Fuzzy parameter estimation of the Rayleigh distribution

Fuzziness describes event ambiguity by means of membership functions. Probability describes the uncertainty of an event's occurrence. The primary objective of this paper is to interconnect these two disciplines by suggesting several membership function in case of the scale parameter of a Rayleigh distribution. They are based on confidence intervals and on pivotal quantities which have a normal or a chi(2) - distribution. We have succeeded in designing fuzzy numbers with a sharpness which is related to the underlying sample size. We found that a small sample size has an appreciable adverse impact on the likelihood of the parameter. We were able to improve the estimation by using upper record values.