Abstract
Multi-criteria decision making (MCDM) is one of the well-known topics of decision making. Fuzzy logic provides a useful way to approach a MCDM problem. Very often in MCDM problems, data are imprecise and fuzzy. In a real-world decision situation, the application of the classic MCDM method may face serious practical constraints, because of the criteria containing imprecision or vagueness inherent in the information. For these cases, fuzzy multi-attribute decision making (MADM) and fuzzy multi-objective decision making (MODM) methods have been developed. In this chapter, crisp MADM and MODM methods are first summarized briefly and then the diffusion of the fuzzy set theory into these methods is explained. Some examples of recently published papers on fuzzy MADM and MODM are given.
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References
Abo-Sinna, M.A., 2004, Multiple objective (fuzzy) dynamic programming problems: a survey and some applications, Applied Mathematics and Computation, 157: 861-888.
Abo-Sinna, M.A., and Abou-El-Enien, T.H.M., 2006, An interactive algorithm for large scale multiple objective programming problems with fuzzy parameters through TOPSIS approach, Applied Mathematics and Computation, forthcoming.
Baas, S.M., and Kwakernaak, H., 1977, Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica, 13: 47-58.
Bellman, R., and Zadeh, L. A., 1970, Decision-making in a fuzzy environment, Management Science, 17B: 141-164.
Borges, A.R., and Antunes, C.H., 2002, A weight space-based approach to fuzzy multiple-objective linear programming, Decision Support Systems, 34: 427-443.
Charnes, A., Cooper, W.W., and Rhodes, E., 1978, Measuring the efficiency of decision making units, European Journal of Operations Research, 2: 429-444.
Chen, S.J., and Hwang, C.L., 1992, Fuzzy Multiple Attribute decision-making, Methods and Applications, Lecture Notes in Economics and Mathematical Systems, 375: Springer, Heidelberg.
Chen, Y-W., and Larbani, M., 2006, Two-person zero-sum game approach for fuzzy multiple attribute decision making problems, Fuzzy Sets and Systems, 157: 34-51.
Dubois, D., and Prade, H., 1980, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.
Dutta, D., Tiwari, R.N., and Rao, J.R., 1992, Multiple objective linear fractional programming problem—a fuzzy set theoretic approach, Fuzzy Sets and Systems, 52(1): 39-45.
El-Wahed, W.F.A., and Abo-Sinna, M.A., 2001, A hybrid fuzzy-goal programming approach to multiple objective decision making problems, Fuzzy Sets and Systems, 119: 71-85.
Fan, Z-P., Hu, G-F., and Xiao, S-H., 2004, A method for multiple attribute decision-making with the fuzzy preference relation on alternatives, Computers and Industrial Engineering, 46: 321-327.
Fan, Z-P., Ma, J., and Zhang, Q., 2002, An approach to multiple attribute decision making based on fuzzy preference information on alternatives, Fuzzy Sets and Systems, 131: 101-106.
Fodor, J.C., and Roubens, M.,1994, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht.
Grabisch, M., 1992, The application of fuzzy integrals in multicriteria decision making, European Journal of Operational Research, 89: 445-456.
Gu, X., and Zhu, Q., 2006, Fuzzy multi-attribute decision-making method based on eigenvector of fuzzy attribute evaluation space, Decision Support Systems, 41: 400-410.
Guu, S.M., and Wu, Y.K., 1999, Two-phase approach for solving the fuzzy linear programming problems, Fuzzy Sets and Systems, 107: 191-195.
Hua, L., Weiping, C., Zhixin, K., Tungwai, N., and Yuanyuan, L., 2005, Fuzzy multiple attribute decision making for evaluating aggregate risk in green manufacturing, Journal of Tsinghua Science and Technology, 10(5): 627-632.
Hwang, C-L., and Yoon, K., 1981, Multiple Attribute Decision Making, Lecture Notes in Economics and Mathematical Systems, Heidelberg, Berlin, Springer-Verlag.
Kickert, W.J.M., 1978, Towards an analysis of linguistic modeling, Fuzzy Sets and Systems, 2 (4): 293-308.
Li, X., Zhang, B., and Li, H., 2006, Computing efficient solutions to fuzzy multiple objective linear programming problems, Fuzzy Sets and Systems, 157: 1328-1332.
Ling, Z., 2006, Expected value method for fuzzy multiple attribute decision making, Journal of Tsinghua Science and Technology, 11(1): 102-106.
Luhandjula, M.K., 1984, Fuzzy approaches for multiple objective linear fractional optimization, Fuzzy Sets and Systems, 13(1): 11-23.
Luhandjula, M.K., 1989, Fuzzy optimization: an appraisal, Fuzzy Sets and Systems, 30: 257-282.
Omero, M., D’Ambrosio, L., Pesenti, R., and Ukovich, W., 2005, Multiple-attribute decision support system based on fuzzy logic for performance assessment, European Journal of Operational Research, 160: 710-725.
Rasmy, M.H., Lee, S.M., Abd El-Wahed, W.F., Ragab, A.M., and El-Sherbiny, M.M., 2002, An expert system for multiobjective decision making: application of fuzzy linguistic preferences and goal programming, Fuzzy Sets and Systems, 127: 209-220.
Ravi, V., and Reddy, P.J., 1999, Ranking of Indian coals via fuzzy multi attribute decision making, Fuzzy Sets and Systems, 103: 369-377.
Riberio, R.A., 1996, Fuzzy multiple attribute decision making: a review and new preference elicitation techniques, Fuzzy Sets and Systems, 78: 155-181.
Saaty, T.L., 1980, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, McGraw-Hill, New York.
Saaty, T.L., 1996, The Analytic Network Process, RWS Publications, Pittsburgh, PA.
Sakawa, M., 1993, Fuzzy Sets and Interactive Multiobjective Optimization, Applied Information Technology, Plenum Press, New York.
Stancu-Minasian, I.M., and Pop, B., 2003, On a fuzzy set approach to solving multiple objective linear fractional programming problem, Fuzzy Sets and Systems, 134: 397-405.
Sugeno, M., 1974, Theory of fuzzy integrals and its applications, PhD thesis, Tokyo Institute of Technology, Tokyo, Japan.
Wang, Y-M., and Parkan, C., 2005, Multiple attribute decision making based on fuzzy preference information on alternatives: ranking and weighting, Fuzzy Sets and Systems, 153: 331-346.
Wu, F., Lu, J., and Zhang, G., 2006, A new approximate algorithm for solving multiple objective linear programming problems with fuzzy parameters, Applied Mathematics and Computation, 174: 524-544.
Xu, Z-S., and Chen, J., 2007, An interactive method for fuzzy multiple attribute group decision making, Information Sciences, 177(1): 248-263.
Yager, R.R., 1978, Fuzzy decision making including unequal objectives, Fuzzy Sets and Systems, 1: 87-95.
Zadeh, L.A., 1965, Fuzzy sets, Information and Control, 8: 338-353.
Zimmermann, H.J., 1978, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1: 45-55.
Zimmermann, H.J.,1985, Fuzzy Set Theory and Its Applications, Kluwer, Nijhoff Publishing, Boston.
Zimmermann, H.J., 1987, Fuzzy Sets, Decision Making, and Expert Systems, Kluwer, Boston.
Zimmermann, H.J., and Zysno, P., 1985, Quantifying vagueness in decision model, European Journal of Operational Research, 22: 148-158.
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Kahraman, C. (2008). Multi-Criteria Decision Making Methods and Fuzzy Sets. In: Kahraman, C. (eds) Fuzzy Multi-Criteria Decision Making. Springer Optimization and Its Applications, vol 16. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76813-7_1
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DOI: https://doi.org/10.1007/978-0-387-76813-7_1
Publisher Name: Springer, Boston, MA
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