@misc{Klukowski_Leszek_Estimation_2012, author={Klukowski, Leszek}, copyright={Creative Commons Attribution BY 4.0 license}, address={Warszawa}, journal={Raport Badawczy = Research Report}, howpublished={online}, year={2012}, publisher={Instytut BadaƄ Systemowych. Polska Akademia Nauk}, publisher={Systems Research Institute. Polish Academy of Sciences}, language={eng}, abstract={The paper presents the estimators of three relations: equivalence, tolerance and preference in a finite set on the basis of multiple pairwise comparisons, disturbed by random errors. The estimators can rest on: binary, multivalent and combined comparisons. The estimates are obtained on the basis of discrete programming tasks. The estimators have good statistical properties, in particular consistency. Precision of the estimators can be determined also with the use of simulation methods. The estimates can be validated in versatile way. The approach allows verification of the relation type - equivalence or tolerance (using binary comparisons).}, title={Estimation of: the relations of equivalence, tolerance and preference on the basis of pairwise comparisons in binary and multivalent Form with Random errors}, type={Text}, URL={http://www.rcin.org.pl/Content/103553/PDF/RB-2012-16.pdf}, keywords={Relations estimation, Pairwise comparisons with random errors, Nearest adjoining order}, }