Determining of an Estimate of the Equivalence Relation on the Basis of Pairwise Comparisons

Abstract

The paper presents two approaches for solving of a discrete programming problem necessary for determining of estimates of the equivalence relation on the basis of pairwise comparisons with random errors. The problem minimizes sum of absolute differences between relation form and comparisons. The problem is NP hard and can be solved with the use of exact algorithms for moderate size of sets - about 50 elements. In the case of larger sets, at least 100 elements and/or multiple comparisons, it is necessary to apply heuristic algorithms. The paper presents original results: a statistical preprocessing, based on two tests proposed, which allows determining of the optimal or suboptimal solution for large sets with acceptable computational cost.