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This paper is interested in the Bayesian and non-Bayesian estimation of the stress-strength model and the mean remaining strength when there is fuzziness for stress and strength random variables having Lindley's distribution with different parameters. A fuzzy is defined as a function of the difference between stress and strength variables. In the context of Bayesian estimation, two approximate algorithms are used importance sampling algorithm and the Monte Carlo Markov chain algorithm. For non-Bayesian estimation, maximum likelihood estimation and maximum product of spacing method are used. The Monte Carlo simulation study is performed to compare between different estimators for our proposed models using statistical criteria. Finally, to show the ability of our proposed models in real life, real medical application is introduced., Competing Interests: No conflict-of-interest statement was included., (Copyright © 2023 Marwa K. H. Hassan and Abdisalam Hassan Muse.)