Czasopismo
2014
|
Vol. 133, nr 4
|
367--386
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
The Heuristic Ratio Estimation (HRE) approach proposes a new way of using the pairwise comparisons matrix. It allows the assumption that the weights of some alternatives (herein referred to as concepts) are known and fixed, hence the weight vector needs to be estimated only for the other unknown values. The main purpose of this paper is to extend the previously proposed iterative HRE algorithm and present all the heuristics that create a generalized approach. Theoretical considerations are accompanied by a few numerical examples demonstrating how the selected heuristics can be used in practice.
Czasopismo
Rocznik
Tom
Strony
367--386
Opis fizyczny
Bibliogr. 42 poz., rys.
Twórcy
autor
- Department of Applied Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland, konrad.kulakowski@agh.edu.pl
Bibliografia
- [1] Bagnara, R.: A Unified Proof For The Convergence Of Jacobi And Gauss-Seidel Methods, SIAM Review, 37, 1995.
- [2] Barzilai, J., Golany, B.: AHP rank reversal, normalization and aggregation rules, INFOR – Information Systems and Operational Research, 32 (2), 1994, 57–64.
- [3] Bodzoń-Kułakowska, A., Kułakowski, K., Drabik, A., Moszczynski, A., Silberring, J., Suder, P.: Morphinome–a meta-analysis applied to proteomics studies in morphine dependence., Proteomics, 11(1), January 2011, 5–21.
- [4] Bozóki, S.: Solution of the least squares method problem of pairwise comparison matrices, Central European Journal of Operations Research, 16(4), 2008, 345–358.
- [5] Bozóki, S., Fülöp, J., Rónyai, L.: On optimal completion of incomplete pairwise comparison matrices, Mathematical and Computer Modelling, 52(1–2), 2010, 318 – 333, ISSN 0895-7177.
- [6] Bozóki, S., Rapcsak, T.: On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices, Journal of Global Optimization, 42(2), 2008, 157–175.
- [7] Brunelli, M., Canal, L., Fedrizzi, M.: Inconsistency indices for pairwise comparison matrices: a numerical study, Annals of Operations Research, February 2013.
- [8] Colomer, J. M.: Ramon Llull: from ‘Ars electionis’ to social choice theory, Social Choice and Welfare, 40(2), October 2011, 317–328.
- [9] Bana e Costa, C. A., Vansnick, J.: A critical analysis of the eigenvalue method used to derive priorities in AHP, European Journal of Operational Research, 187(3), June 2008, 1422–1428.
- [10] Crawford, G. B.: The geometric mean procedure for estimating the scale of a judgement matrix, Mathematical Modelling, 9(3–5), 1987, 327 – 334, ISSN 0270-0255.
- [11] Dyer, J. S.: Remarks on the analytic hierarchy process, Management Science, 36(3), 1990, 249–258.
- [12] Fechner, G. T.: Elements of psychophysics, vol. 1, Holt, Rinehart and Winston, New York, 1966.
- [13] Fedrizzi, M., Brunelli, M.: On the priority vector associated with a reciprocal relation and a pairwise comparison matrix, Journal of Soft Computing, 14(6), January 2010, 639–645, ISSN 1432-7643.
- [14] Fedrizzi, M., Giove, S.: Incomplete pairwise comparison and consistency optimization, European Journal of Operational Research, 183(1), 2007, 303–313.
- [15] Greco, S., Matarazzo, B., Słowiński, R.: Dominance-Based Rough Set Approach on Pairwise Comparison Tables to Decision Involving Multiple Decision Makers, in: Rough Sets and Knowledge Technology (J. Yao, S. Ramanna, G. Wang, Z. Suraj, Eds.), vol. 6954 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2011, ISBN 978-3-642-24424-7, 126–135.
- [16] Ho, W.: Integrated analytic hierarchy process and its applications - A literature review, European Journal of Operational Research, 186(1), March 2008, 18–18.
- [17] Ishizaka, A., Labib, A.: Analytic hierarchy process and expert choice: Benefits and limitations, OR Insight, 22(4), 2009, 201–220.
- [18] Ishizaka, A., Labib, A.: Review of the main developments in the analytic hierarchy process, Expert Systems with Applications, 38(11), October 2011, 14336–14345.
- [19] Ishizaka, A., Lusti, M.: How to derive priorities in AHP: a comparative study, Central European Journal of Operations Research, 14(4), December 2006, 387–400.
- [20] Janicki, R., Zhai, Y.: On a pairwise comparison-based consistent non-numerical ranking, Logic Journal of the IGPL, 20(4), 2012, 667–676.
- [21] Koczkodaj, W. W.: A new definition of consistency of pairwise comparisons, Math. Comput. Model., 18(7), October 1993, 79–84, ISSN 0895-7177.
- [22] Koczkodaj, W. W., Herman, M. W., Orlowski, M.: Managing Null Entries in Pairwise Comparisons, Knowledge and Information Systems, 1(1), 1999, 119–125.
- [23] Koczkodaj, W. W., Orłowski, M.: Computing a consistent approximation to a generalized pairwise comparisons matrix, Computers & Mathematics with Applications, 37(3), 1999, 79–85.
- [24] Koczkodaj, W. W., Szarek, S. J.: On distance-based inconsistency reduction algorithms for pairwise comparisons, Logic Journal of the IGPL, 18(6), October 2010, 859–869.
- [25] Kułakowski, K.: A heuristic rating estimation algorithm for the pairwise comparisons method, Central European Journal of Operations Research, 2013, 1–17, ISSN 1435-246X.
- [26] Liberatore, M. J., Nydick, R. L.: The analytic hierarchy process in medical and health care decision making: A literature review, European Journal of Operational Research, 189(1), August 2008, 14–14.
- [27] Mikhailov, L.: Deriving priorities from fuzzy pairwise comparison judgements, Fuzzy Sets and Systems, 134(3), March 2003, 365–385.
- [28] Ministry of Science and Higher Education: Regulation on principles of science financing (Polish: Rozporządzenie Ministra Nauki i Szkolnictwa Wyższego w sprawie kryteriów i trybu przyznawania kategorii naukowej jednostkom naukowym), Dziennik Ustaw Rzeczypospolitej Polskiej, 877, 2012.
- [29] Quarteroni, A., Sacco, R., Saleri, F.: Numerical mathematics, Springer Verlag, 2000.
- [30] Saaty, T. L.: A scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology, 15(3), 1977, 234 – 281, ISSN 0022-2496.
- [31] Saaty, T. L.: An Exposition on the AHP in Reply to the Paper "Remarks on the Analytic Hierarchy Process", Management Science, 36(3), March 1990, 259–268.
- [32] Saaty, T. L.: The Analytic Hierarchy and Analytic Network Processes for the Measurement of Intangible Criteria and for Decision-Making, in: Multiple Criteria Decision Analysis: State of the Art Surveys, vol. 78 of International Series in Operations Research and Management Science, Springer New York, 2005, ISBN 978-0-387-23067-2, 345–405.
- [33] Saaty, T. L.: Relative Measurement and Its Generalization in Decision Making. Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors. The Analytic Hierarchy/Network Process, Estadísticae Investigación Operativa / Statistics and Operations Research (RACSAM), 102, November 2008, 251–318.
- [34] Saaty, T. L., Hu, G.: Ranking by eigenvector versus other methods in the analytic hierarchy process, Applied Mathematics Letters, 11(4), 1998, 121–125.
- [35] Schlager, N., Lauer, J., Eds.: Science and its times: understanding the social significance of scientific discovery, vol. 2, Schlager Information Group, 2000.
- [36] Smith, J. E., VonWinterfeldt, D.: Anniversary article: decision analysis in management science, Management Science, 50(5), 2004, 561–574.
- [37] Subramanian, N., Ramanathan, R.: A review of applications of Analytic Hierarchy Process in operations management, International Journal of Production Economics, 138(2), August 2012, 215–241.
- [38] Thurstone, L. L.: A Law of Comparative Judgment, reprint of an original work published in 1927, Psychological Review, 101, 1994, 266–270.
- [39] Vaidya, O. S., Kumar, S.: Analytic hierarchy process: An overview of applications, European Journal of Operational Research, 169(1), February 2006, 1–29.
- [40] Yuen, K. K. F.: Analytic hierarchy prioritization process in the AHP application development: A prioritization operator selection approach, Appl. Soft Comput., 10(4), 2010, 975–989.
- [41] Yuen, K. K. F.: Membership Maximization Prioritization Methods for Fuzzy Analytic Hierarchy Process, Fuzzy Optimization and Decision Making, 11(2), June 2012, 113–133, ISSN 1568-4539.
- [42] Yuen, K. K. F.: Fuzzy Cognitive Network Process: Comparison with Fuzzy Analytic Hierarchy Process in New Product Development Strategy, Fuzzy Systems, IEEE Transactions on, PP(99), 2013, 1–1, ISSN 1063-6706.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-f7edef45-1fc2-45bf-ab3f-e7943212ae3c