aspg-33-3197-1792223088 20261017074448 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2024 11 2 Shams Najy Elaiwey Department of statistics, Faculty of Administration & Economics, University of Kerbala, Kerbala, Iraq Mahdi Wahab Neama Department of statistics, Faculty of Administration & Economics, University of Kerbala, Kerbala, Iraq 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 01 14 3197 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.0110201 https://americaspg.com/journal/33/article/3197 https://americaspg.com/storage/31725212866.pdf