Neutrosophic Sets and Systems
Abstract
The Quadratic Transmuted Generalized Exponential Distribution (QTGED) enhances the general ized exponential distribution, making it a significant development for handling complex decision-making con texts. Traditional statistical distributions often focus on representing degrees of truth or membership in fuzzy sets, yet they struggle to capture situations involving incomplete, vague, or contradictory data accurately. This study introduces the Neutrosophic Quadratic Transmuted Generalized Exponential Distribution (NQTGED), specifically designed to address indeterminacy and transmuted data. Neutrosophic theory is essential here, as it overcomes the limitations of classical and fuzzy set theories by effectively managing uncertainty, indetermi nacy, and inconsistency in data. By simultaneously representing truth, indeterminacy, and falsity, neutrosophic sets offer a comprehensive framework for modeling uncertainty. Traditional distributions lack the adaptability needed for evolving data complexities, often falling short when faced with non-standard data distributions or outliers. Addressing these challenges requires innovative approaches that incorporate advanced mathematical models for uncertainty. This is especially valuable in real-world situations, where data is frequently incomplete, imprecise, or contradictory, and sometimes transmuted. The study derives various mathematical properties of the model, assesses parameter estimation using maximum likelihood and simulation, and demonstrates practical applications with cancer remission data. Simulation results reveal that Neutrosophic Average Biases (NABs) and Neutrosophic Mean Square Errors (NMSEs) decrease as sample sizes increase, indicating strong and ac curate parameter estimation. NQTGED provides superior fit and performance, offering significant insights for applications in reliability engineering and biomedical sciences.
Recommended Citation
Gnanasegaran, Kumarapandiyan; Benitta Susan Aniyan; and Abdul Kani Jabarali. "Neutrosophic Formulation of the Quadratic Transmuted Generalized Exponential Distribution: Properties and Applications." Neutrosophic Sets and Systems 80, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol80/iss1/2
