模糊多屬性決策及模糊多屬性群體決策是重要的研究課題。在某些情況下，模糊多屬性決策及模糊多屬性群體決策中的各個屬性之權重資訊並不完整。近年來，已有一些處理權重資訊不完整的模糊多屬性決策問題的方法及一些處理模糊多屬性群體決策問題的方法被提出。在本論文中，我們根據區間直覺模糊集合、粒子群最佳化技術、及證據推理法提出一個新的模糊多屬性決策方法以處理權重資訊不完整的模糊多屬性決策問題。我們所提之新的模糊多屬性決策方法能克服目前已存在之模糊多屬性決策方法之缺點。另外，我們亦根據直覺模糊集合及證據推理法提出一個新的模糊多屬性群體決策方法以處理模糊多屬性群體決策問題。我們所提之新的模糊多屬性群體決策方法能克服目前已存在之模糊多屬性群體決策方法之缺點。

Fuzzy multiattribute decision making and fuzzy multiattribute group decision making are important research topics. There may be situations that the weights of attributes of fuzzy multiattribute decision making problems and fuzzy multiattribute group decision making problems are incomplete. In recent years, some methods have been presented to deal with fuzzy multiattribute decision making problems and fuzzy multiattribute group decision making problems with incomplete certain information on the weights of attributes. In this thesis, we propose a new fuzzy multiattribute decision making method for dealing with fuzzy multiattribute decision making problems with incomplete certain information on the weights of attributes based on interval-valued intuitionistic fuzzy sets, particle swarm optimization techniques and the evidential reasoning methodology. The proposed fuzzy multiattribute decision making method can overcome the drawbacks of the existing fuzzy multiattribute decision making methods. Moreover, we also propose a new fuzzy multiattribute group decision making method for dealing with fuzzy multiattribute group decision making problems based on intuitionistic fuzzy sets and the evidential reasoning methodology. The proposed fuzzy multiattribute group decision making method can overcome the drawbacks of the existing fuzzy multiattribute group decision making methods.

[1] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986.
[2] K. T. Atanassov and G. Gargov, “Interval-valued Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 31, no. 3, pp. 343-349, 1989.
[3] G. Beliakov, H. Bustince, S. James, T. Calvo, and J. Fernandez, “Aggregation for Atanassov’s intuitionistic and interval valued fuzzy sets: the median operator,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 3, pp. 487-498, Jun. 2012.
[4] F. E. Boran, “A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method,” Expert Systems with Applications, vol. 36, no. 8, pp. 11363-11368, 2009.
[5] H. Bustince and P. Burillo, “Vague sets are intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 79, no. 3, pp. 403-405, 1996.
[6] J. Chai and J. N. K. Liu, “A novel multicriteria group decision making approach with intuitionistic fuzzy SIR method,” in Proceedings of the 2010 World Automation Congress Kobe, Japan, 2010.
[7] T. Chaira, “Intuitionistic fuzzy segmentation of medical images,”IEEE Transactions on Biomedical Engineering, vol. 57, no. 6, pp. 1430-1436, 2010.
[8] S. M. Chen, “Analyzing fuzzy system reliability using vague set theory,” International Journal of Applied Science and Engineering, vol. 1, no. 1, pp. 82-88, 2003.
[9] S. M. Chen and C. H. Chiou, “A new method for multiattribute decision making based on interval-valued intuitionistic fuzzy sets, PSO techniques and evidential reasoning methodology,” in Proceedings of the 2014 International Conference on Machine Learning and Cybernetics, Lanzhou, China, 2014.
[10] S. M. Chen, L. W. Lee, H. C. Liu, and S. W. Yang, “Multiattribute decision making based on interval-valued intuitionistic fuzzy values,” Expert Systems with Applications, vol. 39, no. 12, pp. 10343-10351, 2012.
[11] S. M. Chen, M. W. Yang, S. W. Yang, T. W. Sheu, and C. J. Liau, “Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets,” Expert Systems with Applications, vol. 39, no. 15, pp. 12085-12091, 2012.
[12] W. L. Gau and D. J. Buehrer, “Vague sets,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 23, no. 2, pp. 610-614, 1993.
[13] Z. T. Gong and Y. Ma, “Multicriteria fuzzy decision making method under interval-valued intuitionistic fuzzy environment,” in Proceedings of the 2009 International Conference on Machine Learning and Cybernetics, Boading, Hebei, China, 2012, vol. 2, pp. 728-731.
[14] X. Jiang, Y. Hong, and Y. Zhang, “New energy marketing risk’s assessment and sorting in power supply enterprise based on interval-valued intuitionistic fuzzy multi-attribute decision making model,” in Proceedings of the 2012 World Automation Congress, Puerto Vallarta, Mexico, 2012.
[15] D. F. Li, “Fractional programming methodology for multi-attribute group decision-making using IFS,” Applied Soft Computing, vol. 9, no. 1, pp. 219-225, 2009.
[16] D. F. Li, “Mathematical-programming approach to matrix games with payoffs represented by Atanassov’s interval-valued intuitionistic fuzzy sets,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 6, pp. 1112-1128, 2010.
[17] D. F. Li, “TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 2, pp. 299-311, Apr. 2010.
[18] J. Liu, X. Deng, D. Wei, Y. Li, and Y. Deng, “Multu-attribute decision-making method based on interval-valued intuitionistic fuzzy sets and D-S theory of evidence,” in Proceedings of the 2012 24th Chinese Control and Decision Conference, Taiyuan, China, 2012, pp. 2651-2654.
[19] V. L. G. Nayagam, S. Muralikrishnan and G. Sivaraman, “Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets,” Expert Systems with Applications, vol. 38, no. 3, pp. 1464-1467, 2011.
[20] Z. Pei, “Rational decision making models with incomplete weight information for production line assessment,” Information Sciences, vol. 222, no. 10, pp. 696-716, 2013.
[21] Y. Shi and R. C. Eberhart, “Empirical study of particle swarms optimization,” in Proceedings of the 1999 Congress on Evolutionary Computation, vol. 3, pp. 1945-1949, 1999.
[22] E. Szmidt and J. Kacprzyk, “Distances between intuitionistic fuzzy sets, ”Fuzzy Sets and Systems, vol. 114, no. 3, pp. 505-518, 2000.
[23] E. Szmidt and J. Kacprzyk, “Using intuitionistic fuzzy sets in group decision making,” Control and Cybernetics, vol. 31, no. 4, pp. 1055-1057, 2002.
[24] E. Szmidt and J. Kacprzyk, “Ranking of intuitionistic fuzzy alternatives in a multi-criteria decision making problem,” in Proceedings of the 2009 Annual Meeting North American Fuzzy Information Processing Society, 2009, pp. 1-6.
[25] C. Tan, B. Ma, and X. Chen, “Intuitionistic fuzzy geometric aggregation operator based on fuzzy measure for multi-criteria group decision making,” in Proceedings of the 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery, Tianjin, China, 2009, pp. 545-549.
[26] C. Tan and Q. Zhang, “Fuzzy multiple attribute decision making based on interval valued intuitionistic fuzzy sets,” in Proceedings of the 2006 IEEE International Conference on Systems, Man, and Cybernetics, 2006, Taipei, Taiwan, vol. 2, pp. 1404-1407.
[27] Z. J. Wang, K. W. Li and W. Wang, “An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights,” Information Sciences, vol. 179, no. 17, pp. 3026-3040, 2009.
[28] Z. Wang, J. Xu, and W. Wang, “Intuitionistic fuzzy multiple attribute group decision making based on projection method,” in Proceedings of the 2009 Chinese Control and Decision Conference, Guilin, China, 2009, pp. 17-19.
[29] J. Q. Wang and H. Y. Zhang, “Multicriteria decision-making approach based on Atanassov’s intuitionistic fuzzy sets with incomplete certain information on weights,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 3, pp. 510-515, Jun. 2013.
[30] G. Wei, “Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making,” Applied Soft Computing, vol. 10, no. 2, pp. 423-431, 2010.
[31] L. Wen, “Intuitionistic fuzzy group decision making for supply chain information collaboration partner selection,” in Proceedings of the 2010 International Conference of Information Science and Management Engineering, Xian, China, 2010, pp. 43-46.
[32] Z. Xu, “Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making,” Control and Decision, vol. 22, no. 2, pp. 215-219, 2007.
[33] Z. Xu, “Intuitionistic fuzzy aggregation operators,” IEEE Transactions on Fuzzy
Systems, vol. 15, no. 6, pp. 1179-1187, 2007.
[34] Z. Xu, “Multi-person multi-attribute decision making models under intuitionistic fuzzy environment,” Fuzzy Optimization and Decision Making, vol. 6, no. 3, pp. 221-236, 2007.
[35] Z. Xu, “A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making,” Group Decision and Negotiation, vol. 19, no. 1, pp. 57-76, 2010.
[36] Z. Xu, “Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators,” Knowledge-Based Systems, vol. 24, no. 6, pp. 749-760, 2011.
[37] Z. Xu and R. R. Yager, “Dynamic intuitionistic fuzzy multi-attribute decision making,” International Journal of Approximate Reasoning, vol. 48, no. 1, pp. 246-262, 2008.
[38] J. B. Yang, “Rule and utility based evidential reasoning approach for multi-attribute decision analysis under uncertainty,” European Journal of Operational Research, vol. 131, no. 1, pp. 31-61, 2001.
[39] J. Ye, “Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment,” Expert Systems with Applications, vol. 36, no. 3, pp. 6899-6902, 2009.
[40] J. Ye, “Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets,” Applied Mathematical Modelling, vol. 34, no. 12, pp. 3864-3870, 2010.
[41] Z. Yue, “TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting,” Information Sciences, vol. 277, pp. 141-153, 2014.
[42] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
[43] S. Zeng and W. Su, “Intuitionistic fuzzy ordered weighted distance operator,” Knowledge-Based Systems, vol. 24, no. 8, pp. 1224-1232, 2011.
[44] H. Zhang and L. Yu, “MADM method based on cross-entropy and extended TOPSIS with interval-valued intuitionistic fuzzy sets,” Knowledge-Based Systems, vol. 30, pp. 115-120, 2012.
[45] Z. Zhitao and Z. Yingjun, “Multiple attribute decision making method in the frame of interval-valued intuitionistic fuzzy sets,” in Proceedings of the 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery, Shanghai, China, 2011, pp. 192-196.