Survival Function Estimation for Weibull Distribution Based on Granular Hesitant Fuzzy Set

Adel  Abbood Najm; Bashar  Khalid Ali

Adel Abbood Najm Department of Statistics, Administration and Economics College, Sumer University, Iraq
Bashar Khalid Ali Department of Statistics, Administration and Economics College, Kerbala University, Iraq

Keywords: Survival function, Weibull distribution, Set of fuzzy, Hesitant set, Granular hesitation set, Estimation

Abstract

This paper proposes a set of fuzzy with granular hesitation (FSGH) that combines the features of set of fuzzy with Hesitation (FSH) and Fuzzy Granular set (FGS) to allow the analysis of fuzzy data by considering multiple possible values of belonging at different levels of granularity, capturing the details of the data and the ambiguity associated with determining the exact belonging, making it particularly useful in the context of complex decision making. The suggested set is applied to the Weibull distribution, and Monte Carlo simulation studies are conducted to explain behavior of the suggested approach and compare it to the standard sample method. It is found that the suggested FSGH outperforms the typical Weibull distribution data set, with the approach achieving the lowest error criteria, particularly in big data sets. The method's accuracy improves as the frequency and granularity increase.

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