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

• Autorzy: Klukowski L.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

multiple pairwise comparisons; nearest adjoining order method; difference of ranks

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2008
• Tom: Vol. 37, no 3
• Strony: 711--729
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Klukowski L.

• Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland,

Bibliografia

• DAVID, H.A. (1970) Order Statistics. J. Wiley, New York.
• DAVID, H.A. (1988) The Method of Paired Comparisons. 2nd ed. Ch. Griffin, London.
• HASTIE, T., TIBSHIRANI, R. and FRIEDMAN, J. (2001) The Elements of Statistical Learning. Springer, New York-Berlin-Heidelberg.
• HOEFFDING, W. (1963) Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13-30.
• KAMISHIMA, T. and AKAHO, S. (2006) Supervised Ordering by Regression combined Thurstone’s Model. Artificial Intelligence Review 25, 231-246.
• KLUKOWSKI, L. (1994) Some probabilistic properties of the nearest adjoining order method and its extensions. Annals of Operations Research 51, 241-261.
• KLUKOWSKI, L. (2000) The nearest adjoining order method for pairwise comparisons in the form of difference of ranks. Annals of Operations Research 97, 357-378.
• KLUKOWSKI, L. (2007) Estimation of tolerance relation the basis of multiple pairwise comparisons with random errors. Control and Cybernetics 36, 443-466.
• MARDEN, J.I. (1995) Analyzing and Modelling Rank Data. Monograph on Statistics and Applied Probability 64. Chapman & Hall.
• SLATER, P. (1961) Inconsistencies in a schedule of paired comparisons. Biometrika 48, 303-312.
• YAGER, R.R. (2007) Aggregation of ordinal information. Fuzzy Optim. Dec. Making 6, 199-219.