Air Defense Threat Evaluation using Fuzzy Bayesian Classifier

Wei Mei

Abstract

The connection between probability and fuzzy sets has been investigated among the community of approximate reasoning for decades. A typical viewpoint is that the grade of membership could be interpreted as a conditional probability. This note extend this viewpoint a step further by introducing the concepts of conditional probability mass function (CPMF) and the likelihood mass function (LMF). We draw the conclusion that conditional probability can be used for describing either randomness or fuzziness depending on how it is interpreted. If expanded to CPMF, then it can be used for modelling randomness; if expanded to LMF, then it can be a useful expression for modelling fuzziness. A fuzzy Bayesian theorem is derived based on the fuzziness interpretation of conditional probability. Its successful application to an example of target recognition demonstrates that the proposed fuzzy Bayesian theorem provides alternative approach for handling uncertainty.

References

  1. Bailadora, G., TriviƱo, G., 2010. Pattern recognition using temporal fuzzy automata. Fuzzy Sets and Systems, 161, 37-55.
  2. Clausewitz, C. V., Graham, J. J., Honig, J. W., 2004. On War, Barnes & Noble Publishing.
  3. Cheeseman, P., 1988. Probabilistic versus fuzzy reasoning. Uncertainty in Artificial Intelligence, North-Holland, Amsterdam, Vol. 1, 85-102.
  4. Chen, C. H., Ho, P. P., 2008. Statistical pattern recognition in remote sensing. Pattern Recognition, 41(9), 2731- 2741.
  5. Coletti, G., Scozzafava, R., 2004. Conditional probability, fuzzy sets, and possibility: a unifying view. Fuzzy Sets and Systems, 144, 227-249.
  6. Delmotte, F., Smets, P., 2004. Target identification based on the transferable belief model interpretation of Dempster-Shafer model. IEEE Trans. On Systems, Man, and Cybernetics - Part A: Systems and Humans, 34, 457-471.
  7. Dubois, D., Moral, S., Prade, H., 1997. A semantics for possibility theory based on likelihoods. Journal of Mathematic Analysis and Applications, 205, 359-380.
  8. Dubois, D., Foulloy, L., etc, 2004. Probability-possibility transformations, Triangular fuzzy sets, and probabilistic inequalities, Reliable Computing, 10, 273-297
  9. Jain, A. K., Duin, R. P. W., Mao, J., 2000. Statistical pattern recognition: a review. IEEE Trans. On Pattern Analysis and Machine Intelligence, 22, 4-37.
  10. Jan, T., 2004. Neural network based threat assessment for automated visual surveillance. Proc. of 2004 IEEE International Joint Conference on Neural Networks, Vol.2, 1309 - 1312.
  11. Lane, R.O., Nevell, D.A., Hayward, S.D., Beaney, T.W., 2010. Maritime anomaly detection and threat assessmen. Proc. of the 13th Conference on Information Fusion, QinetiQ, UK, pp1-8.
  12. Leung, H., Wu, J., 2000. Bayesian and Dempster-Shafer target identification for radar surveillance. IEEE Trans. on Aerospace and Electronic Systems, 36, 432- 447.
  13. Mouchaweh, M. S., Billaudel, P., 2006. Variable Probability-Possibility Transformation for the Diagnosis by Pattern Recognition. International Journal of Computational Intelligence: Theory and Practice, 1(1 ).
  14. Oussalah, M., 2000. On the probability/possibility transformations: a comparative analysis. Journal of General Systems, 29(5), 671-718.
  15. Paradis, S., Benaskeur, A., Oxenham, M.G., Cutler, P., 2005. Threat evaluation and weapon allocation in network-centric warfare. Proc. of the 7th International Conference on Information Fusion, Stockholm, 1078- 1085
  16. Roux, J. N., Vuuren, J. H., 2007. Threat evaluation and weapon assignment decision support: a review of the state of the art. ORiON, 23(2), 151-187.
  17. Steinberg, A. N., 2005. An approach to threat assessment. Proc. of the 8th International Conference on Information Fusion, Vol. 2, Philadelphia, USA, 1256- 1263.
  18. Xu, Y., Wang, Y., Miu, X., 2012. Multi-attribute decision making method for air target threat evaluation based on intuitionistic fuzzy sets. Journal of Systems Engineering and Electronics, 23(6), 891-897.
  19. Young, S.S., Scott, P.D., Nasrabadi, N.M., 1997. Object recognition using multilayer Hopfield neural network. IEEE Trans. On Image processing, 357-372.
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Paper Citation


in Harvard Style

Mei W. (2013). Air Defense Threat Evaluation using Fuzzy Bayesian Classifier . In Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013) ISBN 978-989-8565-77-8, pages 227-232. DOI: 10.5220/0004512602270232


in Bibtex Style

@conference{fcta13,
author={Wei Mei},
title={Air Defense Threat Evaluation using Fuzzy Bayesian Classifier},
booktitle={Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013)},
year={2013},
pages={227-232},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004512602270232},
isbn={978-989-8565-77-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013)
TI - Air Defense Threat Evaluation using Fuzzy Bayesian Classifier
SN - 978-989-8565-77-8
AU - Mei W.
PY - 2013
SP - 227
EP - 232
DO - 10.5220/0004512602270232