Abstract
The paper presents a new fuzzy set based description which helps to distinguish the expected values of the statistical experiment from the outliers. Since the Neyman-Pearson criterion is not adequate in some real applications for such purpose, we propose to use triangular norms for conjuction of two propositions about typical and non-typical values and describe both of them as a fuzzy set that is called the typical transform. We also investigate such a property of the typical transform as stability.
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References
Bronevich, A.G., Karkishchenko, A.N.: Statistical classes and fuzzy set theoretical classification of probability distributions. In: Statistical Modeling, Analysis and Management of Fuzzy Data, pp. 173–198. Physica-Verl., Heidelberg (2002)
Chateauneuf, A.: Decomposable capacities, distorted probabilities and concave capacities. Mathematical Social Sciences 31, 19–37 (1996)
Dubois, D., Prade, H.: Fuzzy sets and probability: misunderstandings, bridges and gaps In. In: Proc. of the Second IEEE Conderence on Fuzzy Systems, pp. 1059–1068. IEEE (1993)
Hodge, V.J., Austin, J.: A survey of outlier detection methodologies. Artificial Intelligence Review 22(2), 85–126 (2004)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms, 1st edn., p. 387. Springer, Heidelberg (2000)
Mesiarova, A.: Triangular norms and k-Lipschitz property. In: EUSFLAT Conf., pp. 922–926 (2005)
Wallner, A.: Bi-elastic neighbourhood models. In: Proc. of the 3rd International Symposium on Imprecise Probabilities and Their Applications, Lugano, Switzerland, pp. 591–605 (2003)
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Matsypaev, D.A., Bronevich, A.G. (2015). The Fuzzy Representation of Prior Information for Separating Outliers in Statistical Experiments. In: Grzegorzewski, P., Gagolewski, M., Hryniewicz, O., Gil, M. (eds) Strengthening Links Between Data Analysis and Soft Computing. Advances in Intelligent Systems and Computing, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-319-10765-3_20
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DOI: https://doi.org/10.1007/978-3-319-10765-3_20
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10764-6
Online ISBN: 978-3-319-10765-3
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