Parameters Estimation in a Non-Homogeneous Poisson Process with Fuzzy Data Through a Modified Fuzzy Maximum Likelihood Approach Using Artificial Intelligence

The research presents a new framework which enhances spinoff parameter determination of Non-Homogeneous Poisson Processes (NHPP) through the application of Inverse Gompertz distribution as a two-parameter model suitable for survival time evaluation and fuzzy dataset imprecision control. Conventional estimation methods show poor performance in fuzzy datasets, so the research adopts Modified Fuzzy Maximum Likelihood Estimation (MFMLE) together with Particle Swarm Optimization (PSO) which operate in fuzzy environments. Performance evaluations of the proposed methods are based on Root Mean Square Error (RMSE) through extensive Monte Carlo simulations with different parameter settings and sample size scenarios. The researchers applied MATLAB tools to implement and validate this project. Real-world survival data from brain tumor patients in the Holy Governorate of Karbala were used for validating the proposed framework. Research findings benefit the advancement of estimation methods for fuzzy data parameters which specifically focus on survival analysis conditions.