• PhD Student:
  • Chouaib Fellah
  • Co-Supervisor :
  • Patricia Everaere (CRIStAL)
  • Funding : ANR
  • PhD defended on :
  • Dec 18, 2023

This work constitutes a contribution to the study of information fusion, primarily using propositional logic for information representation. More specifically, we are examining fusion processes that are precisely described by mathematical functions called belief merging operators.

Belief merging operators aim to construct a coherent belief base that satisfies integrity constraints and is best aligned with a set of belief bases (a profile), which often contains conflicting information. This framework, proposed by Konieczny and Pino Pérez (2002), serves as the starting point for our work. In this framework, it is assumed that all the bases in the set of belief bases comprising the profile have the same importance (reliability). However, in many situations, the bases have different degrees of importance. Therefore, it is necessary to have a formal framework where operators exist to rationally consider a set of belief bases with varying degrees of importance. It is in response to this necessity that we develop the framework of weighted merging operators with integrity constraints.

We provide a syntactic characterization in terms of rationality postulates and a semantic representation theorem. This semantic representation theorem is the fundamental tool that allows us to define important families of operators using distances, weight functions, and aggregation functions.

We also define families of operators using utilities, utility weight functions, and utility aggregation functions. These families differ from those defined using distances, and some exhibit remarkable egalitarian behavior. Another contribution of our work lies again in the realm of classical merging, i.e., within the framework of merging operators with integrity constraints. In particular, we study two families of operators inspired by two different views of the Borda rule. We define a new fusion property, inspired by the property of social choice cancellation, and prove that one of the families is characterized by this new property.