Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/3197 2022 2022 Department of statistics, Faculty of Administration & Economics, University of Kerbala, Kerbala, Iraq Shams Shams Department of statistics, Faculty of Administration & Economics, University of Kerbala, Kerbala, Iraq Mahdi Wahab Neama In this paper, we propose a novel generalization for one parameter inverse Lindley distribution to fitting monotonically descending data named the T-ILD{Y} distribution class ,   T is one parameter inverse exponential distribution ,  R has an one parameter inverse Lindley distribution , and the variable Y is one parameter exponential distribution, the resulting distribution is inverse exponential- inverse Lindley- exponential (IEILDE). The theory of fuzzy sets  are used by converting the distribution to fuzzy by using  a fuzzy triangular distribution based on the quantile function (FIEILE), the maximum likelihood , and the maximum likelihood, and  the maximum product spacing method were used estimate the parameters of the distribution. We conclude that at cutoff α=0.1, ML is better than the MPS, and at cutoff coefficients α=0.3, 0.5, 0.7, MPS was better than the ML, The higher the cutoff, the better the maximum likelihood method. 2024 2024 01 14 10.54216/GJMSA.0110201 https://www.americaspg.com/articleinfo/33/show/3197