mcda-analyzer

Business

Multi-criteria decision analysis skill with AHP, TOPSIS, and weighted scoring methods.

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mcda-analyzer

You are mcda-analyzer - a specialized skill for multi-criteria decision analysis including AHP, TOPSIS, and weighted scoring methods.

Overview

This skill enables AI-powered decision analysis including:

Analytic Hierarchy Process (AHP)
TOPSIS (Technique for Order Preference by Similarity)
Weighted scoring methods
Pairwise comparison matrices
Consistency ratio calculation
Sensitivity analysis
Decision visualization
Criteria weighting

Capabilities

1. Analytic Hierarchy Process (AHP)

import numpy as np
import pandas as pd

def ahp_analysis(criteria: list, pairwise_matrix: np.ndarray):
    """
    Analytic Hierarchy Process for criteria weighting

    criteria: list of criterion names
    pairwise_matrix: n x n matrix of pairwise comparisons
    """
    n = len(criteria)

    # Calculate priority vector (principal eigenvector)
    # Simplified: normalized column average method
    col_sums = pairwise_matrix.sum(axis=0)
    normalized = pairwise_matrix / col_sums
    priorities = normalized.mean(axis=1)

    # Calculate consistency
    weighted_sum = pairwise_matrix @ priorities
    lambda_max = np.mean(weighted_sum / priorities)

    # Consistency Index
    ci = (lambda_max - n) / (n - 1) if n > 1 else 0

    # Random Index (for n = 1 to 10)
    ri_values = {1: 0, 2: 0, 3: 0.58, 4: 0.90, 5: 1.12,
                 6: 1.24, 7: 1.32, 8: 1.41, 9: 1.45, 10: 1.49}
    ri = ri_values.get(n, 1.49)

    # Consistency Ratio
    cr = ci / ri if ri > 0 else 0

    return {
        "criteria": criteria,
        "priorities": dict(zip(criteria, priorities)),
        "lambda_max": round(lambda_max, 4),
        "consistency_index": round(ci, 4),
        "consistency_ratio": round(cr, 4),
        "is_consistent": cr < 0.10,
        "interpretation": "Consistent" if cr < 0.10 else "Inconsistent - revise judgments"
    }

def create_pairwise_matrix(judgments: dict, criteria: list):
    """
    Create pairwise comparison matrix from judgments

    judgments: {(criterion1, criterion2): value} where value is relative importance
    Scale: 1=equal, 3=moderate, 5=strong, 7=very strong, 9=extreme
    """
    n = len(criteria)
    matrix = np.ones((n, n))

    idx = {c: i for i, c in enumerate(criteria)}

    for (c1, c2), value in judgments.items():
        i, j = idx[c1], idx[c2]
        matrix[i, j] = value
        matrix[j, i] = 1 / value

    return matrix

2. TOPSIS Analysis

def topsis_analysis(alternatives: list, criteria: list, decision_matrix: np.ndarray,
                   weights: list, criteria_types: list):
    """
    TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)

    alternatives: list of alternative names
    criteria: list of criterion names
    decision_matrix: m alternatives x n criteria matrix
    weights: criterion weights (sum to 1)
    criteria_types: list of 'benefit' or 'cost' for each criterion
    """
    m, n = decision_matrix.shape

    # Step 1: Normalize decision matrix
    # Vector normalization
    norm_divisors = np.sqrt((decision_matrix ** 2).sum(axis=0))
    normalized = decision_matrix / norm_divisors

    # Step 2: Weighted normalized matrix
    weighted = normalized * weights

    # Step 3: Determine ideal and anti-ideal solutions
    ideal = np.zeros(n)
    anti_ideal = np.zeros(n)

    for j in range(n):
        if criteria_types[j] == 'benefit':
            ideal[j] = weighted[:, j].max()
            anti_ideal[j] = weighted[:, j].min()
        else:  # cost criterion
            ideal[j] = weighted[:, j].min()
            anti_ideal[j] = weighted[:, j].max()

    # Step 4: Calculate distances
    dist_to_ideal = np.sqrt(((weighted - ideal) ** 2).sum(axis=1))
    dist_to_anti = np.sqrt(((weighted - anti_ideal) ** 2).sum(axis=1))

    # Step 5: Calculate relative closeness
    closeness = dist_to_anti / (dist_to_ideal + dist_to_anti)

    # Rank alternatives
    ranking = np.argsort(-closeness) + 1  # 1 is best

    results = []
    for i, alt in enumerate(alternatives):
        results.append({
            'alternative': alt,
            'closeness_coefficient': round(closeness[i], 4),
            'distance_to_ideal': round(dist_to_ideal[i], 4),
            'distance_to_anti_ideal': round(dist_to_anti[i], 4),
            'rank': int(ranking[i])
        })

    results.sort(key=lambda x: x['rank'])

    return {
        "ranking": results,
        "best_alternative": results[0]['alternative'],
        "ideal_solution": dict(zip(criteria, ideal)),
        "anti_ideal_solution": dict(zip(criteria, anti_ideal))
    }

3. Weighted Scoring Method

def weighted_scoring(alternatives: list, criteria: list,
                    scores: np.ndarray, weights: list):
    """
    Simple weighted scoring method

    alternatives: list of alternative names
    criteria: list of criterion names
    scores: m x n matrix of scores (0-10 scale typical)
    weights: criterion weights (sum to 1)
    """
    # Calculate weighted scores
    weighted_scores = scores * weights
    total_scores = weighted_scores.sum(axis=1)

    # Rank
    ranking = np.argsort(-total_scores) + 1

    results = []
    for i, alt in enumerate(alternatives):
        criterion_contributions = dict(zip(criteria, weighted_scores[i]))
        results.append({
            'alternative': alt,
            'total_score': round(total_scores[i], 2),
            'criterion_scores': criterion_contributions,
            'rank': int(ranking[i])
        })

    results.sort(key=lambda x: x['rank'])

    return {
        "ranking": results,
        "best_alternative": results[0]['alternative'],
        "score_range": {
            "max": round(max(total_scores), 2),
            "min": round(min(total_scores), 2),
            "spread": round(max(total_scores) - min(total_scores), 2)
        }
    }

4. Sensitivity Analysis

def sensitivity_analysis(base_weights: list, criteria: list, decision_matrix: np.ndarray,
                        alternatives: list, criteria_types: list, method: str = 'topsis'):
    """
    Analyze sensitivity of ranking to weight changes
    """
    n_criteria = len(criteria)
    sensitivity_results = []

    for i in range(n_criteria):
        # Vary weight from 0 to 0.5
        weight_variations = np.linspace(0, 0.5, 11)

        criterion_sensitivity = []
        for new_weight in weight_variations:
            # Redistribute remaining weight proportionally
            remaining = 1 - new_weight
            modified_weights = np.array(base_weights) * (remaining / (1 - base_weights[i]))
            modified_weights[i] = new_weight

            if method == 'topsis':
                result = topsis_analysis(alternatives, criteria, decision_matrix,
                                        modified_weights, criteria_types)
            else:
                result = weighted_scoring(alternatives, criteria, decision_matrix,
                                         modified_weights)

            criterion_sensitivity.append({
                'weight': new_weight,
                'best_alternative': result['best_alternative'],
                'ranking': [r['alternative'] for r in result['ranking']]
            })

        # Find switching points
        switching_points = []
        for j in range(1, len(criterion_sensitivity)):
            if criterion_sensitivity[j]['best_alternative'] != criterion_sensitivity[j-1]['best_alternative']:
                switching_points.append({
                    'weight': criterion_sensitivity[j]['weight'],
                    'from': criterion_sensitivity[j-1]['best_alternative'],
                    'to': criterion_sensitivity[j]['best_alternative']
                })

        sensitivity_results.append({
            'criterion': criteria[i],
            'base_weight': base_weights[i],
            'variations': criterion_sensitivity,
            'switching_points': switching_points,
            'is_sensitive': len(switching_points) > 0
        })

    return {
        "sensitivity": sensitivity_results,
        "most_sensitive_criterion": max(sensitivity_results,
                                        key=lambda x: len(x['switching_points']))['criterion'],
        "robust_range": identify_robust_range(sensitivity_results)
    }

def identify_robust_range(sensitivity_results):
    """Identify weight ranges where ranking is stable"""
    # Simplified - find narrowest switching gap
    for result in sensitivity_results:
        if result['switching_points']:
            return {"criterion": result['criterion'],
                   "stable_up_to": result['switching_points'][0]['weight']}
    return {"status": "Ranking is robust across all weight variations"}

5. Criteria Weighting Methods

def rank_order_centroid(n_criteria: int, ranking: list = None):
    """
    Rank Order Centroid (ROC) method for weight generation

    ranking: list of ranks (1 = most important)
    """
    if ranking is None:
        ranking = list(range(1, n_criteria + 1))

    weights = []
    for rank in ranking:
        weight = sum(1/j for j in range(rank, n_criteria + 1)) / n_criteria
        weights.append(weight)

    return {
        "method": "ROC",
        "weights": weights,
        "normalized_weights": [w / sum(weights) for w in weights]
    }

def swing_weights(criteria: list, swings: dict):
    """
    Swing weighting method

    swings: {criterion: swing_value} where highest value = most important
    """
    max_swing = max(swings.values())
    weights = {c: swings[c] / max_swing for c in criteria}
    total = sum(weights.values())
    normalized = {c: w / total for c, w in weights.items()}

    return {
        "method": "Swing Weights",
        "raw_weights": weights,
        "normalized_weights": normalized
    }

6. Decision Matrix Visualization

def create_decision_summary(alternatives: list, criteria: list,
                           decision_matrix: np.ndarray, weights: list,
                           ranking_result: dict):
    """
    Create comprehensive decision summary
    """
    summary = {
        "decision_matrix": pd.DataFrame(
            decision_matrix,
            index=alternatives,
            columns=criteria
        ).to_dict(),
        "criteria_weights": dict(zip(criteria, weights)),
        "ranking": ranking_result['ranking'],
        "recommendation": {
            "best_choice": ranking_result['best_alternative'],
            "confidence": assess_confidence(ranking_result)
        },
        "visualization_data": {
            "spider_chart": prepare_spider_chart_data(alternatives, criteria, decision_matrix),
            "bar_chart": prepare_bar_chart_data(ranking_result)
        }
    }

    return summary

def assess_confidence(result):
    """Assess confidence in the recommendation"""
    scores = [r['total_score'] if 'total_score' in r else r['closeness_coefficient']
              for r in result['ranking']]
    if len(scores) >= 2:
        gap = scores[0] - scores[1]
        if gap > 0.2:
            return "High - clear winner"
        elif gap > 0.1:
            return "Medium - some differentiation"
        else:
            return "Low - alternatives are close"
    return "N/A"

def prepare_spider_chart_data(alternatives, criteria, matrix):
    """Prepare data for spider/radar chart"""
    # Normalize to 0-1 scale for visualization
    normalized = (matrix - matrix.min(axis=0)) / (matrix.max(axis=0) - matrix.min(axis=0) + 0.0001)
    return {alt: dict(zip(criteria, normalized[i])) for i, alt in enumerate(alternatives)}

def prepare_bar_chart_data(result):
    """Prepare data for ranking bar chart"""
    return [{"alternative": r['alternative'],
             "score": r.get('total_score', r.get('closeness_coefficient'))}
            for r in result['ranking']]

Process Integration

This skill integrates with the following processes:

multi-criteria-decision-analysis.js
supplier-selection-evaluation.js
project-prioritization.js

Output Format

{
  "method": "TOPSIS",
  "ranking": [
    {"alternative": "Option A", "score": 0.72, "rank": 1},
    {"alternative": "Option C", "score": 0.65, "rank": 2},
    {"alternative": "Option B", "score": 0.48, "rank": 3}
  ],
  "weights": {"cost": 0.3, "quality": 0.4, "delivery": 0.3},
  "sensitivity": {
    "most_sensitive": "quality",
    "robust": true
  },
  "recommendation": {
    "best_choice": "Option A",
    "confidence": "High"
  }
}

Best Practices

Define criteria clearly - Measurable, independent criteria
Involve stakeholders - Consensus on weights
Test sensitivity - Understand robustness
Document rationale - Record judgment basis
Consider multiple methods - Compare results
Iterate if needed - Refine based on insights

Constraints

AHP limited to ~9 criteria effectively
Requires consistent judgments
Weight elicitation can be subjective
Results depend on criteria selection