6,051 research outputs found
Consensus in the Presence of Multiple Opinion Leaders: Effect of Bounded Confidence
The problem of analyzing the performance of networked agents exchanging
evidence in a dynamic network has recently grown in importance. This problem
has relevance in signal and data fusion network applications and in studying
opinion and consensus dynamics in social networks. Due to its capability of
handling a wider variety of uncertainties and ambiguities associated with
evidence, we use the framework of Dempster-Shafer (DS) theory to capture the
opinion of an agent. We then examine the consensus among agents in dynamic
networks in which an agent can utilize either a cautious or receptive updating
strategy. In particular, we examine the case of bounded confidence updating
where an agent exchanges its opinion only with neighboring nodes possessing
'similar' evidence. In a fusion network, this captures the case in which nodes
only update their state based on evidence consistent with the node's own
evidence. In opinion dynamics, this captures the notions of Social Judgment
Theory (SJT) in which agents update their opinions only with other agents
possessing opinions closer to their own. Focusing on the two special DS
theoretic cases where an agent state is modeled as a Dirichlet body of evidence
and a probability mass function (p.m.f.), we utilize results from matrix
theory, graph theory, and networks to prove the existence of consensus agent
states in several time-varying network cases of interest. For example, we show
the existence of a consensus in which a subset of network nodes achieves a
consensus that is adopted by follower network nodes. Of particular interest is
the case of multiple opinion leaders, where we show that the agents do not
reach a consensus in general, but rather converge to 'opinion clusters'.
Simulation results are provided to illustrate the main results.Comment: IEEE Transactions on Signal and Information Processing Over Networks,
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Evidence Propagation and Consensus Formation in Noisy Environments
We study the effectiveness of consensus formation in multi-agent systems
where there is both belief updating based on direct evidence and also belief
combination between agents. In particular, we consider the scenario in which a
population of agents collaborate on the best-of-n problem where the aim is to
reach a consensus about which is the best (alternatively, true) state from
amongst a set of states, each with a different quality value (or level of
evidence). Agents' beliefs are represented within Dempster-Shafer theory by
mass functions and we investigate the macro-level properties of four well-known
belief combination operators for this multi-agent consensus formation problem:
Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging
operator. The convergence properties of the operators are considered and
simulation experiments are conducted for different evidence rates and noise
levels. Results show that a combination of updating on direct evidence and
belief combination between agents results in better consensus to the best state
than does evidence updating alone. We also find that in this framework the
operators are robust to noise. Broadly, Yager's rule is shown to be the better
operator under various parameter values, i.e. convergence to the best state,
robustness to noise, and scalability.Comment: 13th international conference on Scalable Uncertainty Managemen
Other uncertainty theories based on capacities
International audienceThe two main uncertainty representations in the literature that tolerate imprecision are possibility distributions and random disjunctive sets. This chapter devotes special attention to the theories that have emerged from them. The first part of the chapter discusses epistemic logic and derives the need for capturing imprecision in information representations. It bridges the gap between uncertainty theories and epistemic logic showing that imprecise probabilities subsume modalities of possibility and necessity as much as probability. The second part presents possibility and evidence theories, their origins, assumptions and semantics, discusses the connections between them and the general framework of imprecise probability. Finally, chapter points out the remaining discrepancies between the different theories regarding various basic notions, such as conditioning, independence or information fusion and the existing bridges between them
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