根據區間直覺模糊集合以作多屬性決策及多屬性群體決策是一個重要的研究課題。在本論文中，我們根據區間直覺模糊幾何平均運算子提出一個多屬性決策之新方法。首先，我們提出區間直覺模糊數之乘法運算子及區間直覺模糊數之乘冪運算子，進而提出區間直覺模糊加權幾何平均運算子、區間直覺模糊有序加權幾何平均運算子、及區間直覺模糊混合幾何平均運算子。根據我們所提之區間直覺模糊加權幾何平均運算子、區間直覺模糊有序加權幾何平均運算子、及區間直覺模糊混合幾何平均運算子，我們提出一個作多屬性決策之新方法。實驗結果顯示我們所提之新的多屬性決策方法可以克服目前已存在之方法的缺點，其提供一個很有用的方法以在區間直覺模糊之環境下作多屬性決策。另外，在本論文中，我們亦提出區間直覺模糊數之加法運算子，進而提出區間直覺模糊加權平均運算子、區間直覺模糊有序加權平均運算子、及區間直覺模糊混合平均運算子。根據我們所提之區間直覺模糊加權平均運算子、區間直覺模糊有序加權平均運算子、及區間直覺模糊混合平均運算子，我們亦提出一個作多屬性群體決策之新方法。實驗結果顯示我們所提之新的多屬性群體決策方法可以克服目前已存在之方法的缺點，其提供一個很有用的方法以在區間直覺模糊之環境下作多屬性群體決策。

Multiple attribute decision making and multiple attribute group decision making based on interval-valued intuitionistic fuzzy sets are important research topic. In this thesis, we propose a new multiple attribute decision making method based on the proposed interval-valued intuitionistic fuzzy geometric averaging operators. First, we propose the interval-valued intuitionistic fuzzy weighted geometric averaging (IVIFWGA) operator, the interval-valued intuitionistic fuzzy ordered weighted geometric averaging (IVIFOWGA) operator and the interval-valued intuitionistic fuzzy hybrid geometric averaging (IVIFHGA) operator based on the proposed multiplication operator between interval-valued intuitionistic fuzzy values and the proposed power operator of an interval-valued intuitionistic fuzzy value. Based on the proposed IVIFWGA operator, IVIFOWGA operator and the IVIFHGA operator, we also propose a new method for multiple attribute decision making. The experimental results show that the proposed multiple attribute decision making method can overcome the drawbacks of the existing multiple attribute decision making methods. It provides us with a useful way for multiple attribute decision making in interval-valued intuitionistic fuzzy environments. Moreover, we propose the interval-valued intuitionistic fuzzy weighted averaging (IVIFWA) operator, the interval-valued intuitionistic fuzzy ordered weighted averaging (IVIFOWA) operator and the interval-valued intuitionistic fuzzy hybrid averaging (IVIFHA) operator based on the proposed addition operator between interval-valued intuitionistic fuzzy values. Based on the proposed IVIFWA operator, IVIFOWA operator and the IVIFHA operator, we also propose a new method for multiple attribute group decision making. The experimental results show that the proposed multiple attribute group decision making method can overcome the drawbacks of the existing methods. It provides us with a useful way for multiple attribute group decision making in interval-valued intuitionistic fuzzy environments.

[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] T. Y. Chen, “A prioritized aggregation operator-based approach to multiple criteria decision making using interval-valued intuitionistic fuzzy sets: A comparative perspective,” Information Sciences, vol. 281, pp. 97-112, 2014.
[4] T. Y. Chen, “Multiple criteria decision analysis using a likelihood-based outranking method based on interval-valued intuitionistic fuzzy sets,” Information Sciences, vol. 286, pp. 188-208, 2014.
[5] T. Y. Chen, “Interval-valued fuzzy multiple criteria decision-making methods based on dual optimistic/pessimistic estimations in averaging operations,” Applied Soft Computing, vol. 24, pp. 923-947, 2014.
[6] T. Y. Chen, “Interval-valued intuitionistic fuzzy QUALIFLEX method with a
likelihood-based comparison approach for multiple criteria decision analysis,”
Information Sciences, vol. 261, pp. 149-169, 2014.
[7] T. Y. Chen, “The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making,” Applied Soft Computing, vol. 26, pp. 57-73, 2015
[8] S. M. Chen and C. H. Chang, “A novel similarity measure between Atanassov’s
intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition,” Information Sciences, vol. 291, pp. 96-114, 2015.
[9] S. M. Chen and C. H. Chang, “A new method for multiple attribute decision making based on intuitionistic fuzzy geometric averaging operators,” in Proceedings of the 2015 International Conference on Machine Learning and Cybernetics, Guangzhou, China, 2015, vol. 1, pp. 426-432.
[10] 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, vol. 1, pp. 403-409.
[11] 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.
[12] 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.
[13] J. Chu and X. Liu, “A mathematical programming method for multiple attribute decision making with interval-valued intuitionistic fuzzy values,” in Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, Beijing, China, 2014, pp. 1671-1677.
[14] S. Das, M. B. Kar, T. Pal, and S. Kar, “Multiple attribute group decision making using interval-valued intuitionistic fuzzy soft matrix,” in Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, Beijing, China, 2014, pp. 2222-2229.
[15] 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.
[16] H. Hashemi, J. Bazargan, S. M. Mousavi, and B. Vahdani, “An extended compromise ratio model with an application to reservoir flood control operation under an interval-valued intuitionistic fuzzy environment,” Applied Mathematical Modelling, vol. 38, no. 14, pp. 3495-3511, 2014.
[17] Y. He, H. Chen, L. Zhou, J. Liu, and Z. Tao, “Intuitionistic fuzzy geometric
interaction averaging operators and their application to multi-criteria decision making,” Information Sciences, vol. 259, pp. 142-159, 2014.
[18] 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.
[19] F. Jin, L. Pei, H. Chen, and L. Zhou, “Interval-valued intuitionistic fuzzy continuous weighted entropy and its application to multi-criteria fuzzy group decision making,” Knowledge-Based Systems, vol. 59, pp. 132-141, 2014.
[20] A. Kaufmann and M. M. Gupta, Fuzzy Mathematical Models in Engineering and
Management Science, Elsevier Science Publishers B.V., Amsterdam, The Netherlands, 1988.
[21] Y. Li, Y. Deng, F. T. S. Chan, J. Liu, and X. Deng, “An improved method on group decision making based on interval-valued intuitionistic fuzzy prioritized operators,” Applied Mathematical Modelling, vol. 38, no. 9-10, pp. 2689-2694, 2014.
[22] B. Liu, Y. Shen, W. Zhang, X. Chen, and X. Wang, “An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision making,” European Journal of Operational Research, vol. 245, no. 1, pp. 209-225, 2015.
[23] J. Liu, X. Deng, D. Wei, Y. Li, and Y. Deng, “Multi-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.
[24] P. Liu, “Some Hamacher aggregation operators based on the interval-valued
intuitionistic fuzzy numbers and their application to group decision making,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 83-97, 2014.
[25] W. Liu and S. H. Yang, “A novel method for multi-attribute group decision making with interval-valued intuitionistic uncertain linguistic information based on TOPSIS,” in Proceedings of the 2014 International Conference on Management Science & Engineering, Helsinki, Finland, 2014, pp. 193-199.
[26] 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.
[27] L. De Miguel, H. Bustince, J. Fernandez, E. Indurain, A. Kolesarova, and R. Mesiar, “Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making,” Information Fusion, vol. 27, pp. 189-197, 2016.
[28] X. Qi, C. Liang, and J. Zhang, “Generalized cross-entropy based group decision making with unknown expert and attribute weights under interval-valued intuitionistic fuzzy environment,” Computer & Industrial Engineering, vol. 79, pp. 52-64, 2015.
[29] Z. Pei, “Rational decision making models with incomplete weight information for production line assessment,” Information Sciences, vol. 222, no. 10, pp. 696-716, 2013.
[30] C. Tan, “A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS,” Expert Systems with Applications, vol. 38, no. 4, pp. 3023-3033, 2011.
[31] 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, Taipei, Taiwan, 2006, vol. 2, pp. 1404-1407.
[32] S. P. Wan and J. Y. Dong, “A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making,” Journal of Computer and System Sciences, vol. 80, pp. 237-256, 2014.
[33] S. P. Wan and J. Y. Dong, “Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees,” Information Fusion, vol. 26, pp. 49-65, 2015.
[34] S. P. Wan, G. L. Xu, F. Wang, and J. Y. Dong, “A new method for Atanassov’s interval-valued intuitionistic fuzzy MAGDM with incomplete attribute weight information,” Information Sciences, vol. 316, pp. 329-347, 2015.
[35] J. Q. Wang, K. J. Li, and H. Y. Zhang, “Interval-valued intuitionistic fuzzy multi-criteria decision making approach based on prospect score function,” Knowledge-Based Systems, vol. 27, pp. 119-125, 2012.
[36] J. Q. Wang, P. Wang, J. Wang, and H. Y. Zhang, and X. H. Chen, “Atanassov’s interval-valued intuitionistic linguistic multi-criteria group decision making method based on trapezium cloud model,” IEEE Transactions on Fuzzy Systems, , vol. 23, no. 3, pp. 542-554, Apr. 2014.
[37] W. Wang and X. Liu, “Intuitionistic fuzzy geometric aggregation operators based on Einstein operations,” International Journal of Intelligent Systems, vol. 26, pp. 1049-1075, 2011.
[38] W. Wang and X. Liu, “Intuitionistic fuzzy information aggregation using Einstein operations,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 5, pp. 923-938, 2012.
[39] W. Wang and X. Liu, “Interval-valued intuitionistic fuzzy hybrid weighted averaging operator based on Einstein operation and its application to decision making,” Journal of Intelligent & Fuzzy Systems, vol. 25, no. 2, pp. 279-290, 2013.
[40] W. Wang and X. Liu, “The multi-attribute decision making method based on
interval-valued intuitionistic fuzzy Einstein hybrid weighted geometric operator,” Computers and Mathematics with Applications, vol. 66, no. 10, pp. 1845-1856, 2013.
[41] 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.
[42] Z. X. Wang, L. L. Niu, R. X. Wu, and J. B. Lan, “Multicriteria decision-making method based on risk attitude under interval-valued intuitionistic fuzzy environment,” Fuzzy Information and Engineering, vol. 6, no. 4, pp. 489-504, 2014.
[43] G. W. Wei and X. R. Wang, “Some geometric aggregation operators based on interval-valued intuitionistic fuzzy sets and their application to group decision making,” in Proceedings of the 2007 International Conference on Computational Intelligence and Security, Harbin, China, 2007, pp. 495-499.
[44] J. Xu and F. Shen, “A new outranking choice method for group decision making under Atanassov’s interval-valued intuitionistic fuzzy environment,” Knowledge-Based Systems, vol. 70, pp. 177-188, 2014.
[45] Z. Xu, “A method based on distance measure for interval-valued intuitionistic fuzzy group decision making,” Information Sciences, vol. 180, no. 1-2, pp. 181-190, 2010.
[46] Z. S. Xu, “Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making,” Control and Decision, vol. 22, no. 2, pp. 2015-2019, 2007. (in Chinese)
[47] Z. Xu and J. Chen, “On geometric aggregation over interval-valued intuitionistic
fuzzy information,” in Proceedings of the Fourth International Conference on Fuzzy Systems and Knowledge Discovery, Haikou, China, vol. 2, pp. 466-471, 2007.
[48] 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.
[49] 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.
[50] J. Ye, “Multicriteria fuzzy decision-making method using entropy weights-based
correlation coefficients of interval-valued intuitionistic fuzzy sets,” Applied Mathematical Modeling, vol. 34, no. 12, pp. 3864-3870, 2010.
[51] D. Yu, Y. Wu, and T. Lu, “Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making,” Knowledge-Based Systems, vol. 30, pp. 57-66, 2012.
[52] Z. Yue, “Deriving decision maker’s weights based on distance measure for interval-valued intuitionistic fuzzy group decision making,” Expert Systems with Applications, vol. 38, no. 9, pp. 11665-11670, 2011.
[53] Z. Yue, “A group decision making approach based on aggregating interval data into interval-valued intuitionistic fuzzy information,” Applied Mathematical Modeling, vol. 38, no. 2, pp. 683-698, 2014.
[54] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338-356, 1965.
[55] 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.
[56] Q. Zhang, H. Xing, F. Liu, and Y. Huang, “An enhanced grey relational analysis method for interval-valued intuitionistic fuzzy multiattribute decision making,” Journal of Intelligent & Fuzzy Systems, vol. 26, no. 1, pp. 317-326, 2014.
[57] X. Zhang and Z. Xu, “Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making,” Applied Soft Computing, vol. 26, pp. 42-56, 2015.
[58] Y. J. Zhang, P. J. Ma, X. H. Su, and C. P. Zhang, “Multi-attribute group decision making under interval-valued intuitionistic fuzzy environment,” Acta Automatica Sinica, vol. 38, no. 2, pp. 220-227, 2012.
[59] Z. Zhang, Chao Wang, Dazeng Tian, and Kai Li, “A novel approach to interval-valued intuitionisitic fuzzy soft set based decision making,” Applied Mathematical Modelling, vol. 38, pp. 1255-1270, 2014.
[60] L. Zhou, Z. Tao, H. Chen, and J. Liu, “Continuous interval-valued intuitionistic fuzzy aggregation operators and their application to group decision making,” Applied Mathematical Modelling, vol. 38, no. 7-8, pp. 2190-2205, 2014.