A system approach to decision support on basis of hierarchical and network models
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2018.1.01Keywords:
expert judgements, fuzzy pairwise comparison matrix, inconsistency, confidence intervals, sensitivity, ranking stability, a decision support system, reliability in the analytical hierarchy processAbstract
A methodology and a system approach to decision support based on hierarchical and network models are proposed, which include methods for estimating and improving the consistency of pairwise comparison matrices (PCM), calculating fuzzy local weights for model elements based on fuzzy PCM, calculating confidence intervals for local weights, finding aggregated weights and aggregated belief functions for model elements, estimating the sensitivity of the results, tools for analyzing the effectiveness of the methods and an expert evaluation modeling system. A decision support system is built on basis of the proposed methodology. The proposed methodology makes it possible to increase the reliability of solutions of practical weakly structured decision-making problems by using more efficient methods at each of the stages of solving the problem. Reliability of results of application of the methodology while solving a practical decision-making problem can be assessed by means of sensitivity analysis using the stability indices of the computed local and global rankings of the decision alternatives.References
Saati T.L. Prinjatie reshenij pri zavisimostjah i obratnyh svjazjah: Analiticheskie seti / T.L. Saati. — 2-e izd. — M.: Knizhn. dom "LIBROKOM", 2009. — 360 s.
Pankratova N.D. Modeli i metody analizu iyerarkhij: Teorija. Zastosuvannja: navch. posib. / N.D. Pankratova, N.I. Nedashkivs'ka. — K: IVTs "Vydavnytstvo "Politekhnika", 2010. — 371 s.
Vidaletal L.-A. Applying AHP to select drugs to be produced by anticipation in a chemotherapy compounding unit / L.-A. Vidaletal // Expert Systems with Applications. — Vol. 37. — 2010. — P. 1528–1534.
Kumar A. Analyzing customer preference and measuring relative efficiency in telecom sector: A hybrid fuzzy AHP/DEA study / A. Kumar, R. Shankar, R.M. Debnath // Telematics and Informatics. — Vol. 32, Issue 3. — 2015. — P. 447–462.
Garbuzova-Schlifter M. AHP-based risk analysis of energy performance contracting projects in Russia / Maria Garbuzova-Schlifter, Reinhard Madlener // Energy Policy. — Vol. 97. — 2016. — P. 559–581.
Krejčí Jana. Fuzzy eigenvector method for obtaining normalized fuzzy weights from fuzzy pairwise comparison matrices / Jana Krejčí // Fuzzy Sets and Systems. — Vol. 315. — 2017. — P. 26–43.
Koczkodaj W.W. Pairwise comparisons simplified / W.W. Koczkodaj, J. Szybowski // Applied Mathematics and Computation. — Vol. 253. — 2015. — P. 387–394.
Bozóki S. An application of incomplete pairwise comparison matrices for ranking top tennis players / Sándor Bozóki. // European Journal of Operational Research. — Vol. 248, Issue 1. — 2016. — P. 211–218.
Benítez J. Improving consistency in AHP decision-making processes / J. Benítez et al. // Applied Mathematics and Computation. — Vol. 219, Issue 5. — 2012. — P. 2432–2441.
Systema pidtrymannja pryjnjattja rishen' SuperDecisions. — Available at: http://www. superdecisions.com
Systema pidtrymannja pryjnjattja rishen' DecisionLens. — Available at: http://www. decisionlens.com
Systema pidtrymannja pryjnjattja rishen' MakeItRational. — Available at: http://makeitrational.com/, http://www.transparentchoice.com/
Systema pidtrymannja pryjnjattja rishen' LogicalDecisions. — Available at: http://www.logicaldecisions.com/
Nedashkivs'ka N.I. Metod uzhodzhenykh parnykh porivnjan' pry otsinjuvanni al'ternatyv rishen' za jakisnym kryteriyem / N.I. Nedashkivs'ka // Systemni doslidzhennja ta informatsijni tekhnolohiyi. — 2013. — №4. — S. 67–79.
Nedashkovskaya N.I. Method for Evaluation of the Uncertainty of the Paired Comparisons Expert Judgements when Calculating the Decision Alternatives Weights / I. Nedashkovskaya // Journal of Automation and Information Sciences. — 2015. — Vol. 47, Issue 10. — P.69–82.
Nedashkovskaja N.I. Postroenie doveritel'nyh intervalov dlja vesov al'ternativ reshenij na osnove ekspertnyh parnyh sravnenij / N.I. Nedashkovskaja // Systemni doslidzhennja ta informatsijni tekhnolohiyi. — 2015. — №3. — S. 121–130.
Saaty Thomas L. On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process / Thomas L. Saaty, Liem T. Tran // Mathematical and Computer Modelling. — Vol. 46, Issues 7–8. — 2007. — P. 962–975.
Nedashkivs'ka N.I. Otsinjuvannja stijkosti lokal'nykh vah al'ternatyv rishen' na osnovi metodu parnykh porivnjan' / N.I. Nedashkivs'ka // Systemni doslidzhennja ta informatsijni tekhnolohiyi. — 2016. — №4. — S. 14–22.
Aguarón J. Consistency stability intervals for a judgement in AHP decision support systems / Juan Aguarón, Marı́a Teresa Escobar, José Marı́a Moreno-Jiménez // European J. of Operational Research. — Vol. 145, Issue 2. — 2003. — P. 382–393.
Pankratova N. Sensitivity analysis of a decision-making problem using the Analytic Hierarchy Process / N. Pankratova, N. Nedashkovskaya // International Journal "Information Theories and Applications". — 2016. — Vol. 23, N 3. — P. 232–251.
Pankratova N.D. Hybrid Method of Multicriteria Evaluation of Decision Alternatives / N.D. Pankratova and N.I. Nedashkovskaya // Cybernetics and Systems Analysis. — 2014. — Vol. 50 (5). — P. 701–711.
Pankratova N. Estimation of Sensitivity of the DS/AHP Method While Solving Foresight Problems with Incomplete Data / N. Pankratova, N. Nedashkovskaya // Intelligent Control and Automation. — 2013. — Vol. 4, N 1. — P. 80–86.
Nedashkovskaya N. Investigation of methods for improving consistency of a pairwise comparison matrix / N. Nedashkovskaya // Journal of the Operational Research Society. — Published online: 02 Feb 2018.
Lipovetsky S. Robust estimation of priorities in the AHP / S. Lipovetsky, W.M. Conklin // European Journal of Operational Research. — Vol. 137 (1). — 2002. — P. 110–122.
Siraj S. A heuristic method to rectify intransitive judgments in pairwise comparison matrices / S. Siraj, L. Mikhailov, J. Keane // European Journal of Operational Research. — Vol. 216 (2). — 2012. — P. 420–428.
Stein William E. The harmonic consistency index for the analytic hierarchy process / William E. Stein, Philip J. Mizzi // European Journal of Operational Research. — Volume 177, Issue 1. — 2007. — P. 488–497.
Peláez J.I. A new measure of consistency for positive reciprocal matrices / J.I. Peláez, M.T. Lamata // Computer and Mathematics with Applications. — Vol. 46 (12). — 2003. — P. 1839–1845.
Totsenko V.G. Metody i sistemy podderzhki prinjatija reshenij. Algoritmicheskij aspekt / V.G. Totsenko. — K.: Nauk. dumka, 2002. — 381 s.
Pankratova N. Methods of evaluation and improvement of consistency of expert pairwise comparison judgements / N. Pankratova, N. Nedashkovskaya // International Journal "Information Theories and Applications". — 2015. — Vol. 22, N 3. — P.203–223.
Bidjuk P.I. Proektuvannja komp’juternykh informatsijnykh system pidtrymky pryjnjattja rishen': navch. posib. / P.I. Bidjuk, L.O. Korshevnjuk. — K.: NNK "IPSA" NTUU "KPI", 2010. — 340 s.