Using the Nanogonal Membership Function and   Fuzzy Parameters for The Exponential-Rayleigh Distribution of Coved-19

In this paper, we discuss estimating the fuzzy parameters of the Exponential-Rayleigh distribution using the Progressive Censored sample for the Rank Set method to become the proposed Rank Set Sampling estimation Method (RSSEM) in Censoring sample using the Newton-Raphson method to determine the parameter estimate values. Then utilizing Al Karkh General Hospital-Ministry of Health and Environment in Iraq for providing information about the actual data for COVID-19. To ascertain the Chi-square test was used. The distribution of the using sample is the Exponential-Rayleigh distribution. (ER). Then, we estimate the probability density function, hazard function, and survival function. To follow the estimation of the parameters and ER distribution's fuzzy parameters, we use the suggested approach. Moreover, to find the efficiency of the estimators, we use the mean square error of the survival function: