user: craft a reference note about what MCDA is [Context: Notes: 04-RESOURCES/Definitions/Multi-Criteria Decision Analysis (MCDA).md] [Timestamp: 2025/12/13 13:44:14]
ai: # Multi-Criteria Decision Analysis (MCDA)
Summary
- Multi-Criteria Decision Analysis (MCDA) is a family of structured methods used to support decision-making when multiple, often conflicting, criteria must be considered.
- It helps convert qualitative and quantitative criteria into a transparent, repeatable evaluation that ranks, scores, or selects alternatives.
Key concepts
- Decision alternatives: the options being compared (projects, sites, designs, investments).
- Criteria: attributes used to evaluate alternatives (cost, risk, benefit, accessibility, environmental impact).
- Weights: the relative importance assigned to each criterion.
- Performance/score matrix: values of alternatives on each criterion.
- Normalization: converting different units/scales into a common scale.
- Aggregation rule: the mathematical method for combining criteria (e.g., weighted sum).
- Sensitivity/robustness analysis: checking how results change with different weights or assumptions.
Common MCDA methods (overview)
- Weighted Sum Model (WSM / MAUT / MAVT)
- Simple and widely used; aggregate normalized scores with weights.
- Analytic Hierarchy Process (AHP)
- Pairwise comparisons to derive weights and derive priorities; checks consistency.
- TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)
- Ranks alternatives by closeness to an ideal best and farthest from an ideal worst.
- ELECTRE (ELimination Et Choix Traduisant la REalité)
- Outranking method; handles incomparabilities and veto thresholds.
- PROMETHEE
- Outranking with preference functions and net flow scores.
- Multi-Attribute Utility Theory (MAUT)
- Builds utility functions to represent stakeholder preferences, often used when risk attitudes matter.
Basic MCDA workflow
- Define the decision problem and objectives.
- Identify feasible alternatives.
- Select and define criteria (ensure coverage and independence where possible).
- Measure or estimate performance of each alternative against each criterion.
- Choose weighting method and elicit weights (stakeholder elicitation, AHP, direct rating).
- Normalize criterion scores if needed.
- Aggregate scores using chosen MCDA method.
- Rank alternatives and perform sensitivity/robustness checks.
- Present results and support decision with documentation of assumptions.
Core mathematics (examples)
- Weighted sum (WSM/MAUT):
- Given alternatives and criteria : , where are weights and are normalized scores.
- Normalization examples:
- Min–max: .
- Benefit/cost direction handling: reverse scale for cost criteria.
- AHP weight derivation:
- Pairwise comparison matrix , eigenvector method: find such that .
Simple worked example (weighted sum)
- Criteria: Cost (weight 0.6, lower is better), Quality (weight 0.4, higher is better).
- Alternatives A and B:
- Cost: A = 80, B = 60 (lower better)
- Quality: A = 70, B = 60 (higher better)
- Normalize (min–max, invert cost):
- Cost normalized (benefit form): so A: , B: .
- Quality normalized: A: , B: .
- Scores: ; → B preferred.
Weighting and stakeholder involvement
- Weight elicitation methods:
- Direct rating (point allocation), swing weighting, pairwise comparisons (AHP), rank-order centroid, budget allocation.
- Document who set weights, how trade-offs were elicited, and provide alternate weight scenarios for transparency.
Sensitivity and robustness
- Test how rankings change under:
- Perturbations of weights (one-at-a-time, Monte Carlo sampling).
- Different normalization or aggregation rules.
- Alternative performance estimates (uncertain data).
- Report stability: if rankings flip under small changes, decision is fragile.
Strengths and limitations
- Strengths:
- Makes multiple criteria and trade-offs explicit.
- Flexible: handles qualitative and quantitative data.
- Supports stakeholder participation and transparent documentation.
- Limitations:
- Results depend on choice of criteria, normalization, and weights.
- Some methods (e.g., AHP) can be sensitive to inconsistent judgments.
- Outranking methods can produce incomparabilities that require interpretation.
Applications (examples)
- Urban planning and site selection (GIS-integrated MCDA).
- Environmental impact assessment and resource management.
- Supplier selection and procurement.
- Portfolio selection in finance and real estate.
- Policy evaluation and health technology assessment.
Practical tips for implementation
- Keep criteria few and meaningful; avoid redundant criteria.
- Separate measurement scales and directions clearly (benefit vs cost).
- Use visualizations: scorecards, radar charts, sensitivity plots.
- Record assumptions and all intermediate matrices so results are reproducible.
- For GIS MCDA, use raster or vector overlays with weighted combination but be careful with scale and normalization.
Suggested note structure in this vault
-
- Purpose / Summary
- Key concepts
- Workflow / Checklist
- Worked examples and templates
- References and further reading
References and further reading (selection)
- Keeney, R. L., & Raiffa, H. (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs.
- Saaty, T. L. (1980). The Analytic Hierarchy Process.
- Hwang, C.-L., & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications.
- Belton, V., & Stewart, T. J. (2002). Multiple Criteria Decision Analysis: An Integrated Approach.
If you want, I can:
-
- generate a ready-to-use MCDA template (performance matrix + weight elicitation + calculation steps) for this note,
- create linked subnotes for AHP, TOPSIS, PROMETHEE with method-specific steps,
- or produce a small Obsidian table or Dataview-ready structure to manage alternatives and criteria.