skcriteria.ranksrev.rank_transitivity_check module

Transitivity Checker for MCDM Robustness Evaluation.

This module evaluates the logical consistency and stability of Multi-Criteria Decision Making (MCDM) methods through transitivity analysis. It decomposes decision problems into pairwise comparisons and reconstructs global rankings to assess method robustness.

The module validates whether rankings satisfy the transitivity property (if A ≻ B and B ≻ C, then A ≻ C) and provides mechanisms to handle violations.

Key Features

  • Transitivity validation through pairwise decomposition

  • Ranking recomposition with cycle-breaking strategies

  • Comprehensive diagnostic reporting

class skcriteria.ranksrev.rank_transitivity_check.RankTransitivityChecker(dmaker, *, allow_missing_alternatives=False, ranking_strategy='generations', max_toposort_rankings=50, preferred_parallel_backend=None, n_jobs=None, parallel_backend=None)[source]

Bases: SKCMethodABC

Robustness evaluator for Multi-Criteria Decision Making (MCDM) methods.

This class validates the logical consistency and stability of MCDM method rankings by analyzing transitivity properties through pairwise alternative comparisons. It identifies ranking inconsistencies and provides alternative ranking reconstructions when transitivity violations occur.

The evaluation process is the following:

  1. Pairwise Dominance Analysis: Evaluates all possible pairs of alternatives using the provided MCDM method to construct a directed dominance graph representing preference relationships.

  2. Transitivity Validation (Test Criterion 2): Detects cycles in the dominance graph that violate the transitivity property. A transitive ranking requires that if A > B and B > C, then A > C must hold.

  3. Ranking Stability Assessment (Test Criterion 3): Compares the original ranking with reconstructed rankings to evaluate consistency when the decision problem is decomposed and recomposed.

  4. Ranking Reconstruction: When transitivity violations exist, applies cycle-breaking strategies to generate alternative valid rankings through graph decomposition techniques.

Parameters:

  • dmaker (object) – Decision maker instance that must implement an evaluate(dm) method. This represents the MCDM method or pipeline to be evaluated for robustness.

  • allow_missing_alternatives (bool, default=False) – Whether to allow rankings that don’t include all original alternatives (using a pipeline that implements a filter, for example can remove alternatives). When False, raises ValueError if any alternative is missing from results. When True, missing alternatives are assigned the worst ranking + 1.

  • ranking_strategy (str, default="generations") –

    Strategy for generating reconstructed rankings from the dominance graph:

    • ”generations”: Generate a single ranking based on topological layers (alternatives in the same layer receive the same rank, producing ties)

    • ”cycle_permutations”: Generate multiple rankings from topological sorts (number controlled by max_toposort_rankings parameter)

  • max_toposort_rankings (int or None, default=50) – Cap on the number of rankings generated from topological sorts, to bound computational cost. Must be at least 1, or None for no limit (all possible rankings). Only used when ranking_strategy=”cycle_permutations”; ignored otherwise.

  • preferred_parallel_backend (str or None, default=None) – Backend for parallel computation of pairwise evaluations. Options include ‘threading’, ‘multiprocessing’, or None for sequential. Improves performance for large numbers of alternatives.

  • n_jobs (int or None, default=None) – Number of parallel jobs for pairwise evaluation. When None, uses all available processors. Set to 1 for sequential processing.

  • parallel_backend (str or None, default=None (deprecated)) – Use preferred_parallel_backend instead.

Raises:

  • TypeError – If dmaker doesn’t implement the required evaluate() method.

  • ValueError – If allow_missing_alternatives=False and alternatives are missing from results. If max_toposort_rankings is less than 1 (when not None). If ranking_strategy is not “generations” or “cycle_permutations”.

Examples

Basic usage evaluating transitivity of a decision maker:

>>> from skcriteria.agg import simple
>>> from skcriteria import mkdm
>>>
>>> # Create a decision matrix
>>> dm = mkdm(
...     matrix=[[1, 2], [3, 4], [5, 6]],
...     objectives=[max, max],
...     alternatives=["A", "B", "C"]
... )
>>>
>>> # Create checker with generations strategy
>>> dmaker = simple.WeightedSum()
>>> checker = RankTransitivityChecker(
...     dmaker, ranking_strategy="generations")
>>>
>>> # Evaluate transitivity
>>> result = checker.evaluate(dm)
>>> print(result.extra_["test_criterion_2"])  # Transitivity test
>>> print(result.extra_["test_criterion_3"])  # Stability test
>>>
>>> # Or use toposorts strategy for multiple rankings
>>> checker2 = RankTransitivityChecker(
...     dmaker, ranking_strategy="cycle_permutations",
...     max_toposort_rankings=10
... )
>>> result2 = checker2.evaluate(dm)
property dmaker

The MCDA method, or pipeline to evaluate.

property allow_missing_alternatives

Whether rankings are allowed that don’t contain all original alternatives.

property ranking_strategy

Strategy for generating reconstructed rankings (‘generations’ or ‘toposorts’).

property max_toposort_rankings

Maximum number of toposort rankings to generate (must be >= 1, None means unlimited).

property preferred_parallel_backend

The parallel backend used to generate all the alternatives.

property parallel_backend

The parallel backend used to generate all the alternatives.

Deprecated since version 0.10.0: Use ‘preferred_parallel_backend’ instead

property n_jobs

The number of parallel jobs used in the pairwise evaluations.

evaluate(dm)[source]

Execute the complete transitivity test and ranking analysis.

This method performs a comprehensive transitivity analysis, including dominance graph construction, transitivity testing, and ranking recomposition. It provides multiple ranking perspectives when cycles are present and diagnostic information about the decision problem’s structure.

Parameters:

dm (DecisionMatrix) – The decision matrix to be evaluated, containing alternatives and criteria values for multi-criteria decision analysis.

Returns:

A comprehensive result object containing:

  • Multiple named rankings (original + recompositions)

  • Diagnostic information in the extra attribute:

    • test_criterion_2: Transitivity consistency test result

    • test_criterion_3: Ranking stability test result

    • pairwise_dominance_graph: The constructed dominance graph

    • transitivity_break: List of transitivity violations

    • transitivity_break_rate: Normalized violation rate

    • dag: Condensed reduced DAG used to reconstruct rankings

    • mpr: Maximum possible number of distinct rankings derivable from the dag

    • pairwise_comparisons: All pairwise comparison results

Return type:

RanksComparator