Abstract
This paper considers the problem of the possibility representation of measurement uncertainty in the cases of information shortage: very few measurements, poor knowledge about the underlying probability distribution. After having related possibility distribution to probability confidence intervals, we present a procedure to build a possibility distribution for one measurement issued from an unimodal probability distribution. We consider then the addition of other measurements and more knowledge about the probability distribution. The key role of the uniform distribution as the probability distribution leading to the least specific possibility distribution is highlighted. The approach is compared and discussed versus the conventional one based on the Student distribution.
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References
Anděl, J.: Confidence intervals for the mode based on one observation. Zb Rad. 5, 87–96 (1991)
Baudrit, C., Dubois, D.: Practical representation of incomplete probabilistic information. Comput. Statist. Data Anal. 51(1), 86–108 (2006)
Dubois, D., Fodor, J.C., Prade, H., Roubens, M.: Aggregation of decomposable measures with applications to utility theory. Theory and Decision 41(1), 195–223 (1996)
Dubois, D., Foulloy, L., Mauris, G., Prade, H.: Probability-possibility transformations, triangular fuzzy sets and probabilistic inequalities. Reliab. Comput. 10(4), 273–297 (2004)
Dubois, D., Prade, H.: On several representations of an uncertain body of evidence. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes, pp. 167–181. North-Holland, Amsterdam (1982)
Dubois, D., Prade, H., Sandri, S.: On possibility/probability transformations. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic, pp. 103–112 (1993)
Ferrero, A., Salicone, S.: The random-fuzzy variables: a new approach to the expression of uncertainty. IEEE Trans. Instrum. Meas. 53(5), 1370–1377 (2004)
ISO-IEC-OIML-BIPM, Guide to the Expression of Uncertainty in Measurement, 2nd edn. (1995)
Kendall, M., Stuart, A.: The Advanced Theory of Statistics, vol. 1. Charles Griffin, London (1977)
Machol, R.E., Rosenblatt, J.: Confidence interval based on single observation. Proceedings of IEEE 54(8), 1087–1088 (1966)
Mari, L., Zingales, G.: Uncertainty in measurement science. In: Proceedings of the Int. Workshop on Advances of Measurement Science (Kyoto, Japan), pp. 177–189 (1999)
Mauris, G., Lasserre, V., Foulloy, L.: Fuzzy modeling of measurement data acquired from physical sensors. IEEE Trans. Instrum. Meas. 49(6), 1201–1205 (2000)
Mauris, G., Lasserre, V., Foulloy, L.: A fuzzy approach for the expression of uncertainty in measurement. Measurement 29(3), 165–177 (2001)
Moore, R.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)
Moral, M.: Constructing of possibility distribution from a probability distribution. In: Jones, A., Kauffmann, A., Zimmermann, H.J. (eds.) Fuzzy Sets Theory and Applications, pp. 51–60 (1986)
Reznik, L., Dabke, K.P.: Evaluation of uncertainty in measurement: a proposal for application of intelligent methods. In: Proceedings of the XV IMEKO World Congress (Osaka, Japan), vol. II, pp. 93–100 (1999)
Urbanski, M., Wasowski, J.: Fuzzy approach to the theory of measurement inexactness. Measurement 34, 67–74 (2003)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1(1), 3–28 (1978)
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Mauris, G. (2008). Inferring a Possibility Distribution from Very Few Measurements. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85027-4_12
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DOI: https://doi.org/10.1007/978-3-540-85027-4_12
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