Estimation of Tolerance Relation on the Basis of Pairwise Comparisons

Abstract

The methods of estimation of the tolerance relation (overlapping partition) in a finite set on the basis of multiple pairwise comparisons with random errors - developed by the author - are discussed in the paper. Two types of comparisons are considered. The first type (binary) answers the question whether a pair of elements belongs to intersection of two or more subsets. The second type (multivalent) expresses the number of subsets of intersection comprising a pair. The estimates of the relation are determined on the basis of an appropriate discrete programming task. Two estimators are considered: the first one minimizes the sum of differences between relation form and comparisons. The second estimator rests on differences between relation form and medians from comparisons of each pair. The properties of the estimators are based on probabilistic inequalities and simulations.