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Exploiting Vagueness for Multi-agent Consensus

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Multi-agent and Complex Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 670))

Abstract

A framework for consensus modelling is introduced using Kleene’s three valued logic as a means to express vagueness in agents’ beliefs. Explicitly borderline cases are inherent to propositions involving vague concepts where sentences of a propositional language may be absolutely true, absolutely false or borderline. By exploiting these intermediate truth values, we can allow agents to adopt a more vague interpretation of underlying concepts in order to weaken their beliefs and reduce the levels of inconsistency, so as to achieve consensus. We consider a consensus combination operation which results in agents adopting the borderline truth value as a shared viewpoint if they are in direct conflict. Simulation experiments are presented which show that applying this operator to agents chosen at random (subject to a consistency threshold) from a population, with initially diverse opinions, results in convergence to a smaller set of more precise shared beliefs. Furthermore, if the choice of agents for combination is dependent on the payoff of their beliefs, this acting as a proxy for performance or usefulness, then the system converges to beliefs which, on average, have higher payoff.

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Notes

  1. 1.

    In preliminary experiments we found that 50, 000 was an upper bound on the number of iterations required for the system to reach steady state across a range of parameter settings.

  2. 2.

    As a result of this Boolean initialisation, a language size of 5 now produces a total of \(2^5\) (32) possible valuations, as opposed to \(3^5\) (243) possible valuations.

References

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Acknowledgments

This research is partially funded by an EPSRC PhD studentship as part of a doctoral training partnership (DTP).

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Authors and Affiliations

  1. Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1UB, UK

    Michael Crosscombe & Jonathan Lawry

Authors
  1. Michael Crosscombe
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  2. Jonathan Lawry
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Corresponding author

Correspondence to Michael Crosscombe .

Editor information

Editors and Affiliations

  1. Auckland University of Technology, Auckland, New Zealand

    Quan Bai

  2. University of Wollongong, Wollongong, New South Wales, Australia

    Fenghui Ren

  3. Tokyo University of Agriculture and Technology, Koganei, Tokyo, Japan

    Katsuhide Fujita

  4. University of Wollongong, Wollongong, New South Wales, Australia

    Minjie Zhang

  5. Nagoya Institute of Technology, Nagoya, Japan

    Takayuki Ito

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Crosscombe, M., Lawry, J. (2017). Exploiting Vagueness for Multi-agent Consensus. In: Bai, Q., Ren, F., Fujita, K., Zhang, M., Ito, T. (eds) Multi-agent and Complex Systems. Studies in Computational Intelligence, vol 670. Springer, Singapore. https://doi.org/10.1007/978-981-10-2564-8_5

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  • DOI: https://doi.org/10.1007/978-981-10-2564-8_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2563-1

  • Online ISBN: 978-981-10-2564-8

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