On estimation of priority vectors derived from inconsistent pairwise comparison matrices

• Autorzy: Kazibudzki Paweł Tadeusz

Identyfikatory

DOI

10.17512/jamcm.2022.4.05

• Języki publikacji: EN

Abstrakty

EN

The most critical and purely heuristic assumption about priority vector estimation on the basis of pairwise comparisons is that which states a positive relationship between the consistency of decision makers’ judgments and the quality of estimates of their priorities. As this issue constitutes the area of interest of the Multi-Criteria Decision Making theory in relation to AHP, it’s examined in this paper via Monte Carlo simulations from the perspective of a new measure of PCM consistency i.e. Index of Square Logarithm Deviations. It needs to be emphasized that such problems of applied mathematics have been already studied via computer simulations as the only way of this phenomenon examination.

Słowa kluczowe

EN

approximate reasoning; pairwise comparisons; consistency; priorities; AHP

PL

wnioskowanie przybliżone; porównanie parami; konsystencja; priorytety; AHP

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2022
• Tom: Vol. 21, nr 4
• Strony: 52--59
• Opis fizyczny: Bibliogr. 19 poz., rys., tab.

Twórcy

autor

Kazibudzki Paweł Tadeusz

• Faculty of Economics and Management, Opole University of Technology Opole, Poland

Bibliografia

• [1] Saaty, T.L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281. https://doi.org/10.1016/0022-2496(77)90033-5.
• [2] Saaty, T.L. (2008). Decision making with the analytic hierarchy process. International Journal of Services Sciences, 1(1), 83. https://doi.org/10.1504/IJSSCI.2008.017590.
• [3] Kou, G., Ergu, D., Chen, Y., & Lin, C. (2016). Pairwise comparison matrix in multiple criteria decision making. Technological and Economic Development of Economy, 22(5), 738-765. https://doi.org/10.3846/20294913.2016.1210694.
• [4] Grzybowski, A.Z., & Starczewski, T. (2017). Remarks about inconsistency analysis in the pairwise comparison technique. 2017 IEEE 14th International Scientific Conference on Informatics, 227-231. https://doi.org/10.1109/INFORMATICS.2017.8327251.
• [5] Kazibudzki, P.T. (2019). An examination of ranking quality for simulated pairwise judgments in relation to performance of the selected consistency measure. Advances in Operations Research, 2019, e3574263. https://doi.org/10.1155/2019/3574263.
• [6] Franek, J., & Kresta, A. (2014). Judgment scales and consistency measure in AHP. Procedia Economics and Finance, 12, 164-173. https://doi.org/10.1016/S2212-5671(14)00332-3.
• [7] Cavallo, B., & Ishizaka, A. (2022). Evaluating scales for pairwise comparisons. Annals of Operations Research. https://doi.org/10.1007/s10479-022-04682-8.
• [8] Silva Lopez, J.O., Salas Lopez, R., Rojas Briceno, N.B., Gomez Fernandez, D., Terrones Murga, R.E., Iliquin Trigoso, D., Barboza Castillo, E., Oliva Cruz, M., & Barrena Gurbillon, M.A. (2022). Analytic Hierarchy Process (AHP) for a landfill site selection in Chachapoyas and Huancas (NW Peru): Modeling in a GIS-RS Environment. Advances in Civil Engineering, 2022, 9733322. https://doi.org/10.1155/2022/9733322.
• [9] Li, L., Liu, Z., & Du, X. (2021). Improvement of analytic hierarchy process based on grey correlation model and its engineering application. Asce-Asme Journal of Risk and Uncertainty in Engineering Systems Part a-Civil Engineering, 7(2), 04021007. https://doi.org/10.1061/AJRUA6.0001126.
• [10] Ba, Z., Wang, Y., Fu, J., & Liang, J. (2022). Corrosion risk assessment model of gas pipeline based on improved AHP and its engineering application. Arabian Journal for Science and Engineering, 47(9), 10961-10979. https://doi.org/10.1007/s13369-021-05496-9.
• [11] Wang, P., Xue, Y., Su, M., Qiu, D., & Li, G. (2022). A TBM tunnel collapse risk prediction model based on AHP and normal cloud model. Geomechanics and Engineering, 30(5), 413-422. https://doi.org/10.12989/gae.2022.30.5.413.
• [12] Zhu, H., Xiang, Q., Luo, B., Du, Y., & Li, M. (2022). Evaluation of failure risk for prestressed anchor cables based on the AHP-ideal point method: An engineering application. Engineering Failure Analysis, 138, 106293. https://doi.org/10.1016/j.engfailanal.2022.106293.
• [13] Grzybowski, A.Z. (2016). New results on inconsistency indices and their relationship with the quality of priority vector estimation. Expert Systems with Applications, 43, 197-212. https://doi.org/10.1016/j.eswa.2015.08.049.
• [14] Grzybowski, A.Z., & Starczewski, T. (2020). New look at the inconsistency analysis in the pairwise-comparisons-based prioritization problems. Expert Systems with Applications, 113549. https://doi.org/10.1016/j.eswa.2020.113549.
• [15] Kazibudzki, P.T. (2021). On the statistical discrepancy and affinity of priority vector heuristics in pairwise-comparison-based methods. Entropy, 23(9), Article 9. https://doi.org/10.3390/e23091150.
• [16] Kazibudzki, P.T. (2016). Redefinition of triad’s inconsistency and its impact on the consistency measurement of pairwise comparison matrix. Journal of Applied Mathematics and Computational Mechanics, 15(1), 71-78. https://doi.org/10.17512/jamcm.2016.1.07.
• [17] Aguarón, J., & Moreno-Jiménez, J.M. (2003). The geometric consistency index: Approximated thresholds. European Journal of Operational Research, 147(1), 137-145. https://doi.org/10.1016/ S0377-2217(02)00255-2.
• [18] Koczkodaj, W.W. (1993). A new definition of consistency of pairwise comparisons. Mathematical and Computer Modelling, 18(7), 79-84. https://doi.org/10.1016/0895-7177(93)90059-8.
• [19] Botelho, M. (2022). Analyzing priority vectors: Going beyond inconsistency indexes. International Journal of the Analytic Hierarchy Process, 14(2). https://doi.org/10.13033/ijahp.v14i2.922.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).