New Results on the Quality of Recently Introduced Index for a Consistency Control of Pairwise Judgments

• Authors: Kazibudzki Paweł Tadeusz
• Languages of publication: EN

Abstracts

EN

A system exists which meets a prescription of the efficacious multiple criteria decision making support methodology. It is called the Analytic Hierarchy Process (AHP). The consistency control of human pairwise judgments about their preferences towards alternative choices appears to be the crucial issue in this concept. This research examines the efficiency of a recently proposed consistency index grounded on the redefined idea of triads inconsistency within Pairwise Comparison Matrices. The quality of the recently introduced proposal is studied and compared to other ideas with application of Monte Carlo simulations coded and run in Wolfram Mathematica 8.0.

Keywords

EN

Analytic Hierarchy Process (AHP); Monte Carlo simulations

PL

Analityczny proces hierarchiczny; Symulacja Monte Carlo

• Publisher: Uniwersytet Ekonomiczny w Katowicach
• Journal: Multiple Criteria Decision Making
• Year: 2017
• Volume: 12
• Pages: 90-102

Contributors

author

Kazibudzki Paweł Tadeusz

• Jan Długosz University in Częstochowa. Department of Law, Administration and Management. Częstochowa, Poland

References

• Aguarón J., Escobar M.T., Moreno-Jiménez J.M. (2014), The Precise Consistency Consensus Matrix in a Local AHP-group Decision Making Context, Annals of Operational Research, DOI:10.1007/s10479-014-1576-8.
• Aguarón J., Moreno-Jiménez J.M. (2003), The Geometric Consistency Index Approximate Thresholds, European Journal of Operational Research, 147(1), 137-145.
• Altuzarra A., Moreno-Jiménez J.M., Salvador M. (2010), Consensus Building in AHP-Group Decision Making: A Bayesian Approach, Operations Research, 58, 1755-1773.
• Benítez J., Delgado-Galván X., Izquierdo J., Pérez-García R. (2012), Improving Consistency in AHP Decision-making Processes, Applied Mathematics and Computation, 219, 2432-2441.
• Bozóki S., Fülöp J., Koczkodaj W.W. (2011), An LP-based Inconsistency Monitoring of Pairwise Comparison Matrices, Mathematical and Computer Modeling, 54(1-2), 789-793.
• Brunelli M., Fedrizzi M. (2015), Boundary Properties of the Inconsistency of Pairwise Comparisons in Group Decisions, European Journal of Operational Research, 240(3), 765-773.
• Bulut E., Duru O., Kececi T., Yoshida S. (2012), Use of Consistency Index, Expert Prioritization and Direct Numerical Inputs for Generic Fuzzy-AHP Modeling: A Process Model for Shipping Asset Management, Expert Systems with Applications, 39, 1911-1923.
• Choo E.U., Wedley W.C. (2004), A Common Framework for Deriving Preference Values from Pairwise Comparison Matrices, Computers & Operations Research, 31, 893-908.
• Crawford G., Williams C.A. (1985), A Note on the Analysis of Subjective Judgment Matrices, Journal of Mathematical Psychology, 29, 387-405.
• Dijkstra T.K. (2013), On the Extraction of Weights from Pairwise Comparison Matrices, Central European Journal of Operations Research, 21(1), 103-123.
• Dong Y., Xu Y., Li H., Dai M. (2008), A Comparative Study of the Numerical Scales and the Prioritization Methods in AHP, European Journal of Operational Research, 186, 229-242.
• Farkas A. (2007), The Analysis of the Principal Eigenvector of Pairwise Comparison Matrices, Acta Polytech. Hung., 4(2), http://uni-obuda.hu/journal/ Farkas_10.pdf.
• 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.
• Grzybowski A.Z. (2012), Note on a New Optimization Based Approach for Estimating Priority Weights and Related Consistency Index, Expert Systems with Applications, 39, 11699-11708.
• Ho W. (2008), Integrated Analytic Hierarchy Process and Its Applications – A Literature Review, European Journal of Operation Research, 186, 211-228.
• Ishizaka A., Labib A. (2011), Review of the Main Developments in the Analytic Hierarchy Process, Expert Systems with Applications, 11(38), 14336-14345.
• Jarek S. (2016), Removing Inconsistency in Pairwise Comparison Matrix in the AHP, Multiple Criteria Decision Making, 11, 63-76.
• Kazibudzki P. (2016a), 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.
• Kazibudzki P. (2016b), An Examination of Performance Relations among Selected Consistency Measures for Simulated Pairwise Judgments, Annals of Operations Research, 244(2), 525-544.
• Koczkodaj W.W., Szarek S.J. (2010), On Distance-based Inconsistency Reduction Algorithms for Pairwise Comparisons, Logic Journal of the IGPL, 18(6), 859-869.
• Koczkodaj W.W. (1993), A New Definition of Consistency of Pairwise Comparisons, Mathematical and Computer Modeling, 18(7), 79-84.
• Lin CC. (2007), A Revised Framework for Deriving Preference Values from Pairwise Comparison Matrices, European Journal of Operational Research, 176, 1145-1150.
• Miller G.A. (1956), The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Information Processing, Psychological Review, 63, 81-97.
• Peláez P., Lamata M. (2003), A New Measure of Consistency for Positive Reciprocal Matrices, Computers & Mathematics with Applications, 46, 1839-1845.
• Saaty T.L. (2008), Decision Making with the Analytic Hierarchy Process, International Journal of Services Sciences, 1(1), 83-98.
• Saaty T.L. (1977), Scaling Method for Priorities in Hierarchical Structures, Journal of Mathematical Psychology, 15(3), 234-281.
• Saaty T.L. (1980), The Analytic Hierarchy Process, McGraw-Hill, New York.
• Saaty T.L. (2004), Decision Making – The Analytic Hierarchy and Network Processes, Journal of Systems Science and Systems Engineering, 13(1), 1-35.
• Saaty T.L., Vargas L.G. (1984), Comparison of Eigenvalue, Logarithmic Least Square and Least Square Methods in Estimating Ratio, Mathematical Modeling, 5, 309-324.
• Vaidya O.S., Kumar S. (2006), Analytic Hierarchy Process: An Overview of Applications, European Journal of Operation Research, 169, 1-29.
• Xia M., Xu Z., Chen J. (2013), Algorithms for Improving Consistency or Consensus of Reciprocal [0,1]-valued Preference Relations, Fuzzy Sets and Systems, 216, 108-133.
• Zhang G., Dong Y., Xu Y. (2012), Linear Optimization Modeling of Consistency Issues in Group Decision Making Based on Fuzzy Preference Relations, Expert Systems with Applications, 39, 2415-2420.

Identifiers

ISSN

2084-1531