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2 Control and Cybernetics

2 Klukowski L.

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w słowach kluczowych: nearest adjoining order method

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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.

Tests for relation type - equivalence or tolerance - in a finite set of elements

Klukowski L.

Control and Cybernetics

2006

Vol. 35, no 2

369-384

The statistical procedure for determination of the type of relation - equivalence or tolerance - in a finite set of elements, estimated on the basis of pairwise comparisons with random errors, is presented. The procedure consists of two tests based on Chebyshev's inequality for variance of a random variable; the test statistic is a mixture of some random variables. An example of application of the procedure - determination of relation type in the set of functions expressing profitability of treasury securities sold at auctions in Poland - is presented, too.