Neutrosophic PPS sampling design

In sampling theory, PPS (probability proportional to size) design is a sampling procedure used in situations where the population units have unequal probabilities of selection. The existing PPS sampling design works only with precise, determinate, and complete measurements on all units. In practice, data points with imprecise, indeterminate, and incomplete measurements are inevitable issues often faced by survey statisticians. This study modifies the traditional PPS sampling design to incorporate both precise and imprecise measurements. Using hypothetical populations with indeterminate measurements, the sample selection procedure for sampling with and without replacement methods have been explained. Additionally, a neutrosophic ratio estimator is proposed for use with populations containing imprecise, incomplete, and indeterminate values. A neutrosophic real-world data set on daily temperatures has been used for assessment of the performance of various neutrosophic ratio estimators. The comparative analysis reveals that the proposed neutrosophic estimator performs better than its competitors.