Estimation of tolerance relation on the basis of multiple pairwise comparisons with random errors

The methods of tolerance relation estimation on the basis of pairwise comparisons with random errors, in the case of multiple comparisons for each pair, are proposed in the paper. Each comparison expresses the number of common features of both elements or the number of their missing features. The assumptions made about distributions of comparison errors are very weak, in particular they may be unknown. Two approaches are discussed: the first one, based on averaging of comparisons for each pair and the second, based on the median from comparisons. The estimated form of the relation is determined (in both cases) on the basis of the appropriate discrete programming task. The properties of estimators are based on some probabilistic inequalities. An example of application of the estimators proposed is presented.