Preference fusion and Condorcet's Paradox under uncertainty

Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences over certain alternatives under uncertainty, to get a collective representative opinion of the whole community, a preference fusion process is required. The aim of this work is to propose a preference fusion method that copes with uncertainty and escape from the Condorcet paradox. To model preferences under uncertainty, we propose to develop a model of preferences based on belief function theory that accurately describes and captures the uncertainty associated with individual or collective preferences. This work improves and extends the previous results. This work improves and extends the contribution presented in a previous work. The benefits of our contribution are twofold. On the one hand, we propose a qualitative and expressive preference modeling strategy based on belief-function theory which scales better with the number of sources. On the other hand, we propose an incremental distance-based algorithm (using Jousselme distance) for the construction of the collective preference order to avoid the Condorcet Paradox.Comment: International Conference on Information Fusion, Jul 2017, Xi'an, Chin

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, to appea

The Pseudo-Pascal Triangle of Maximum Deng Entropy

PPascal triangle (known as Yang Hui Triangle in Chinese) is an important model in mathematics while the entropy has been heavily studied in physics or as uncertainty measure in information science. How to construct the the connection between Pascal triangle and uncertainty measure is an interesting topic. One of the most used entropy, Tasllis entropy, has been modelled with Pascal triangle. But the relationship of the other entropy functions with Pascal triangle is still an open issue. Dempster-Shafer evidence theory takes the advantage to deal with uncertainty than probability theory since the probability distribution is generalized as basic probability assignment, which is more efficient to model and handle uncertain information. Given a basic probability assignment, its corresponding uncertainty measure can be determined by Deng entropy, which is the generalization of Shannon entropy. In this paper, a Pseudo-Pascal triangle based the maximum Deng entropy is constructed. Similar to the Pascal triangle modelling of Tasllis entropy, this work provides the a possible way of Deng entropy in physics and information theory

Fusion of Information and Analytics: A Discussion on Potential Methods to Cope with Uncertainty in Complex Environments (Big Data and IoT)

International audienceInformation overload and complexity are core problems to most organizations of today. The advances in networking capabilities have created the conditions of complexity by enabling richer, real-time interactions between and among individuals, objects, systems and organizations. Fusion of Information and Analytics Technologies (FIAT) are key enablers for the design of current and future decision support systems to support prognosis, diagnosis, and prescriptive tasks in such complex environments. Hundreds of methods and technologies exist, and several books have been dedicated to either analytics or information fusion so far. However, very few have discussed the methodological aspects and the need of integrating frameworks for these techniques coming from multiple disciplines. This paper presents a discussion of potential integrating frameworks as well as the development of a computational model to evolve FIAT-based systems capable of meeting the challenges of complex environments such as in Big Data and Internet of Things (IoT)

A Decentralized Architecture for Active Sensor Networks

This thesis is concerned with the Distributed Information Gathering (DIG) problem in which a Sensor Network is tasked with building a common representation of environment. The problem is motivated by the advantages offered by distributed autonomous sensing systems and the challenges they present. The focus of this study is on Macro Sensor Networks, characterized by platform mobility, heterogeneous teams, and long mission duration. The system under consideration may consist of an arbitrary number of mobile autonomous robots, stationary sensor platforms, and human operators, all linked in a network. This work describes a comprehensive framework called Active Sensor Network (ASN) which addresses the tasks of information fusion, decistion making, system configuration, and user interaction. The main design objectives are scalability with the number of robotic platforms, maximum flexibility in implementation and deployment, and robustness to component and communication failure. The framework is described from three complementary points of view: architecture, algorithms, and implementation. The main contribution of this thesis is the development of the ASN architecture. Its design follows three guiding principles: decentralization, modularity, and locality of interactions. These principles are applied to all aspects of the architecture and the framework in general. To achieve flexibility, the design approach emphasizes interactions between components rather than the definition of the components themselves. The architecture specifies a small set of interfaces sufficient to implement a wide range of information gathering systems. In the area of algorithms, this thesis builds on the earlier work on Decentralized Data Fusion (DDF) and its extension to information-theoretic decistion making. It presents the Bayesian Decentralized Data Fusion (BDDF) algorithm formulated for environment features represented by a general probability density function. Several specific representations are also considered: Gaussian, discrete, and the Certainty Grid map. Well known algorithms for these representations are shown to implement various aspects of the Bayesian framework. As part of the ASN implementation, a practical indoor sensor network has been developed and tested. Two series of experiments were conducted, utilizing two types of environment representation: 1) point features with Gaussian position uncertainty and 2) Certainty Grid maps. The network was operational for several days at a time, with individual platforms coming on and off-line. On several occasions, the network consisted of 39 software components. The lessons learned during the system's development may be applicable to other heterogeneous distributed systems with data-intensive algorithms