Combining the Information of Multiple Ranker in Ranked Set Sampling with Fuzzy Set Approach

Ranked set sampling (RSS) is a useful alternative sampling method for parameter estimation. Compared to other sampling methods, it uses the ranking information of the units in the ranking mechanism before the actual measurement. The ranking mechanism can be described as a visual inspection of an expert or a highly-correlated concomitant variable. Accuracy for ranking of the sample units affects the precision of the estimation. This study proposes an alternative approach, called Fuzzy-weighted Ranked Set Sampling (FwRSS), to RSS for dealing with the uncertainty in ranking using fuzzy set. It assumes that there are K (\(K>1\)) rankers for rank decisions and uses three different fuzzy norm operators to combine the decisions of all rankers in order to provide the accuracy of ranking. A simulation study is constructed to see the performance of the mean estimators based on RSS and FwRSS.