TOPSIS Ranker Skill | Agent Skills

TOPSIS Ranker

Overview

The TOPSIS Ranker skill implements the Technique for Order of Preference by Similarity to Ideal Solution methodology for multi-criteria decision analysis. It ranks alternatives based on their geometric distance from ideal and anti-ideal solutions, providing intuitive and mathematically sound rankings.

Capabilities

Decision matrix normalization (vector, linear, max-min)
Weighted normalized matrix calculation
Ideal and anti-ideal solution identification
Euclidean distance calculation
Relative closeness coefficient computation
Alternative ranking generation
Sensitivity analysis on weights
Visualization of results

Used By Processes

Multi-Criteria Decision Analysis (MCDA)
Tech Stack Evaluation
Geographic Market Analysis

Usage

Decision Matrix Construction

# Define decision matrix (alternatives x criteria)
decision_matrix = {
    "alternatives": ["Option A", "Option B", "Option C", "Option D"],
    "criteria": ["Cost", "Quality", "Time", "Risk"],
    "values": [
        [100000, 85, 12, 3],   # Option A
        [150000, 92, 8, 2],    # Option B
        [80000, 78, 15, 4],    # Option C
        [120000, 88, 10, 2]    # Option D
    ],
    "weights": [0.3, 0.35, 0.2, 0.15],
    "criteria_type": ["cost", "benefit", "cost", "cost"]  # minimize/maximize
}

Normalization Methods

Vector Normalization: r_ij = x_ij / sqrt(sum(x_ij^2))
Linear Normalization: r_ij = x_ij / max(x_j) for benefit, min(x_j) / x_ij for cost
Max-Min Normalization: r_ij = (x_ij - min) / (max - min)

TOPSIS Algorithm Steps

Construct normalized decision matrix
Calculate weighted normalized matrix
Determine ideal (A+) and anti-ideal (A-) solutions
Calculate separation measures (S+ and S-)
Calculate relative closeness coefficient (C*)
Rank alternatives by C* (higher is better)

Relative Closeness

C* = S- / (S+ + S-)

C* = 1: Alternative is ideal solution
C* = 0: Alternative is anti-ideal solution

Input Schema

{
  "decision_matrix": {
    "alternatives": ["string"],
    "criteria": ["string"],
    "values": "2D array of numbers",
    "weights": ["number"],
    "criteria_type": ["benefit|cost"]
  },
  "options": {
    "normalization_method": "vector|linear|max_min",
    "sensitivity_analysis": "boolean",
    "visualization": "boolean"
  }
}

Output Schema

{
  "ranking": [
    {
      "alternative": "string",
      "rank": "number",
      "closeness_coefficient": "number",
      "distance_to_ideal": "number",
      "distance_to_anti_ideal": "number"
    }
  ],
  "ideal_solution": "object",
  "anti_ideal_solution": "object",
  "sensitivity_results": {
    "weight_sensitivity": "object",
    "rank_stability": "object"
  },
  "visualization_path": "string"
}

Best Practices

Ensure all criteria are on comparable scales or use appropriate normalization
Validate that weights sum to 1.0
Correctly identify benefit vs. cost criteria
Perform sensitivity analysis when alternatives are closely ranked
Consider using with AHP for systematic weight derivation
Document criteria definitions and measurement methods

Advantages

Intuitive geometric interpretation
Accounts for both best and worst performance
Works with any number of criteria and alternatives
Computationally efficient
Results are easy to explain to stakeholders

Limitations

Assumes linear trade-offs between criteria
Sensitive to weight assignments
Does not handle uncertainty in input values directly

Integration Points

Receives weights from AHP Calculator
Feeds into Decision Visualization for ranking charts
Connects with Sensitivity Analyzer for robustness testing
Integrates with Stakeholder Preference Elicitor for weight collection

Agent Skills: TOPSIS Ranker

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