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Autor
Klukowski Leszek (Polish Academy of Sciences)
Tytuł
Estimators of the Relations of Equivalence, Tolerance and Preference Based on Pairwise Comparisons with Random Errors
Źródło
Operations Research and Decisions, 2012, vol. 22, no. 2, s. 15-34, tab., bibliogr. 47 poz.
Słowa kluczowe
Estymatory, Symulacja, Zmienne losowe
Estimators, Simulation, Random variable
Uwagi
summ.
Abstrakt
This paper presents a review of results of the author in the area of estimation of the relations of equivalence, tolerance and preference within a finite set based on multiple, independent (in a stochastic way) pairwise comparisons with random errors, in binary and multivalent forms. These estimators require weaker assumptions than those used in the literature on the subject. Estimates of the relations are obtained based on solutions to problems from discrete optimization. They allow application of both types of comparisons - binary and multivalent (this fact relates to the tolerance and preference relations). The estimates can be verified in a statistical way; in particular, it is possible to verify the type of the relation. The estimates have been applied by the author to problems regarding forecasting, financial engineering and bio-cybernetics. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Szkoły Głównej Handlowej w Warszawie
Biblioteka Główna Uniwersytetu Ekonomicznego w Katowicach
Biblioteka Główna Uniwersytetu Ekonomicznego w Poznaniu
Biblioteka Główna Uniwersytetu Ekonomicznego we Wrocławiu
Pełny tekst
Pokaż
Bibliografia
Pokaż
  1. Swarm Intelligence in Data Mining, A. Abraham, C. Grosan (Eds.), Springer, Berlin 2006.
  2. BRADLEY R.A., Science, Statistics and Paired Comparisons, Biometrics, 1976, 32, 213-232.
  3. BRADLEY R.A., Paired comparisons: some basic procedures and examples, [in:] Handbook of Statistics 4, P.R. Krishnaiah, P.K. Se (Eds.), North-Holland, Amsterdam 1984, 299-326.
  4. BRUNK H.D., Mathematical models for ranking from paired comparisons, JASA, 1960, 55, 503-520.
  5. DANIEL W.W., Applied Nonparametric Statistics (2nd Ed.), PWS-Kent Publishing Company, Boston 1990.
  6. DAVID H.A., Order Statistics, Wiley, New York 1970.
  7. DAVID H.A., The Method of Paired Comparisons, 2nd ed. C. Griffin, London 1988.
  8. DAVIDSON R.R., A bibliography on the Method of Paired Comparisons, Biometrics, 1976, 32, 241-251.
  9. DOMAŃSKI C., Statistical Tests, PWE, Warszawa 1990 (in Polish).
  10. FALKENAUER E., Genetic Algorithms and Grouping Data, Wiley, New York 1998.
  11. GORDON A.D., Classification, 2nd Ed., Chapman & Hall/CRC, Boca Raton, 1999.
  12. HAND D.J., Discrimination and Classification, Wiley, New York 1986.
  13. HANSEN P., JAUMARD B., SANLAVILLE E., Partitioning Problems in Cluster Analysis: A Review of Mathematical Programming Approaches, Studies in Classification, Data Analysis, and Knowledge Organization, Springer, Berlin 1994.
  14. HARTIGAN J.J., Clustering Algorithms, Wiley, New York 1975.
  15. HASTIE T., TIBSHIRANI R., FRIEDMAN J., The Elements of Statistical Learning. Data Mining, Inference and Prediction, Springer, Berlin 2002.
  16. HOEFFDING W., Probability inequalities for sums of bounded random variables. JASA, 1963, 58, 13-30.
  17. HOLLANDER M., WOLFE D.A., Nonparametric Statistical Methods, Wiley, 1973.
  18. KLUKOWSKI L., A Method of Forecasting Time Series Including a Piecewise Linear Component, (unpublished Ph.D. dissertation), Systems Research Institute, Polish Academy of Sciences, Warsaw 1986 (in Polish).
  19. KLUKOWSKI L., Algorithm for the classification of samples in the case of an unknown number of random variables generating them, Przegląd Statystyczny, 1990, 37, 167-177 (in Polish).
  20. KLUKOWSKI L., Ranking items on the basis of pairwise comparisons in the case of random errors, [in:] Systems Research, 3, R. Kulikowski, J. Kacprzyk (Eds.), Omnitech Press, Warsaw 1990, 212-268 (in Polish).
  21. KLUKOWSKI L., Classification of hormonal profiles, II Conf. on Operational and Systems Research, Z. Nahorski (Ed.), IBS PAN, Warsaw 1991, 155-163 (in Polish).
  22. KLUKOWSKI L., Some probabilistic properties of the nearest adjoining order method and its extensions, Annals of Operational Research, 1994, 51, 241-261.
  23. KLUKOWSKI L., The nearest adjoining order method for pairwise comparisons in the form of difference of ranks, Annals of Operations Research, 2000, 97, 357-378.
  24. KLUKOWSKI L., Tests for relation type - equivalence or tolerance - in a finite set of elements, Control and Cybernetics, 2006, 35, 369-384.
  25. KLUKOWSKI L., Estimation of the preference relation on the basis of medians from pairwise comparisons in the form of difference of ranks, [in:] Computer Recognition Systems 2, M. Kurzynski, E. Puchala, M. Wozniak, A. Zolnierek (Eds.), Advances in Soft Computing, Springer, 2007, 45, 232-241.
  26. KLUKOWSKI L., Estimation of tolerance relation on the basis of multiple pairwise comparisons with random errors, Control and Cybernetics, 2007, 36, 443-466.
  27. KLUKOWSKI L., Estimation of the preference relation on the basis of multiple pairwise comparisons with random errors, [in:] Modelling of Preferences vs. Risk, T. Trzaskalik (Ed.), University of Economics in Katowice, Katowice 2008, 61-76 (in Polish).
  28. KLUKOWSKI L., Determination of tolerance relation - alternative approach to intuitionistic and fuzzy sets, [in:] Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets an Related Topics, Vol. 2, K. Atanassov, O. Hryniewicz, J. Kacprzyk, M. Krawczak, Z. Nahorski, S. Zadrożny (Eds.), Academic Publishing House Exit, Warsaw 2008.
  29. KLUKOWSKI L., Estimation of the preference relation on the basis of multiple pairwise comparisons in the form of differences of ranks, Control and Cybernetics, 2008, 37, 711-729.
  30. KLUKOWSKI L., Tests for Relation Type - Equivalence or Tolerance - Based on Averaging of Multiple Binary Comparisons, [in:] Development in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. Foundations, Vol. 1, K. Atanassov, K. Bustince, O. Hryniewicz, J. Kacprzyk, M. Krawczak, B. Riecan, E. Szmidt (Eds.), Academic Publishing House Exit, Warsaw 2008, 175-189.
  31. KLUKOWSKI L., Estimation of the preference relation on the basis of medians from pairwise comparisons, [in:] Multicriteria Ordering and Ranking: Partial Orders, Ambiguities and Applied Issues, J. Owsiński, W. Bruggemann (Eds.), IBS PAN, Warsaw 2008, 109-120.
  32. KLUKOWSKI L., Estimation of the relations: preference, equivalence and tolerance on the basis of pairwise comparisons, [in:] Development in Fuzzy Sets, Intuitionistic Fuzzy Sets, I. Foundations, K.T. Atanassov, M. Baczyński, J. Drewniak, J. Kacprzyk, M. Krawczak, E. Szmidt, M. Wygralak, S. Zadrożny (Eds.), IBS PAN, SRI PAS, Warsaw 2010, 109-119.
  33. KLUKOWSKI L., Tests for relation type - equivalence or tolerance based on medians from multiple pairwise comparisons, Materiały i Studia Polskiego Stowarzyszenia Zarządzania Wiedzą, W. Bojar, J.W. Owsiński (Eds.), 31, 338-348, Bydgoszcz 2010.
  34. KLUKOWSKI L., Optimization of public debt management in the case of stochastic budgetary constraints, [in:] Multiple criteria decisions making'09, T. Trzaskalik, T. Wachowicz (Eds.), The University of Economics in Katowice, Katowice 2010.
  35. KLUKOWSKI L., Methods of Estimation of Relations of: Equivalence, Tolerance, and Preference in a Finite Set, IBS PAN, Series: Systems Research, Vol. 69, Warsaw 2011.
  36. KLUKOWSKI L., Estimation of Tolerance Relation on the Basis of Pairwise Comparisons, [in:] Computer Recognition Systems 4, Advances in Intelligent and Soft Computing 95, R. Burduk, M. Kurzyński, M. Woźniak, A. Żołnierek (Eds.), Springer, Berlin 2011, 91-98.
  37. KLUKOWSKI L., Properties of estimators of the preference relation in the form of difference of ranks - simulation survey, [in:] Modelowanie Preferencji a Ryzyko'12, T. Trzaskalik (Ed.), Zeszyty Naukowe Wydziałowe, 97, 119-132, Economic University in Katowice, Katowice 2012 (in Polish).
  38. KLUKOWSKI L., Properties of estimators of the preference relation based on pairwise comparisons: binary and difference of ranks - simulation survey, Submitted to Control and Cybernetics, 2012.
  39. KOHONEN T., Self-Organizing Maps, Springer, Berlin 1995.
  40. KORONACKI J., ĆWIK J., Statistical Learning Systems, WNT, Warsaw 2005 (in Polish).
  41. RANDLES R.H., WOLFE D.A., Introduction to the Theory of Nonparametric Statistics, Wiley, New York 1979.
  42. RIPLEY B.D., Stochastic Simulation, Wiley, New York 2006.
  43. SACHS L., Applied Statistics, Springer, New York 1978.
  44. SHESKIN D.J., Handbook of Parametric and Nonparametric Statistical Procedures, CRC Press, Boca Raton, 1997.
  45. SIEGEL S., CASTELLAN N.J. Jr., Nonparametric Statistics for the Behavioral Sciences (2nd Ed.), McGraw-Hill Book Company, New York 1988.
  46. SLATER P., Inconsistencies in a schedule of paired comparisons, Biometrika, 1961, 48, 303-312.
  47. WITTEN I.H., FRANK E., Data Mining: Practical Machine Learning Tools and Techniques (2nd Ed.), Morgan Kaufmann Publishers, Amsterdam 2005.
Cytowane przez
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ISSN
2081-8858
Język
eng
URI / DOI
http://dx.doi.org/10.5277/ord120201
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