在這快速變遷的時代，人們於現實環境中所需面臨的決策也逐漸複雜。決策問題中，經常包含多個評估屬性與可行方案。當資訊具不確定性，無法以明確值表達，且需同時考慮正向資訊、負向資訊及猶豫資訊時，應以直覺式模糊多屬性決策(Intuitionistic Fuzzy Multiple Attribute Decision Making；IFMADM)問題處理。而欲處理較複雜的決策問題時，通常需要一群專家共同參與該決策，因而產生「群體決策」。現實環境中，愈來愈多決策團隊開始有階級之分，導致各專家意見重要度依不同階級而有所差別。此外，若各專家權重相等，可能造成各專家意見過於分散，難以進行整合；而下層專家權重若僅由上層專家主觀給定，則可能造成專家給予與其意見相似者過高權重，兩種情況皆不利後續評估，欲獲得較集中且不偏頗之專家意見以利後續評估，則應將專家主觀給定權重依各專家意見其與平均意見之相似度進行調整。
根據上述問題，本研究發展一套於階層式群體決策環境下，以直覺式模糊集合及集中趨勢概念，獲得較合理專家直覺式模糊意見之方法，將各專家之權重根據其意見與平均意見之相似程度進行調整，與各專家之意見根據最終權重進行整合，並進行方案排序，幫助決策團隊選出最佳解決方案。接著本研究透過實際範例進行演算，並套用於不同權力比重給定方式之狀況及特殊狀況中，以驗證本研究方法之可行性。最後，本研究針對調整係數進行敏感度分析，進而檢視調整係數之變動對於最終權重與最佳解決方案之影響。根據演算結果，本研究發展之方法可順利於階層式群體決策環境下，專家意見為直覺式模糊值時，調整各專家之權重，並且解決意見分散及最終意見偏頗之問題。

Decision making(DM) is an important part of daily life. It has become more complex in information science and technology. To deal with complex DM problems with positive and negative information, intuitionistic fuzzy multiple attribute decision making (IFMADM) models are useful tools by which to obtain convincing results. In a real environment, more and more decision-making teams have begun to have class divisions, which leads to differences in the importance of experts’ opinions depending on their class. In addition, there are two types of situations that are not conducive to subsequent evaluation. First, the opinions of experts may be too scattered if the correlations among the experts’ weights are not considered. Second, if the weights of the lower-level experts are only subjectively given by upper-level experts, this may cause the upper-level experts to give too much weight to those who have opinions similar to theirs. If one wants to obtain a more concentrated expert opinion with the original information from each expert for subsequent evaluations, the subjectively given weights must be adjusted using a method considering the similarities between each expert opinion and the average opinion.
Based on these concerns, we develop a model for solving the IFMADM problem in hierarchical group decision-making environments with the concept of intuitionistic fuzzy sets and centralized trends. We adjust the experts’ weights according to the similarities among their opinions and the average opinion. Then, we aggregate all expert opinions with their final weights and score and rank these intuitionistic fuzzy sets using intuitionistic fuzzy scoring and ranking functions to help the decision-making team choose the best solution. We use numerical examples and apply them to situations in which there are different power weights and unique situations to verify the feasibility of the proposed method. Lastly, we conduct a sensitivity analysis of the adjustment coefficient, and then examine the influence of the adjustment coefficient on the final weight and the selected best alternative.

Keywords: Intuitionistic Fuzzy Sets, Group Multiple Attribute Decision, Hierarchical Grouping of Experts, Weight Adjustment, Fuzzy Aggregation

中文部分
王秉鈞. (民84).「管理學」. 台北：華泰書局.
燕蜻, 梁吉業. (2011). 混合多屬性群決策中的群體一致性分析方法. 中國管理科學, 19(6), 133-140.
劉宇婷. (2012). 考慮在階層式群體決策環境下之專家模糊意見整合. 成功大學工業與資訊管理學系碩士學位論文, https://hdl.handle.net/11296/ehb43v.
馮源, 宋詞. (2016). 群組決策的專家權重微調整方法. 計算機工程與應用, 52(26), 262-266.
洪舜平. (2018). 應用證據推理法於直覺模糊環境之群體決策模式. 成功大學工業與資訊管理學系碩士學位論文, https://hdl.handle.net/11296/98g686.
荊裕荃. (2019). 應用集群方法於直覺式模糊之群體決策模式.成功大學工業與資訊管理學系碩士學位論文, https://hdl.handle.net/11296/2evx75.
英文部分
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96.
Anandalingam, G. (1988). A mathematical programming model of decentralized multi-level systems. The Journal of the Operational Research Society, 39, 1021-1033.
Boran, F. E., Genc, S., Kurt, M., & Akay, D. (2009). A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Systems with Applications, 36, 11363-11368.
Boran, F. E., & Akay, D. (2014). A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Information Sciences, 255, 45-57.
Borza, M., & Rambely, A. S. (2016). An interactive fuzzy programming approach for the two-level linear programming problem with many leaders. Global Journal of Pure and Applied Mathematics ,12(4), 3585-3600.
Burillo, P., & Bustince, H. (1996). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 78(3), 305-316.
Chen, C. T. (2001). Applying linguistic decision-making method to deal with service quality evaluation problems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9, 103-114.
Chen, G. H., Liao, X. L., Yu, X., Luo, Z. J., & Li, J. C. (2011). An interval intuitionistic fuzzy number portfolio selection model based on genetic algorithms. International Review on Computers and Software, 6(7), 1339-1342.
Chen, L. H., & Tu, C. C. (2014). Dual bipolar measures of Atanassov's intuitionistic fuzzy sets. IEEE Transactions on Fuzzy Systems, 22(4), 966-982.
Chen, S. M., & Tan, J. M. (1994). Handling multi-criteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 67(2), 163-172.
Chen, S. M., & Lee, L. W. (2010). Fuzzy multiple criteria hierarchical group decision-making based on interval type-2 fuzzy sets. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 40, 1120-1128.
Chen, X., & Fan, Z. (2007). Study on assessment level of experts based on difference
preference information. Systems Engineering-Theory & Practice, 27(2), 27-35.
Delgado, M., Herrera, F., Herrera-Viedma, E. & Martinez, L. (1998). Combining numerical and linguistic information in group decision making, Information Sciences, 107, 177-194.
Feng, C. M., Wu, P. J. & Chia, K. C. (2010). A hybrid fuzzy integral decision-making model for locating manufacturing centers in China: A case study. European Journal of Operational Research, 200, 63-73.
Hsu, H. M. and Chen, C. T. (1996). Aggregation of fuzzy opinions under group decision making. Fuzzy Sets and Systems, 79, 279-285.
Henry Mintzberg. (1979). The structure of organization. Englewood Cliffs, N.J.: Prenttice-Hall, 215-297.
Herrera, F., Herrera-Viedma, E. & Verdegay, J. L. (1996). Direct approach processes in group decision making using linguistic OWA operators. Fuzzy sets and systems, 79, 175-190.
Herrera, F., Martinez, L. & Sanchez, P. J. (2005). Managing non-homogeneous information in group decision making. European Journal of Operational Research, 166, 115-132.
Hong, D. H., & Choi, C. H. (2000). Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 114(1), 103-113.
Hwang, C. L., & Yoon, K. P. (1981). Multiple attribute decision making: methods and applications, Springer-Verlag, Berlin.
Hung, W. L., & Yang, M. S. (2004). Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognition Letters, 25(14), 1603-1611.
Kumar, A., & Karmakar, G. (2001). Aggregation of opinions using fuzzy numbers. International Journal of System Science, 32, 1399-1411.
Lee, H. S. (2002). Optimal consensus of fuzzy opinions under group decision making environment. Fuzzy Sets and Systems, 132, 303-315.
Liu, B. S., Shen, Y. H., Chen, Y., Chen, X. H., & Wang, Y. M. (2015). A two-layer weight determination method for complex multi-attribute large-group decision-making experts in a linguistic environment. Information Fusion, 23, 156-165.
Liu, B. S., Guo, S. J., Yan, K. J., Li, L., & Wang, X. Q. (2017). Double weight determination method for experts of complex multi-attribute large-group decision-making in interval-valued intuitionistic fuzzy environment, Journal of Systems Engineering and Electronics, 28(1), 88-96.
Li, D. F., & Cheng, C. T. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1-3), 221-225.
Li, F., & Xu, Z. Y. (2001). Similarity measures between vague sets. J. Software, 12(6), 922-927.
Li, Y., Zhongxian, C., & Degin, Y. (2002). Similarity measures between vague sets and vague entropy. Journal of Computer Science, 29(12), 129-132.
Liang, Z. Z., & Shi, P. F. (2003). Similarity measures on intuitionistic fuzzy sets. Pattern Recognition Letters, 24(15), 2687-2693.
Liao, H. C., Mi, X. M., Xu, Z. S., Xu, J. P., & Herrera, F. (2018). Intuitionistic fuzzy analytic network process, IEEE Transactions on Fuzzy Systems, 26(5), 2578-2590.
Lu, C., Lan, J. & Wang, Z. (2006). Aggregation of fuzzy opinions under group decision-making based on similarity and distance. Journal of Systems Science and Complexity, 19, 63-71.
Mitchell, H. B. (2003). On the Dengfeng-Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Letters, 24(16), 3101-3104.
Moon, Y., & Yao, T. (2011). A robust mean absolute deviation model for portfolio optimization. Computers & Operations Research, 38, 1251-1258.
Olcer, A. I., & Odabasi, A. Y. (2005). “A new multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem,” European Journal of Operational Research, 166, 93-114.
Parreiras, R. O., Ekel, P. Y. Martini, J. S. C., & Palhares, R. M. (2010). A flexible consensus scheme for multicriteria group decision making under linguistic assessments. Information Sciences, 180, 1075-1089.
Saaty, T. L. (1990). How to make a decision: the analytic hierarchy process. European Journal of Operational Research, 48(1), 9-26.
Si, Y., & Wei, F. (2009). Dynamic multiattribute decision making based on the
intuitionistic fuzzy priority rating model. 2009 International Conference on Management Science and Engineering, 239-245.
Stewart, T. J. (1992). A critical survey on the status of multiple criteria decision-making: theory and practice. Omega, 20, 569-586.
Shih, H. S., & Lee, E. S. (2000). Compensatory fuzzy multiple level decision making. Fuzzy Sets and Systems, 114, 71-87.
Song, Y. F., & Wang, X. D. (2017). A new similarity measure between intuitionistic fuzzy sets and the positive definiteness of the similarity matrix. Pattern Analysis and Applications, 20(1), 215-226.
Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114(3), 505-518.
Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118(3), 467-477.
Turban, E. (1988). Decision support systems and expert systems: managerial perspectives. New York: Macmillan.
Tiryaki, F. (2006). Interactive compensatory fuzzy programming for decentralized multi-level linear programming (DMILP) problems. Fuzzy Sets and Systems, 157, 3072-3090.
Wan, S. P., Wang, F., Xu, G. L., Dong, J. Y., & Tang, J. (2017). An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations. Fuzzy Optimal Decision Making, 16, 269-295
Wang, Y. M., & Parkan, C. (2006). Two new approaches for assessing the weights of fuzzy opinions in group decision analysis. Information Sciences, 176, 3538-3555.
Wei, C. P., Wang, P., & Zhang, Y. Z. (2011). Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Information Sciences, 181, 4273-4286.
Wu, D., & Mendel, J. M. (2007). Aggregation using the linguistic weighted average and interval type-2 fuzzy sets. IEEE Transactions on Fuzzy Systems, 15, 1145-1161.
Wu, J., & Chiclana, F. (2014). A social network analysis trust-consensus based approach to group decision-making problems with interval-valued fuzzy reciprocal preference relations. Knowledge-Based Systems, 1-26.
Xu, Z. (2004). A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Information Sciences, 166, 19-30.
Xu, Z. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6), 1179-1187.
Xu, Z. (2012). Intuitionistic fuzzy multiattribute decision making: an interactive
method. IEEE Transactions on Fuzzy Systems, 20(3), 514-525.
Xu, Z. S., & Liao, H. C. (2014). Intuitionistic Fuzzy Analytic Hierarchy Process. IEEE Transactions on Fuzzy Systems, 22(4), 749-761.
Yeh, C. H. (2003). The selection of multiattribute decision making methods for scholarship student selection. International Journal of Selection and Assessment, 11(4), 289-296.
Ye, J. (2011). Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and Computer Modelling, 53(1-2), 91-97.
Yoon, K. P., & Hwang, C. L. (1995). “Multiple attribute decision making: an introduction,” Sage Publications, USA.
Yue, Z. L. (2011). Deriving decision maker’s weights based on distance measure for interval-valued intuitionistic fuzzy group decision making. Expert Systems with Applications, 38, 11665-11670.
Yue, Z. L. (2012). Approach to group decision making based on determining the weights of experts by using projection method. Applied Mathematical Modelling, 36(7), 2896-2906.
Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), 338-353.
Zeleny, M., & Cochrane, J. L. (1982). Multiple Criteria Decision Making. New York:McGraw-Hill.
Zeng, S., & Su, W. (2011). Intuitionistic fuzzy ordered weighted distance operator. Knowledge-Based Systems, 24(8), 1224-1232.
Zhang, H. M., & Yu, L. Y. (2013). New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets. Information Sciences, 245, 181-196.
Zhang, W. C., Xu, Y. J., & Wang, H. M. (2016). A consensus reaching model for 2-tuple linguistic multiple attribute group decision making with incomplete weight information. International Journal of Systems Science,47(2),389-405.