The Fuzzified Log-Rank Test Procedure for Comparing More Than Two Groups

Objectives: To extend the conventional log-rank test to handle fuzzy data, accommodating the inherent uncertainty and vagueness in illustrative data. To create a statistical procedure that can compare survival distributions across more than two groups. Methods: The log-rank test is a familiar non-parametric methodology used to compare the survival experiences of two or more groups of subjects. This study applies fuzzification procedures to survival data, transforming precise survival times and event indicators into fuzzy numbers. Findings: When fuzziness is attributed to the survival data, the proposed method shows less potential and is unable to produce reliable results. However, the fuzzified log-rank test outperforms conventional methods when dealing with uncertain or imprecise data, providing more reliable results. Novelty: Unlike conventional log-rank tests that are typically limited to two groups, the proposed method can simultaneously compare survival distributions across three groups, providing a more comprehensive survival analysis. This article suggests a new procedure that can accommodate the fuzziness in the data. The fuzzified log-rank test enhances the analytical capability of survival analysis and represents a novel contribution to statistical methodologies in medical and survival research. Keywords: Fuzziness, Survival Data, Log-Rank Test, Three Groups, Defuzzification