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2 Control and Cybernetics

2 Klukowski L.

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Estimation of the preference relation on the basis of multiple pairwise comparisons in the form of differences of ranks

Klukowski L.

Control and Cybernetics

2008

Vol. 37, no 3

711-729

The problem of estimation of the preference relation in a finite set on the basis of pairwise comparisons, in the form of differences of ranks with random errors, with the use of nearest adjoining order idea (NAO), is investigated in the paper. The results presented are extension and correction of the earlier works of the author; especially the case of multiple independent comparisons of each pair is examined. The comparisons of each pair are aggregated through the average or the median of comparisons. The estimated form of the relation is obtained in both cases on the basis of discrete programming tasks. The properties of the estimators are obtained under weak assumptions about distributions of comparison errors, in particular, the distributions may be unknown.

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

Klukowski L.

Control and Cybernetics

2007

Vol. 36, no 2

443-466

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.