Modelling uncertain wastewater treatment data using neutrosophic transmuted log-logistic distribution

This study presents the Neutrosophic Transmuted Log-logistic Distribution (NTLLD), which is particularly designed to handle indeterminacy and transmuted data. Since neutrosophic theory successfully manages uncertainty, indeterminacy, and inconsistency in data, it solves the drawbacks of fuzzy set and classical theories. For modelling uncertainty, neutrosophic sets provide a complete framework by capturing truth, indeterminacy, and falsity all at once. Transmuting the log-logistic, another name for the distribution is the quadratic transmuted log-logistic distribution, which extends the log-logistic distribution and is a major advancement for managing intricate decision-making situations. A comprehensive neutrosophic description of the statistical properties of the NTLLD is presented. For estimating neutrosophic parameters, the maximum likelihood estimation approach, based on a neutrosophic environment, is employed. A Monte Carlo simulation study was used to examine the performance of these neutrosophic estimators in terms of their neutrosophic mean squared errors (NMSEs) and neutrosophic average biases (NAB) of the parameters. According to simulation studies, NAB and NMSE decline with increasing sample numbers, suggesting a robust and precise parameter estimate. Superior fit and performance are offered by NTLLD, which also offers important insights for applications in health sciences and reliability engineering. In particular, the produced distribution is useful for modelling uncertain data. The usefulness of the NTLLD for data modelling is illustrated using wastewater treatment data, and a few recently suggested neutrosophic distributions are also contrasted.