M.L. Estimator for Fuzzy Survival Function to the Kidney Failure Patients

Iftikhar Abd Ulhameed Alnaqash, Suha Jafar Abdel Sahib


The dependence of traditional statistical methods in finding estimators and testing hypotheses depends on data that take specific values. However, uncertainty (Fuzzy) appears in most data, including survival time data, which requires researchers to apply Fuzzy methods in general when finding estimators, particularly the estimators of a survival function. In this research, the experimental method (simulation) was used to compare Fuzzy methods (definition of fuzzy logic, cut level -δ, Buckley) at three fuzzy degrees (0, 0.5, 1), for selected survival times (t = 2, 4, 6, 8, 10, 12) in days. To determine the best fuzzy method used to find the Maximum Likelihood Estimators of the fuzzy survival function depends on the Avery Mean Squares Error (AMES) for the lower and upper bound estimators of the fuzzy survival function for each method. From the experimental method, we came to an advantage of defining fuzzy logic for the maximum likelihood estimator for the survival function of Weibull distribution (distribution of survival times data in the research). The maximum likelihood estimator calculated according to the method of defining fuzzy logic for patients' survival times with kidney failure collected from sections of the dialysis department in educational hospitals (Baghdad, Al-Kindi, Al-Karama, Al-Kadhimiya). This research found that the probability of fuzzy survival for two days to the patients with kidney failure reaches 0.7504 and this probability decreases with an increase in the time of stay until it reaches 0.07704 the probability of staying for a month.


fuzzy logic; survival times; fuzzy survival function; cut level -δ; buckley.

Full Text:



Kilpatrick, J. (2011). Expert systems and mass appraisal. Journal of Property Investment and Finance, 29(4-5), 529-550.‏

Chaturvedi, A., Singh, S. K., & Singh, U. (2018). Statistical inferences of type-II progressively hybrid censored fuzzy data with Rayleigh distribution. Austrian Journal of Statistics, 47(3), 40-62.‏

Azadeh, M. A., Keramati, A., Tolouei, H., Parvari, R., & Pashapour, S. (2013). Estimation and optimisation of right-censored data in survival analysis by neural network. International Journal of Business Information Systems, 14(3), 322-334.‏

Jain, S. (2017). Parametric and non parametric distribution analysis of AkT for cell survival/death. International Journal of Artificial Intelligence and Soft Computing, 6(1), 43-55.‏

Hamsyiah, N., Nisa, K., & Warsono, W. (2017). Parameter Estimation of Bernoulli Distribution using Maximum Likelihood and Bayesian Methods. In Prosiding Seminar Nasional METODE KUANTITATIF 2017. Jurusan Matematika FMIPA Unila.‏

Al-Hemyari, Z. A., & Al-Dolami, J. A. (2012). Optimised Shrinkage Testimator of reliability function in a failure-time model. International Journal of Mathematics in Operational Research, 4(6), 607-621.‏

Zhang, J., Stewart, J. M., & Wang, T. (2005). Linkage analysis between gametophytic restorer Rf2 gene and genetic markers in cotton. Crop science, 45(1), 147-156.‏

Yunus, N. A. M., Zainudin, M. A., Sulaiman, N., & Abbas, Z. A. (2018, November). Microfluidic Fluid Flow Design with Arduino Relay and Temperature Controller for Processor. In 2018 IEEE 5th International Conference on Smart Instrumentation, Measurement and Application (ICSIMA) (pp. 1-4). IEEE.

Sharaf, H. K., Ishak, M. R., Sapuan, S. M., Yidris, N., & Fattahi, A. (2020). Experimental and numerical investigation of the mechanical behavior of full-scale wooden cross arm in the transmission towers in terms of load-deflection test. Journal of Materials Research and Technology, 9(4), 7937-7946.‏

Dehkordi, A. N., & Koohestani, S. (2019). The Influence of Signal to Noise Ratio on the Pharmacokinetic Analysis in DCE-MRI Studies. Frontiers in Biomedical Technologies.‏

Compare, M., Martini, F., Mattafirri, S., Carlevaro, F., & Zio, E. (2016). Semi-Markov model for the oxidation degradation mechanism in gas turbine nozzles. IEEE Transactions on Reliability, 65(2), 574-581.‏

Inan, D., & Sancar, N. (2020). Particle swarm optimization based ridge logistic estimator. Communications in Statistics-Simulation and Computation, 49(3), 669-683.‏

Sharaf, H. K., Ishak, M. R., Sapuan, S. M., & Yidris, N. (2020). Conceptual design of the cross-arm for the application in the transmission towers by using TRIZ–morphological chart–ANP methods. Journal of Materials Research and Technology, 9(4), 9182-9188.‏

Chen, T., Zheng, S., & Feng, J. (2017). Statistical dependency analysis of multiple competing failure causes of fuel cell engines. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 231(2), 83-90.‏

Alzabari, S. A. H., Talab, H. R., & Flayyih, H. H. (2019). The Effect of Internal Training and Auditing of Auditors on Supply Chain Management: An Empirical Study in Listed Companies of Iraqi Stock Exchange for the Period 2012-2015. Int. J Sup. Chain. Mgt Vol, 8(5), 1070.‏

Sharaf, H. K., Salman, S., Dindarloo, M. H., Kondrashchenko, V. I., Davidyants, A. A., & Kuznetsov, S. V. (2021). The effects of the viscosity and density on the natural frequency of the cylindrical nanoshells conveying viscous fluid. The European Physical Journal Plus, 136(1), 1-19.‏

Falk, M., & Marohn, F. (2000). On the loss of information due to nonrandom truncation. Journal of multivariate analysis, 72(1), 1-21.‏

Sharaf, H. K., Salman, S., Abdulateef, M. H., Magizov, R. R., Troitskii, V. I., Mahmoud, Z. H., ... & Mohanty, H. (2021). Role of initial stored energy on hydrogen microalloying of ZrCoAl (Nb) bulk metallic glasses. Applied Physics A, 127(1), 1-7.‏

DOI: http://dx.doi.org/10.18517/ijaseit.11.2.14081


  • There are currently no refbacks.

Published by INSIGHT - Indonesian Society for Knowledge and Human Development