Abstract
Several Multi-Criteria Decision Making (MCDM) methods involve pairwise comparisons to obtain the preferences of decision makers (DMs). This paper proposes a fuzzy group prioritization method for deriving group priorities/weights from fuzzy pairwise comparison matrices. The proposed method considers the different importance weights of multiple DMs by extending the Fuzzy Preferences Programming Method (FPP). The elements of the group pairwise comparison matrices are presented as fuzzy numbers rather than exact numerical values in order to model the uncertainty and imprecision in the DMs’ judgments. Unlike the known fuzzy prioritization techniques, the proposed method is able to derive crisp weights from incomplete and fuzzy set of comparison judgments and doesn’t require additional aggregation procedures. A prototype of a decision tool is developed to assist DMs to use the proposed method for solving fuzzy group prioritization problems. A detailed numerical example is used to illustrate the proposed approach.
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References
Choo, E., Wedley, W.: A common framework for deriving preference values from pairwise comparison matrices. Computers & Operations Research 31, 893–908 (2004)
Ittersum, K.V., Pennings, J.M., Wansink, B., van Trijp, H.C.: The validity of attribute-importance measurement: A review. Journa of Business Research 60, 1177–1190 (2007)
Edwards, W.: How to use multiattribute utility measurement for social decision making. IEEE Transactions on Systems, Man, and Cybernetics 7, 326–340 (1977)
Von Winterfeldt, D., Edwards, W.: Decision analysis and behavioural research. Cambridge University Press, Cambridge (1986)
Edwards, W., Barron, F.H.: SMARTS and SMARTER: Improved simple methods for multiattribute utility measurement. Organizational Behavior and Human Decision Processes 60, 306–325 (1994)
Thurstone, L.: A law of comparative judgment. Psychological Review 34, 273–286 (1927)
Saaty, T.L.: The analytic hierarchy process: Planning, Priority setting, resource allocation. McGraw-Hill, NY (1980)
Saaty, T.L.: Decision making with dependence and feedback: the Analytic Network Process. RWA Publications, PA (1996)
Brans, J., Mareschal, B.: Promethee methods: In multiple criteria decision analysis: state of the art surveys. International Series in Operations Research & Management Science 78, 163–186 (2005)
Xu, D.L., Yang, J.B., Lama, J.: Group-based ER–AHP system for product project screening. Expert Systems with Applications 35, 1909–1929 (2008)
Chu, A., Kalaba, R., Springam, K.: A comparison of two methods for determining the weights of belonging to fuzzy sets. Journal of Optimization Theory and Application 27, 531–541 (1979)
Saaty, T.L., Vargas, L.G.: Comparison of Eigenvalue, Logarithmic Least Squares and Least Squares Methods in Estimating Rations. Mathematical Modelling 5, 309–324 (1984)
Mikhailov, L.: A Fuzzy Programming Method for Deriving Prioritises in Analytic Hierarchy Process. The Journal of Operational Research Society 51, 341–349 (2000)
Buckley, J.J.: Fuzzy Hierarchical Analysis. Fuzzy Sets and System 17, 233–247 (1984)
Laarhoven, P.J.M., Pedrycz, W.: A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and System 11, 229–241 (1983)
Chang, D.: Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research 95, 649–655 (1996)
Mikhailov, L.: Deriving priorities from fuzzy pair-wise comparison judgments. Fuzzy Sets and System 134, 365–385 (2003)
Tiwari, R.N., Dharmar, S., Rao, J.R.: Fuzzy goal programming-an additive model. Fuzzy Sets and System 24, 27–34 (1987)
Higham, D.J., Higham, N.J.: MATLAB Guide, 2nd edn. SIAM (2005)
Mikhailov, L., Didehkhani, H., Sadi-Nezhad, S.: Weighted Prioritization Models in the Fuzzy Analytic Hierarchy Process. International Journal of Information Technology & Decision Making 10, 681–694 (2011)
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Almulhim, T.S., Mikhailov, L., Xu, DL. (2013). Deriving Weights from Group Fuzzy Pairwise Comparison Judgement Matrices. In: Rocha, Á., Correia, A., Wilson, T., Stroetmann, K. (eds) Advances in Information Systems and Technologies. Advances in Intelligent Systems and Computing, vol 206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36981-0_50
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DOI: https://doi.org/10.1007/978-3-642-36981-0_50
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