsistent triad and ask the expert to revisit it — do not silently massage numbers.

Aggregation

suit = np.zeros_like(factors[0], dtype="float32")
for w_i, f in zip(weights, factors):   # factors already standardized 0-1
    suit += w_i * f
suit *= constraint_mask                 # binary 0/1, applied last

OWA variant: sort factor values per cell and apply order weights — full AND (min) to full OR (max) continuum; use when stakeholders disagree on risk tolerance and show 2-3 scenarios.

Sensitivity analysis — mandatory

A result that flips with a small weight change is not a result:

• One-at-a-time: perturb each weight ±20% (renormalize), recompute, report % of area changing suitability class and a stability map (cells that never change class across perturbations).
• Scenario: 2-3 alternative weight sets from different stakeholder priorities; present side-by-side.
• If a Monte Carlo budget exists: sample weights from Dirichlet around the AHP vector; per-cell probability of "highly suitable" is a far stronger product than a single map.

Deliverable standard

Suitability map (classified + continuous), constraint mask map, weights table with CR, standardization functions per criterion (with direction), sensitivity/stability summary, and limitations paragraph (data currency, resolution, criteria omitted). Route cartography to cartography-geoviz; network-access criteria come from network-accessibility-analysis.

Pitfalls checklist

• Direction inversion on a criterion (the silent killer — double-check distance-based factors).
• Mixing resolutions without declaring the resampling rule.
• CR ignored or unreported.
• Constraints blended as weights → forbidden zones scored medium.
• Classifying with quantiles then reading them as absolute suitability.
• No sensitivity analysis; single map presented as truth.

Execution contract

• Workflow: define decision and stakeholders; separate constraints from factors; standardize criteria; elicit and validate weights; aggregate; test sensitivity; communicate uncertainty.
• Decision rules: use MCDA for transparent criteria-ranked surfaces, network analysis for route-constrained access, and optimization when discrete placement or capacity decisions dominate.
• Verification protocol: check criterion direction and alignment, AHP consistency, constraint enforcement, weight and threshold perturbations, and stable-versus-fragile areas.
• Failure modes: reject the model when criteria double-count the same construct, weights lack provenance, constraints leak into compensation, or rankings collapse under plausible perturbations.
• Deliverables: continuous and classified suitability maps, constraints, criteria transformations, weights and consistency ratio, sensitivity results, and limitations.
• Source freshness: consult the authoritative source registry before applying methods or implementation APIs and record the checked date.