Abstract
This paper shows how to manage null entries in pairwise comparisons matrices. Although assessments can be imprecise, since subjective criteria are involved, the classical pairwise comparisons theory expects all of them to be available. In practice, some experts may not be able (or available) to provide all assessments. Therefore managing null entries is a necessary extension of the pairwise comparisons method. It is shown that certain null entries can be recovered on the basis of the transitivity property which each pairwise comparisons matrix is expected to satisfy.
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K. M. Dadkhah, F. Zahedi. A mathematical treatment of inconsistency in the analytic hierarchy process, Mathematical and Computer Modelling 17, 111–122, 1993.
G. T. Fechner. Elements of Psychophysics, Vol. 1, Holt, Rinehart and Winston: New York, 1965, translation by H. E. Adler of Elemente der Psychophysik, Breitkopf und Härtel: Leipzig, 1860.
P. T. Harker. Incomplete pairwise comparisons in the analytic hierarchy process, Mathematical Modelling 9(11), 837–848, 1987.
M. Herman, W. W. Koczkodaj. Monte Carlo study of pairwise comparisons, Information Processing Letters 57(1), 25–29, 1996.
W. Holsztynski, W. W. Koczkodaj. Convergence analysis of inconsistency algorithms for the pairwise comparisons method, Information Processing Letters 59(4), 197–202, 1996.
R. Janicki, W. W. Koczkodaj. A weak order solution to a group ranking and consistency-driven pairwise comparisons, Applied Mathematics with Computation bf 94(2/3), 227–242, 1998.
W. W. Koczkodaj. A new definition of consistency of pairwise comparisons, Mathematical and Computer Modelling 18(7), 79–84, 1993.
W. W. Koczkodaj. Statistically accurate evidence of improved error rate by pairwise comparisons, Perceptual and Motor Skills 82, 43–48, 1996.
W. W. Koczkodaj, M. Orlowski, L. Wallenius, R. M. Wilson. A note on using consistency-driven approach to CD-ROM selection, Library Software Review 16(1), 4–11, 1997.
W. W. Koczkodaj. Testing the accuracy enhancement of pairwise comparisons by a Monte Carlo experiment, J. Statistical Planning and Inference 69(1), 21–32, 1998.
W. W. Koczkodaj, W. O. Mackasey. Mineral potential assessment by the consistency-driven pairwise comparisons method, EMG 6(1), 23–33, 1997.
W. W. Koczkodaj, M. Orlowski. An orthogonal basis for computing a consistent approximation to a pairwise comparisons matrix, Computers and Mathematics with Applications 34(10), 41–47, 1997.
W. W. Koczkodaj, M. Orlowski. Computing a consistent approximation to a generalized pairwise comparisons matrix, Computers and Mathematics with Applications, 1998, in press.
T. L. Saaty. A scaling method for priorities in hierarchical structure. J. Mathematical Psychology 15(3), 234–281, 1977.
L. L. Thurstone. A law of comparative judgments, Psychological Reviews 34, 273–286, 1927.
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Koczkodaj, W.W., Herman, M.W. & Orlowski, M. Managing Null Entries in Pairwise Comparisons. Knowledge and Information Systems 1, 119–125 (1999). https://doi.org/10.1007/BF03325094
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DOI: https://doi.org/10.1007/BF03325094