Statistical hypothesis testing under imprecise data using normalized hexagonal fuzzy numbers and fuzzy decision reliability

The classical hypothesis testing makes a strong assumption that precise observations are made, which is frequently violated in aggregations of incomplete, uncertain data. Treating such imprecision as completely precise values led to overconfident and unstable decisions. This paper introduces a unified hypothesis-testing framework for imprecise data handling using normalized hexagonal fuzzy numbers, combining this with an extremely geometrically stable Euler line-based pivotal spot ranking. The ranking maintains both central tendency and dispersion, allowing a more reliable transformation of fuzzy observations to scalar test statistics. In addition, it develops a brand-new fuzzy decision reliability index to evaluate the accuracy of hypothesis decisions under conditions of uncertainty. It therefore supplements classical significance testing methods. Extensive Monte Carlo experiments with controlled fuzziness and a real-world analysis for Ministry of Micro, Small, and Medium Enterprises registration data demonstrate that the proposed normalized hexagonal fuzzy numbers-fuzzy decision reliability framework maintains nominal type-I error, exhibits competitive or superior power as imprecision increases, and provides actionable reliability information that is not available in traditional methods. The framework provides a robust and comprehensive tool for statistical inference in regions of uncertainty.