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Tytuł artykułu

Methods of determining group opinion using pairwise comparisons. Analysis of properties and application aspects

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Języki publikacji
EN
Abstrakty
EN
The problem considered in the paper is formulated as follows. Given a finite set of elements called alternatives, set of properties or attributes and a set of experts. Their task is to estimate the importance of alternatives under consideration wit h respect to the chosen criterion, i.e. to evaluate estimates of alternative weights. Experts can be asked to give their judgements on all the alternatives analyzed or to perform pairwise comparisons only. In the paper the latter case is considered only. Moreover, it is assumed that transitivity conditions do not hold. Methods to solve the problem are analysed. Numerical examples illustrating the application of methods investigated are given.
Rocznik
Strony
145--165
Opis fizyczny
Bibliogr. 30 poz., 10 tab.
Twórcy
autor
autor
autor
  • Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland
Bibliografia
  • [1] J. K. Arrow, Social choice and individual values, J. Wiley Inc., New York 1951, 2nd ed., 1963.
  • [2] V. Belton, T. Gear, On the meaning of relative importance. Discussion Journal of Multi-criteria Decision Analysis, 6 (1997) 335-337.
  • [3] K. O. Cogger, P. L. Yu, Eigenweight vectors and least-distance approximation for revealed preference in pairwise weight ratios, JOTA, 6 (1985) 483-491.
  • [4] R. Corbin, A. Marley, Random utility models with equality. An apparent, but not actual generalization of random utility models, Journal of Mathematical Psychology, 11 (1997) 274-293.
  • [5] J. S. Dyer Remarks on the analytic hierarchy process, Management Science. 36 (1990) 259-268.
  • [6] R. P. Hämäläinen, A. A. Salo, The issue is understanding the weights. Discussion, Journal of Multi-criteria Decision Analysis, 6 (1997) 340-343.
  • [7] J. W. Hołubiec J. W. Mercik, Techniques and arcane of voting (in Polish), Omnitech Press, Warszawa 1992.
  • [8] G. Islei, A. G. Lockett, Judgemental modelling based on geometric least Square EJOR, 36 (1988) 27-35.
  • [9] G. Islei, An approach to measuring consistency of preference vector derivations, In: S. Jahn and W. Krabs (eds.), Recent advances and historical development of vector optimization, Lecture Notes in Economics and Mathematical Systems 294, Springer-Verlag, Berlin (1986) 265-284.
  • [10] J. S. Kelly, Arrow impossibility theorems, Academic Press, New York 1978.
  • [11] J. Krovák, Ranking alternatives - comparison of different methods based on binary comparison matrices, EJOR, 32 (1987) 86-95.
  • [12] L. Księżopolska, D. Wagner, Methods for determining elements weights on the basis of pairwise comparisons in the case when expert judgements are not transitive (In Polish), Modele i decyzje w rozwoju społeczno-ekonomicznym, PTBOiS, WSM Gdynia, (1988) 50-62.
  • [13] B. G. Litwak, Expert information. The acquisition and analysis methods (in Russian), Moscow 1982.
  • [14] F. A. Lootsma, Scale sensitivity in the multiplicative AHP and SMART, Report 93-37, Faculty of Technical Mathematics and Informatics, Delft University of Technology 1992.
  • [15] D. Ma, X. Zheng, 9/9 - 9/1 scale method of AHP Proc. 2nd Int. Symp. on the AHP, Pittsburgh, PA, University of Pittsburgh, 1 (1991) 197-202.
  • [16] C. K. Murphy, Limits on the analytic hierarchy process from its consistency index, EJOR, 65 (1993) 138-139.
  • [17] H. Nurmi, Comparing voting systems, D. Reidel Publ. Co., Dordrecht 1987.
  • [18] Th. L. Saaty, The Analytic Hierarchy Process, Planning, Priority Setting, Resource Allocation, McGraw-Hill, New York 1980.
  • [19] Th. L. Saaty, Ariomatic foundation of the analytic hierarchy process, Management Science,32 (1986) 841-855.
  • [20] Th. L. Saaty, Eigenvector and logarithmic least squares, EJOR, 48 (1990) 156-160.
  • [21] Th. L. Saaty, An exposition of the AHP in reply to the paper "Remarks on the analytic hierarchy process", Management Science, 36 (1990) 259-268.
  • [22] Th. L. Saaty, Highlights and critical points in the theory and application of Analytic Hierarchy Process, EJOR, 74 (1994) 426-447.
  • [23] Th. L. Saaty, That is not the Analytic Hierarchy Process: Discussion. What the AHP is and what is not, Journal of Multi-criteria Decision Analysis, 6 (1997) 324-335.
  • [24] A. A. Salo, R. P. Hämäläinen, On the measurement of preferences in the Analytic Hierarchy Process, Journal of Multi-criteria Decision Analysis, 6 (1997) 309-319.
  • [25] S. S che nker m an, Avoiding rank reversal in AHP decision-support models. EJOR, 74 (1994) 407-419.
  • [26] B. Schoner, W. C. Wedley, Alternative scales in AHP, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag (1989) 345-354.
  • [27] B. Schoner, W. C. Wedley, E. U. Choo, A unified approach to AHF with linking pins, EJOR, 64 (1993) 384-392.
  • [28] E. Takeda, K. O. Cogger, P. L. Yu, Estimating criterion weights using eigenvectors: A comparative study, EJOR, 29 (1987) 360-369.
  • [29] A. Tversky, I. Simonson, Context-dependent preferences, Management Science, 39 (1993) 1179-1189.
  • [30] D. Wagner, Determining weights of research topics on the basis of expert judgements. The case of Systems Research Institute, Consensus under fuzziness, eds. J. Kacprzyk, H. Nurmi, M. Fedrizzi, Kluwer Academic Publishers, Boston (1997) 285-299.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG5-0001-0001
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