Abstract
In this paper we extend a methodology for constructing a frame of discernment from belief functions for one problem, into a methodology for constructing multiple frames of discernment for several different subproblems. The most appropriate frames of discernment are those that let our evidence interact in an interesting way without exhibit too much internal conflict. A function measuring overall frame appropriateness is mapped onto a Potts spin neural network in order to find the partition of all belief functions that yields the most appropriate frames.
This work was supported by the FOI research project “Real-Time Simulation Supporting Effects-Based Planning”, which is funded by the R&D programme of the Swedish Armed Forces.
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Schubert, J.: Constructing and Reasoning about Alternative Frames of Discernment. In: Proceedings of the Workshop on the Theory of Belief Functions, paper 24, pp. 1–6 (2010), http://www.ensieta.fr/belief2010/papers/p24.pdf
Dempster, A.P.: A Generalization of Bayesian Inference. Journal of the Royal Statistical Society B 30, 205–247 (1968)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Schubert, J.: On Nonspecific Evidence. International Journal of Intelligent Systems 8, 711–725 (1993)
Schubert, J.: Specifying Nonspecific Evidence. International Journal of Intelligent Systems 11, 525–563 (1996)
Schubert, J.: Managing Inconsistent Intelligence. In: Proceedings of the Third International Conference on Information Fusion, pp. TuB4/10–16. International Society of Information Fusion, Sunnyvale (2000)
Bengtsson, M., Schubert, J.: Dempster-Shafer Clustering using Potts Spin Mean Field Theory. Soft Computing 5, 215–228 (2001)
Schubert, J.: Clustering Belief Functions Based on Attracting and Conflicting Metalevel Evidence Using Potts Spin Mean Field Theory. Information Fusion 5, 309–318 (2004)
Schubert, J.: Clustering Decomposed Belief Functions Using Generalized Weights of Conflict. International Journal of Approximate Reasoning 48, 466–480 (2008)
Ahlberg, S., Hörling, P., Johansson, K., Jöred, K., Kjellström, H., Mårtenson, C., Neider, G., Schubert, J., Svenson, P., Svensson, P., Walter, J.: An Information Fusion Demonstrator for Tactical Intelligence Processing in Network-Based Defense. Information Fusion 8, 84–107 (2007)
Schubert, J.: Finding a Posterior Domain Probability Distribution by Specifying Nonspecific Evidence. International Journal of Uncertainty, Fuzziness and Knowledge- Based Systems 3, 163–185 (1995)
Schubert, J., Sidenbladh, H.: Sequential Clustering with Particle Filters - Estimating the Number of Clusters from Data. In: Proceedings of the Eighth International Conference on Information Fusion, paper A4-3, pp. 1–8. IEEE, Piscataway (2005)
Chau, C.W.R., Lingras, P., Wong, S.K.M.: Upper and Lower Entropies of Belief Functions Using Compatible Probability Functions. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS (LNAI), vol. 689, pp. 306–315. Springer, Heidelberg (1993)
Maeda, Y., Ichihashi, H.: An Uncertainty Measure with Monotonicity under the Random Set Inclusion. International Journal of General Systems 21, 379–392 (1993)
Harmanec, D., Klir, G.J.: Measuring Total Uncertainty in Dempster-Shafer Theory: A novel approach. International Journal of General Systems 22, 405–419 (1994)
Meyerowitz, A., Richman, F., Walker, E.: Calculating Maximum-Entropy Probability for Belief Functions. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 2, 377–389 (1994)
Harmanec, D., Resconi, G., Klir, G.J., Pan, Y.: On the Computation of Uncertainty Measure in Dempster-Shafer Theory. International Journal of General Systems 25, 153–163 (1996)
Wu, F.Y.: The Potts model. Reviews of Modern Physics 54, 235–268 (1982)
Peterson, C., Söderberg, B.: A New Method for Mapping Optimization Problems onto Neural Networks. International Journal of Neural Systems 1, 3–22 (1989)
Schubert, J.: Fast Dempster-Shafer Clustering Using a Neural Network Structure. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds.) Information, Uncertainty and Fusion. SECS, vol. 516, pp. 419–430. Kluwer Academic Publishers, Boston (1999)
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Schubert, J. (2010). Constructing Multiple Frames of Discernment for Multiple Subproblems. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_20
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DOI: https://doi.org/10.1007/978-3-642-14055-6_20
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