Developing the pentagonal membership function to estimate the fuzzy parameters of the exponential rayleigh model

Mahmood, Ruqaya Shaker; Al-Harere, Manal N.; Hussein, Iden Hasan

doi:10.47974/JIM-1585

Open Access Research Article

Developing the pentagonal membership function to estimate the fuzzy parameters of the exponential rayleigh model

^*Ruqaya Shaker MahmoodCorresponding authorruqaya.s.mahmood@uotechnology.edu.iqDepartment of Applied SciencesMathematics and Computer ApplicationsUniversity of TechnologyBaghdad, IraqView full profile → , Manal N. Al-HarereManal.N.Alharere@uotechnology.edu.iqDepartment of Applied SciencesMathematics and Computer ApplicationsUniversity of TechnologyBaghdad, IraqView full profile → , Iden Hasan Husseiniden alkanani@yahoo.comDepartment of MathematicsCollege of Science for WomenUniversity of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1591–1599Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1585XML

Published Online:: 29 Nov 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1585
Pages:: 1591–1599

Abstract

In statistics, estimation procedures are applied to estimate the parameters of any model or distribution. In the present paper, an advanced procedure has been used to find the fuzzy parameters for one of the mixed models, the Exponential Rayleigh model (ERM). After deriving the classical estimation technique, the ordinary least square estimation method (OLSEM), the numerical values calculated using Newton-Raphson (NR) method, and the fuzzy interval estimation were applied to create the lower and the upper limits of the pentagonal membership function. Then, the ranking function was formed. Following that, the results were compared depending on the estimated values for survival function before and after the fuzzy with actual data via utilizing the mean squared error technique to manifest which result is the best.

Keywords

Exponential-rayleigh model Survival function Pentagonal membership function Ranking function Mean squared error

Subject Classifications

62A86

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