Application de la classification automatique classique et floue au partage équitable des ressources divisibles homogènes

This doctoral research aims to develop and analyze methods for the fair division of homogeneous divisible resources using automatic classification, in both classical and fuzzy environments. The work is based on the observation that traditional division methods (such as proportional, adjusted proportional, or Talmud-based rules) consider only the nature of the resource and the individuals’ claims, while neglecting the plurality and type of variables, as well as the origin of the resources (whether contributed or not). The main objective is to propose distribution procedures that integrate clustering to organize beneficiaries according to their characteristics and claims, while applying inequality-reduction mechanisms to ensure a more equitable allocation, particularly favoring the most disadvantaged individuals. The methods introduced include: PRRC (Resource Distribution Process Based on Classification Results) in classical and fuzzy environments. PRRG (Resource Distribution Process at the Group Level). PCo (Corrected Proportional Rule). These methods are compared to existing rules in the literature (P and PA) to evaluate their performance in terms of equity, beneficiary preferences, and inequality reduction. The study relies on rigorous mathematical and statistical analyses, including data transformation and normalization when variables are heterogeneous, as well as aggregation of multiple values per individual into a total value. Expected outcomes: A formal demonstration that the proposed methods provide more equitable allocations than traditional methods. A comparative analysis showing that the poorest beneficiaries generally prefer the allocations generated by the PRRC, PRRG, and PCo methods. The establishment of a practical framework applicable to homogeneous resource-sharing situations, with potential extensions to fuzzy environments or more complex resources. In summary, this thesis offers an original contribution to both the theory and practice of fair resource allocation by combining clustering with inequality reduction, providing a robust analytical tool for distributive decision-making.