Abstract
This paper presents a method of classifying statistical classes that can be considered as empirical images of probability spaces. For statistical classes we introduce level sets with the help of which set-theoretic operations over statistical classes are defined. Particularly, we define measures of mutual inclusion and equality of arbitrary classes that provide the classification problem solution. We also show that these measures are well justified and consider connection between introduced structure and traditional axiomatic theory of fuzzy sets. Further we algebraically generalize the concept of statistical classes and investigate the connection of generalized classes with the possibility theory.
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© 2002 Springer-Verlag Berlin Heidelberg
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Bronevich, A.G., Karkishchenko, A.N. (2002). Statistical classes and fuzzy set theoretical classification of probability distributions. In: Bertoluzza, C., Gil, MÁ., Ralescu, D.A. (eds) Statistical Modeling, Analysis and Management of Fuzzy Data. Studies in Fuzziness and Soft Computing, vol 87. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1800-0_12
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DOI: https://doi.org/10.1007/978-3-7908-1800-0_12
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2501-5
Online ISBN: 978-3-7908-1800-0
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