Abstract
This paper deals with belief change in the framework of Dempster-Shafer theory in the context where an agent has a prejudice, i.e., a priori knowledge about a situation. This situation is modeled as a sequence (p, m) where p reflects the prejudices of an agent and m is a mass function that represents the agent’s uncertain beliefs. In contrast with the Latent Belief Structure introduced by Smets where a mass is decomposed into a pair of separable mass functions called respectively the confidence and diffidence, m can be any mass function (i.e., not necessarily separable) and p is not a mass. The aim of our study is to propose a framework in which the evolution of prejudices and beliefs are described through the arrival of new beliefs. Several cases of prejudice are described: the strong persistent prejudice (which never evolves and forbids beliefs to change), the prejudice that is slightly decreasing each time a belief contradicts it, etc.
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Notes
- 1.
“(good or bad) opinion that one forms in advance” (Lanoue, Discours pol. et milit., 436 in Littré,1587).
- 2.
A mass is dogmatic when \(m(\varOmega )=0\).
- 3.
Specialization was introduced in [6], m specializes \(m'\) iff there exists a square matrix \(\Sigma \) with general term \(\sigma (A,B)\) being a proportion (i.e., verifying \(\sum _{A}\sigma (A,B)=1\), for any B. \(\sigma (A,B)>0\) implies \(A\subseteq B\) for any A, B) such that \(m(A)=\sum _B \sigma (A,B)m'(B)\) for all A. In [12], the definition of specialization matrix is taken in a broader sense: only imposing that \(\sigma (A,B)>0\) implies \(A\cap B\ne \emptyset \) for any A, B.
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Dupin de Saint-Cyr, F., Faux, F. (2024). Integrating Evolutionary Prejudices in Belief Function Theory. In: Bouraoui, Z., Vesic, S. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2023. Lecture Notes in Computer Science(), vol 14294. Springer, Cham. https://doi.org/10.1007/978-3-031-45608-4_30
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