Fuzzy set representation of a prior distribution
Glen Meeden
Abstract
In the subjective Bayesian approach uncertainty is described by a prior distribution chosen by the statistician. Fuzzy set theory is another way of representing uncertainty. Here we give a decision theoretic approach which allows a Bayesian to convert their prior distribution into a fuzzy set membership function. This yields a formal relationship between these two different methods of expressing uncertainty.
Full-text: Open access
Permanent link to this document: http://projecteuclid.org/euclid.imsc/1209398462
Digital Object Identifier: doi:10.1214/074921708000000075
References
[1] Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion (with discusion). Statist. Sci. 16 101–133.
[2] de Cooman, G. (2005). A behavioural model for vague probability models. Fuzzy Sets and Systems 154 305–358.
[3] Geyer, C. and Meeden, G. (2005). Fuzzy and randomized confidence intervals and p-values (with discussion). Statist. Sci. 20 358–387.
[4] Klir, G. J., St. Clair, U. H. and Yuan, B. (1997). Fuzzy Set Theory: Foundations and Applications. Prentice Hall PTR, Upper Saddle River, NJ.
[5] Singpurwalla, N. D. and Booker, J. M. (2004). Membership functions and probability measures of fuzzy sets (with discussion). J. Amer. Statist. Assoc. 99 867–889.
[6] Taheri, S. M. (2003). Trends in fuzzy sets. Austrian J. Statist. 32 239–257.
[7] Zadeh, L. (1965). Fuzzy sets. Information and Control 8 338–359.
Institute of Mathematical Statistics Collections
