electre-comparator

Business

ELECTRE family methods skill for outranking-based decision support with concordance and discordance analysis

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ELECTRE Comparator

Overview

The ELECTRE Comparator skill implements the ELECTRE (ELimination Et Choix Traduisant la REalite) family of methods for multi-criteria decision analysis. It uses outranking relations based on concordance and discordance indices to handle complex decision problems with incomparability and threshold-based preferences.

Capabilities

ELECTRE I, II, III, IV, TRI implementation
Concordance matrix calculation
Discordance matrix calculation
Credibility degree computation
Outranking relation determination
Kernel and ranking extraction
Threshold sensitivity analysis
Classification into ordered categories (ELECTRE TRI)

Used By Processes

Multi-Criteria Decision Analysis (MCDA)
Portfolio Selection
Project Prioritization

Usage

ELECTRE Method Selection

Method	Purpose	Output
ELECTRE I	Selection	Kernel (best alternatives)
ELECTRE II	Ranking	Strong/weak rankings
ELECTRE III	Ranking	Credibility-based ranking
ELECTRE IV	Ranking	No weights required
ELECTRE TRI	Sorting	Category assignment

Configuration Example

# Define ELECTRE III configuration
config = {
    "alternatives": ["Project A", "Project B", "Project C", "Project D"],
    "criteria": [
        {
            "name": "ROI",
            "weight": 0.35,
            "type": "benefit",
            "thresholds": {"q": 2, "p": 5, "v": 15}  # indifference, preference, veto
        },
        {
            "name": "Risk",
            "weight": 0.25,
            "type": "cost",
            "thresholds": {"q": 1, "p": 3, "v": 8}
        },
        {
            "name": "Strategic Fit",
            "weight": 0.40,
            "type": "benefit",
            "thresholds": {"q": 5, "p": 10, "v": 25}
        }
    ],
    "performance_matrix": [
        [25, 4, 80],   # Project A
        [30, 6, 70],   # Project B
        [20, 3, 85],   # Project C
        [28, 5, 75]    # Project D
    ]
}

Threshold Types

Indifference threshold (q): Difference below which alternatives are indifferent
Preference threshold (p): Difference above which strict preference exists
Veto threshold (v): Difference that prohibits outranking regardless of other criteria

Concordance and Discordance

Concordance Index: Measures support for "a outranks b"

C(a,b) = Sum of weights where a is at least as good as b

Discordance Index: Measures opposition to "a outranks b"

D(a,b) = Maximum scaled difference where b is better than a

ELECTRE TRI Classification

Assigns alternatives to predefined categories:

Define boundary profiles between categories
Compare alternatives to boundaries
Apply pessimistic or optimistic assignment rules

Input Schema

{
  "method": "ELECTRE_I|ELECTRE_II|ELECTRE_III|ELECTRE_IV|ELECTRE_TRI",
  "alternatives": ["string"],
  "criteria": [
    {
      "name": "string",
      "weight": "number",
      "type": "benefit|cost",
      "thresholds": {
        "q": "number",
        "p": "number",
        "v": "number"
      }
    }
  ],
  "performance_matrix": "2D array of numbers",
  "options": {
    "concordance_threshold": "number (for ELECTRE I)",
    "boundary_profiles": "object (for ELECTRE TRI)",
    "assignment_rule": "pessimistic|optimistic"
  }
}

Output Schema

{
  "method_used": "string",
  "concordance_matrix": "2D array",
  "discordance_matrix": "2D array",
  "credibility_matrix": "2D array (ELECTRE III)",
  "outranking_relations": [
    {"from": "string", "to": "string", "credibility": "number"}
  ],
  "kernel": ["string (ELECTRE I)"],
  "ranking": {
    "descending": ["string"],
    "ascending": ["string"],
    "final": ["string"]
  },
  "classifications": "object (ELECTRE TRI)",
  "incomparabilities": ["object"]
}

Best Practices

Select ELECTRE variant based on problem type (selection, ranking, sorting)
Set thresholds based on criterion measurement precision
Validate veto thresholds with stakeholders (they block outranking)
Analyze incomparabilities - they may reveal important trade-offs
Compare results across multiple threshold scenarios
Use ELECTRE TRI for portfolio categorization problems

Integration Points

Receives weights from AHP Calculator
Connects with PROMETHEE Evaluator for method triangulation
Feeds into Decision Visualization for outranking graphs
Supports Sensitivity Analyzer for threshold robustness