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# pELECTRE Tri: A computational framework and Python module for probabilistic ELECTRE Tri-B multiple-criteria decision-making

Christian Ghiaus

► To cite this version:

Christian Ghiaus. pELECTRE Tri: A computational framework and Python module for probabilistic ELECTRE Tri-B multiple-criteria decision-making. Software Impacts, 2025, 25, pp.100781. 10.1016/j.simpa.2025.100781. hal-05252801

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Original software publication

# pELECTRE Tri: A computational framework and Python module for probabilistic ELECTRE Tri-B multiple-criteria decision-making

<figure><img src="image_3.png" /></figure>

Christian Ghiaus

INSA Lyon, CNRS, CETHIL, UMR5008, F-69621, Villeurbanne, France

<figure><img src="image_4.png" /></figure>

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## ARTICLE INFO

### Keywords:

Multiple-criteria decision-making (MCDM)

Sorting and classification method

Imprecise data

Probabilistic performance matrix

Monte Carlo simulation

## ABSTRACT

ELECTRE Tri-B is a sorting and classification method for multiple-criteria decision-making (MCDM) in which alternatives are assigned to categories. The categories are completely ordered and defined by base (or reference) profiles. The *pELECTRE Tri* software implements a probabilistic extension of the ELECTRE Tri-B method designed to handle uncertainty in both the decision matrix values and the base profiles delimiting the categories. Its modular architecture enables step-by-step workflows from data input to results output, ensuring flexibility and transparency in the decision-making process. Implemented as a Python module, *pELECTRE Tri* requires no installation and can be executed locally or online. The software is supported by comprehensive documentation, including tutorials, how-to guides, theoretical explanations, and a user reference manual.

Current code version

Permanent link to code/repository used for this code version

Permanent link to reproducible capsule

Legal code license

Code versioning system used

Software code languages, tools and services used

Compilation requirements, operating environments and dependencies

Link to documentation

Support email for questions

v0.0.2

https://github.com/SoftwareImpacts/SIMPAC-2025-168

https://codeocean.com/capsule/2288379/tree/v1

MIT

none

Python

python 3.11.7

jupyter 1.0.0

jupyterlab 4.2.5

matplotlib 3.8.0

numpy 1.26.4

pandas 2.1.4

https://github.com/SoftwareImpacts/SIMPAC-2025-168/tree/main/docs

christian.ghiaus@insa-lyon.fr

## 1. Introduction

Multiple-Criteria Decision Making (MCDM) or Multiple-Criteria Decision Analysis (MCDA) is a branch of operations research that deals with decision problems involving multiple, often conflicting, criteria. The key components of MCDM are [1]:

* Alternatives (or actions): The available options for the decision-maker. For instance, in an energy retrofit decision, alternatives may include basic measures (e.g., double-glazing windows), moderate interventions (e.g., wall insulation), or extensive renovations (e.g., both).

* Criteria: The attributes used to evaluate alternatives. In the retrofit example, criteria could encompass energy savings, investment costs, and environmental impact.

The aim of Multiple-Criteria Decision Making (MCDM) is to support decision-making by analysing alternatives based on multiple criteria. MCDM problems can be categorized into several types, including choice, sorting, ranking, description, evaluation, and design [2].

Among the various MCDM methods, ELECTRE Tri stands out as a prominent sorting and classification technique, assigning alternatives

<footnote>The code (and data) in this article has been certified as Reproducible by Code Ocean: (https://codeocean.com/). More information on the Reproducibility Badge Initiative is available at https://www.elsevier.com/physical-sciences-and-engineering/computer-science/journals.

**E-mail address:** christian.ghiaus@insa-lyon.fr.</footnote>
to predefined ordered categories. As part of the ELECTRE family of
outranking methods, it excels in handling complex decisions with con-
flicting criteria [3,4]. The problem-solving procedure in ELECTRE Tri
involves comparing alternatives to base profiles that define the bound-
aries between categories. This is done through the construction of an
outranking relation, which validates or invalidates the assertion that an
alternative is at least as good as a profile. The method uses concordance
and discordance indices, along with veto thresholds, to determine the
credibility of the outranking relation. Finally, alternatives are assigned
to categories using either a pessimistic or optimistic procedure, based
on how they compare to the category boundary profiles [3–6].

The importance and significance of ELECTRE Tri lie in its capacity
to [3,7]:

* Handle imprecise data using thresholds for indifference, preference and veto between alternatives and base profiles.

* Consider the indifference and incomparability between alternatives.

* Avoid compensation effects between criteria.

* Integrate both qualitative and quantitative criteria.

Disadvantages include:

* Complexity in understanding and implementing the method.

* Sensitivity to indifference, preference and veto thresholds, which can significantly impact results.

Due to its ability to provide structured decision support in situations
with multiple stakeholders and conflicting objectives [8,9], ELECTRE
Tri has been applied across diverse fields, including environment,
engineering, finance, and transportation [10].

The field of Multi-Criteria Decision-Making (MCDM) has seen signif-
icant advancements in software tools and computational frameworks.
A notable contribution is PySensMCDA, a tool for sensitivity analysis,
allowing decision-makers to assess the stability and reliability of their
results [11]. Another contribution is Crispyn, a library for deter-
mining objectively the criteria weights [12]. Comprehensive MCDM
software packages, such as pymcdm, offers a library for solving multi-
criteria decision-making problems, implementing 15 different MCDM
methods (excluding the ELECTRE family of methods) [13]. MakeDe-
cision was introduced as an online system for the graphical design
of decision-making models in both crisp and fuzzy environments [14].

Focusing specifically on the ELECTRE family of methods, specialized
tools have been produced. The ELECTRE Tri 2.0 provides a dedicated
implementation of this popular outranking method [5,15]. pELECTRE-
Tri introduces a probabilistic approach to the ELECTRE-Tri method,
with a specific application to energy renovation of buildings [16].

ELECTRE Tri method takes into account the fuzziness of comparison
between alternatives and base profiles in estimating the concordance
(i.e., agreement) and discordance (i.e., disagreement) of the outranking
relationship (i.e., a profile is better than another). This approach allows
for a more nuanced evaluation of alternatives, considering the inherent
uncertainty in real-world decision-making scenarios [17,18]. However,
the standard ELECTRE Tri method does not model the uncertainty of
the values of alternatives on different criteria.

## 2. Software description

### 2.1. Contributions

The main contribution of pELECTRE Tri is to model the uncertainty
of the values of performance matrix, i.e. the values of alternatives
for different criteria, through probability distributions, addressing a
key limitation of traditional ELECTRE Tri [16]. pELECTRE Tri module
uses ideas of classical [18] and probabilistic [19] ELECTRE Tri imple-
mentations applied to a specific building energy retrofit application.
pELECTRE Tri uses Monte Carlo simulation to model uncertainties in

the performance matrix values, allowing for a more robust analysis of
decision scenarios [19].

Another key contribution of pELECTRE Tri is its comprehensive
computational explanation of the ELECTRE Tri-B method. By provid-
ing detailed Jupyter notebooks and transparent implementation, the
software enables researchers and practitioners to understand the intri-
cate steps of the ELECTRE Tri sorting procedure. This computational
transparency allows users to explore the method's inner workings,
including the calculation of concordance and discordance indices, the
construction of outranking relations, and the optimist and pessimist
assignment of alternatives to categories.

Summing up, the key features of pELECTRE Tri are:

1. Probabilistic performance matrix: Input data can be represented as probability distributions rather than fixed values.

2. Monte Carlo simulation: Repeated sampling from the input dis-
tributions to generate multiple scenarios.

3. ELECTRE Tri implementation: Application of the outranking
method to each alternative and base profile.

4. Classification probability: likelihood of an alternative belonging to a specific category based on the probability distribution of the performance matrix values.

### 2.2. Usage and integration

Users can easily integrate pELECTRE Tri into their projects without
complex installation procedures. The software's user-friendly approach
involves:

1. Module deployment: simply copy the pELECTRE Tri Python module into the desired project folder.

2. Importing the module: the module can be imported directly into Python scripts or Jupyter notebooks.

3. Data input: input data is in the form of two-dimensional tables stored in .csv files, a format which ensures compatibility and ease of data preparation.

4. Data structures: the module utilizes pandas DataFrames, for readable indexing and data manipulation.

The documentation for pELECTRE Tri follows the “diataxis” frame-
work [20], which organizes information into four distinct categories:

1. Tutorials: step-by-step guides for beginners.

2. How-to guides: practical instructions for specific tasks.

3. Explanations: in-depth discussions of concepts and methodolo-
gies.

4. References: detailed technical information about the module
functions and parameters.

### 2.3. Software architecture

The structure of the module is presented in Fig. 1. The elec-
tre_tri.py module is structured into functional groups:

#### Read functions

These functions handle the input of data describing both crisp
and probabilistic ELECTRE Tri models. They can process base profiles
defined explicitly or derived from extreme levels.

#### Conversion functions

These functions transform extreme levels into base profiles, allowing
for flexibility in how the model is defined.

#### ELECTRE Tri functions

This group implements the ELECTRE Tri method step-by-step, in-
cluding:
<figure><img src="image_5.png" /><figcaption>Fig. 1. Structure of `electre_tri.py` module.</figcaption></figure>

- Concordance

- Discordance

- Global concordance

- Credibility index

- Outranking relation

- Classification

## Composite functions

These functions combine multiple ELECTRE Tri steps into single, more comprehensive operations, streamlining the implementation process.

## Workflows

Complete procedures for both ELECTRE Tri and pELECTRE Tri are implemented here. These workflows encompass the entire process from reading data files to the final classification of alternatives.

## Result functions

Two types of result presentation are provided:

1. Sorted: Classes in ascending order with the alternatives assigned to each class

2. Ranked: Each alternative paired with its assigned class

## Plot functions

These functions generate visual representations of alternatives and base profiles with ranges of indifference, preference, and veto thresholds.

## 3. Impacts

pELECTRE Tri was developed and applied within the framework of the research project *Innovation in Energy Refurbishment* (InER), aimed to tackle energy inefficiency and reduce environmental impact in electrically heated residential buildings. The InER project was initiated and coordinated by Immobilière Rhône Alpes (IRA), Lyon, France, a social housing provider owning more than 20,000 housing units accommodating over 30,000 people [21]. The company refurbishes more than 300 housing units annually [22]. The InER project was supported by ALINOV innovation funds of Action Logement Immobilier, a holding company for all the Action Logement Group's real estate subsidiaries, including 45 social housing enterprises that oversee one million housing units.

This collaboration provided a real-world context for the application of pELECTRE Tri framework and software, addressing the complex challenges of energy renovation in the social housing sector. Two PhD thesis used the framework of pELECTRE Tri [23,24]. A master
thesis that used pELECTRE Tri was awarded the prize Roger Cadiegues 2023 by the French association of engineers of air-conditioning, ventilation, and refrigeration (AICVF) [25] and the 3rd prize at 2024 Student Competition by “Federation of European Heating, Ventilation and Air Conditioning Associations” (REHVA) [26], that represents over 120,000 HVAC designers, building services engineers, technicians, and experts across 27 European countries.

The probabilistic approach introduced by pELECTRE Tri opens up
several new research avenues:

* Exploration of different probability distributions for input parameters and their effects on decision outcomes.

* Development of sensitivity analysis techniques specific to probabilistic MCDM methods.

* Integration of pELECTRE Tri with other decision support tools and methodologies.

## 4. Conclusions

The proposed pELECTRE Tri enhances the traditional ELECTRE Tri Multi-Criteria Decision Making method with probability distributions and Monte Carlo simulation. This innovative methodology offers several key advantages:

1. Provides a more nuanced and realistic representation of complex decision environments, particularly in scenarios with uncertainty, while enabling transparent decision-making that can be interpreted and understood by different actors.

2. Enables better utilization of available resources, especially when dealing with large datasets of measures with diverse features, allowing stakeholders to see how input data influence the decision outcomes.

3. Allows for a more robust categorization of alternatives, supporting informed decision-making processes.

The open-source implementation of pELECTRE Tri in Python ensures accessibility and reproducibility, facilitating further research and practical applications in various fields. Future work could explore the method's applicability, especially how to infer the ELECTRE Tri parameters and standard deviations [27–29].

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

This work was financially supported by 2018 ALINOV innovation funds of Action Logement Immobilier, France, through the project InER - *Innovation dans la Rénovation Énergétique des bâtiments en chauffage collectif électrique* and 3F Immobilière Rhône-Alpes, Groupe Action Logement.

## References

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[25] AICVF, Prix Roger Cadiergues 2023 - Les Lauréats, 2023, [Online]. Available: https://aicvf.org/prix-roger-cadiergues-2023-les-laureats/.

[26] REHVA, REHVA student competition, REHVA Eur. HVAC J. 61 (3) (2024) 63, https://www.rehva.eu/rehva-journal/detail/03-2024.

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[29] E. Fernández, J. Figueira, J. Navarro, An indirect elicitation method for the parameters of the ELECTRE TRI-n-B model using genetic algorithms, Appl. Soft Comput. 77 (2019) 723–733, http://dx.doi.org/10.1016/j.asoc.2019.01.050.