Abstract
The paper presents original tests for verification of estimates of the tolerance relation, obtained of the basis of multiple independent pairwise comparisons, in binary and multivalent form, with random errors. The tolerance relation is the equivalency relation with non-empty intersections. The estimates are obtained with the use of the idea of the nearest adjoining order (NAO), i.e. minimization of differences between relation form and pairwise comparisons. The tests are based on exact or limiting distributions of proposed statistics. The estimates do not require simulations, as the tests presented in Klukowski (2011), i.e. their computational cost is not high.
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References
Bradley, R.A.: Science, statistics and paired comparisons. Biometrics 32, 213–232 (1976)
David, H.A.: The Method of Paired Comparisons, 2nd edn. Ch. Griffin, London (1988)
Domański, C.: Statistical Tests (in Polish). PWE, Warsaw (1990)
Gordon, A.D.: Classification, 2nd edn. Chapman & Hall/CRC (1999)
Garfinkel, R.S., Nemhauser, G.L.: Integer Programming. Wiley, New York (1972)
Hoeffding, W.: Probability inequalities for sums of bounded random variables. JASA 58, 13–30 (1963)
Serfling, R.J.: Approximation Theorems of Mathematical Statistics. Wiley, Hoboken (1980)
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)
Klukowski, L.: Determining an estimate of an equivalence relation for moderate and large sized sets. Oper. Res. Decis. Q. 27(2), 45–58 (2017)
Klukowski, L.: Statistical tests for verification of estimate of the preference relation resulting from pairwise comparisons. In: Atanassov, K.T., Atanassova, V., Kacprzyk, J., Kaluszko, A., Krawczak, M., Owsinski, J.W., Sotirov, S., Sotirova, E., Szmidt, E., Zadrozny, S. (eds.) IWIFSGN 2018. AISC, vol. 1081, pp. 225–238. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-47024-1_24
Klukowski, L.: Pairwise comparisons in the form of difference of ranks - testing of estimates of the preference relation. In: Atanassov, K.T., Atanassova, V., Kacprzyk, J., Kaluszko, A., Krawczak, M., Owsinski, J.W., Sotirov, S., Sotirova, E., Szmidt, E., Zadrozny, S. (eds.) IWIFSGN 2018. AISC, vol. 1081, pp. 214–224. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-47024-1_23
Slater, P.: Inconsistencies in a schedule of paired comparisons. Biometrika 48, 303–312 (1961)
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Klukowski, L. (2021). Tests for Estimates of the Tolerance Relation Based on Pairwise Comparisons in Binary and Multivalent Form. In: Atanassov, K.T., et al. Advances and New Developments in Fuzzy Logic and Technology. IWIFSGN 2019 2019. Advances in Intelligent Systems and Computing, vol 1308. Springer, Cham. https://doi.org/10.1007/978-3-030-77716-6_12
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DOI: https://doi.org/10.1007/978-3-030-77716-6_12
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