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An extension to fuzzy MCDM. (English) Zbl 1165.90697
Summary: An extension to the fuzzy multiple criteria decision making (MCDM) model is suggested in this work, where the ratings of alternatives versus criteria, and the importance weights of all criteria, are assessed in linguistic values represented by fuzzy numbers. Moreover, values of alternatives under objective criteria are normalized by a suggested approach. Meanwhile, the membership function of the final fuzzy evaluation value of each alternative can be developed. In addition, a Riemann integral based mean of removals is suggested to rank all the final fuzzy evaluation values for final decision making, so that the ranking procedure can be clearly formulated. Finally, a numerical example demonstrates the feasibility of the proposed model.
90C70Fuzzy programming
91B06Decision theory
03E72Fuzzy set theory
[1]Zadeh, L. A.: Fuzzy sets, Information and control 8, 338-353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[2]Chen, S. J.; Hwang, C. L.: Fuzzy multiple attribute decision making, (1992) · Zbl 0768.90042
[3]Carlsson, C.; Fuller, R.: Fuzzy multiple criteria decision making: recent developments, Fuzzy sets and systems 78, 139-153 (1996) · Zbl 0869.90078 · doi:10.1016/0165-0114(95)00165-4
[4]Ribeiro, R. A.: Fuzzy multiple attribute decision making: A review and new preference elicitation techniques, Fuzzy sets and systems 78, 155-181 (1996) · Zbl 0869.90083 · doi:10.1016/0165-0114(95)00166-2
[5]Triantaphyllou, E.; Lin, C. T.: Development and evaluation of five fuzzy multi-attribute decision-making methods, International journal of approximate reasoning 14, 281-310 (1996) · Zbl 0956.68535 · doi:10.1016/0888-613X(95)00119-2
[6]Al-Najjar, B.; Alsyouf, I.: Selecting the most maintenance approach using fuzzy multiple criteria decision making, International journal of production economics 84, 85-100 (2003)
[7]Chen, C. T.; Lin, C. T.; Huang, S. F.: A fuzzy approach for supplier evaluation and selection in supplier chain management, International journal of production economics 102, 289-301 (2006)
[8]Chen, C. T.: A fuzzy approach to select the location of the distribution center, Fuzzy sets and systems 118, 65-73 (2001) · Zbl 1151.90453 · doi:10.1016/S0165-0114(98)00459-X
[9]Chen, L. H.; Chiou, T. W.: A fuzzy credit-rating approach for commercial loans: A Taiwan case, Omega, int. J. mgmt. Sci. 27, 407-419 (1999)
[10]Chou, C. C.: A fuzzy MCDM method for solving marine transshipment container port selection problems, Applied mathematics and computation 186, 435-444 (2007) · Zbl 1185.90130 · doi:10.1016/j.amc.2006.07.125
[11]Chou, C. C.: The representation of multiplication operation on fuzzy numbers and application to solving fuzzy multiple criteria decision making problems, Lecture notes in artificial intelligence 4099, 161-169 (2006)
[12]Chou, T. Y.; Chou, S. T.; Tzeng, G. H.: Evaluating IT/IS investments: A fuzzy multi-criteria decision model approach, European journal of operational research 173, 1026-1046 (2006) · Zbl 1131.90375 · doi:10.1016/j.ejor.2005.07.003
[13]Kahraman, C.; Ruan, D.; Dogan, I.: Fuzzy group decision-making for facility location selection, Information sciences 157, 135-153 (2003) · Zbl 1049.90038 · doi:10.1016/S0020-0255(03)00183-X
[14]Liang, G. S.: Fuzzy MCDM based on ideal and anti-ideal concepts, European journal of operational research 112, 682-691 (1999) · Zbl 0933.90070 · doi:10.1016/S0377-2217(97)00410-4
[15]Tsaur, S. H.; Chang, T. Y.; Yen, C. H.: The evaluation of airline service quality by fuzzy MCDM, Tourism management 23, 107-115 (2002)
[16]Wang, Y. M.; Luo, Y.; Hua, Z.: On the extent analysis method for fuzzy AHP and its applications, European journal of operational research 186, 735-747 (2008) · Zbl 1144.90011 · doi:10.1016/j.ejor.2007.01.050
[17]Yeh, C. H.; Deng, H.; Pan, H.: Multi-criteria analysis for dredger dispatching under uncertainty, Journal of the operational research 50, 35-43 (1999) · Zbl 1054.90581
[18]Bortolan, G.; Degani, R.: A review of some methods for ranking fuzzy numbers, Fuzzy sets and systems 15, 1-19 (1985) · Zbl 0567.90056 · doi:10.1016/0165-0114(85)90012-0
[19]Cheng, C. H.: A new approach for ranking fuzzy numbers by distance method, Fuzzy sets and systems 95, 307-317 (1998) · Zbl 0929.91009 · doi:10.1016/S0165-0114(96)00272-2
[20]Wang, X.; Kerre, E. E.: Reasonable properties for the ordering of fuzzy quantities (I) (II), Fuzzy sets and systems 118, 375-385 (2001) · Zbl 0971.03055 · doi:10.1016/S0165-0114(99)00063-9
[21]Abbasbandy, S.; Asady, B.: Ranking of fuzzy numbers by sign distance, Information sciences 176, 2405-2416 (2006)
[22]Chen, L. H.; Lu, H. W.: The preference order of fuzzy numbers, Computers and mathematics with applications 44, 1455-1465 (2002) · Zbl 1104.91300 · doi:10.1016/S0898-1221(02)00270-5
[23]Chu, T. C.; Tsao, C. T.: Ranking fuzzy numbers with an area between the centroid point and the original point, Computers and mathematics with applications 43, 111-117 (2002) · Zbl 1113.62307 · doi:10.1016/S0898-1221(01)00277-2
[24]Liu, X. W.; Han, S. L.: Ranking fuzzy numbers with preference weighting function expectations, Computers and mathematics with applications 49, 1731-1753 (2005) · Zbl 1078.91005 · doi:10.1016/j.camwa.2004.11.014
[25]Y.J. Wang, H.S. Lee, The revised method of ranking fuzzy numbers with an area between the centroid and original points, Computers & Mathematics with Applications (2007), in press (doi:10.1016/j.camwa.2007.07.015) · Zbl 1137.62313 · doi:10.1016/j.camwa.2007.07.015
[26]Yong, D.; Zhu, Z.; Liu, Q.: Ranking fuzzy numbers with an area method using radius of gyration, Computers and mathematics with applications 51, 1127-1136 (2006) · Zbl 1134.68526 · doi:10.1016/j.camwa.2004.11.022
[27]Kaufmann, A.; Gupta, M. M.: Introduction to fuzzy arithmetic: theory and application, (1991) · Zbl 0754.26012
[28]Zadeh, L. A.: The concept of a linguistic variable and its application to approximate reasoning, part 1, 2 and 3, Information science 8, 199-249 (1975) · Zbl 0397.68071
[29]T.M. Chang, T.C Chu, Application of fuzzy MCDM to enterprise’s R&D resources allocation, in: Proceedings of The Fifth Conference on Management Theory and Practice of Electronic Business, Taiwan, 2004
[30]Tsao, C. T.; Chu, T. C.: An improved fuzzy MCDM model based on ideal and anti-ideal concepts, Journal of operations research society of Japan 45, 185-197 (2002) · Zbl 1027.90117
[31]Dubois, D.; Prade, H.: Operations on fuzzy numbers, International journal of systems science 9, 613-626 (1978) · Zbl 0383.94045 · doi:10.1080/00207727808941724
[32]Van Laarhoven, P. J. M.; Pedrycz, W.: A fuzzy extension of satty’s priority theory, Fuzzy sets and systems 11, 199-227 (1983) · Zbl 0528.90054 · doi:10.1016/S0165-0114(83)80083-9
[33]T.C. Chu, J.Y. Liu, S.X. Liu, A fuzzy MCDM model for the evaluation and selection of the locations of distribution centers, in: Proceedings of the Conference of the Chinese Institute of Industrial Engineering, Taiwan, 2006