多階層決策問題(Multi-level decision making problems)為生活中常見之決策問題，在決策組織中，時常存在階層架構，在對問題進行求解時也必須考慮上下階層之領導力，找出各階層都能接受之解。然而，階層間也時常存在著目標衝突，面對衝突時，上階層之決策者往往會限制下階層決策者之求解範圍，使得下階層決策者失去決策之彈性，進而影響整體之目標達成程度，造成無法得到一組好的解。因此，在「領導權力」與「目標達成度」之間要如何取得平衡為多階層決策問題之探討點。近年來，對於多階層決策問題之研究大多使用模糊目標規劃進行求解，對於不滿意現行解之解決方式也有許多學者進行探討，重複調整所求得的解，盡量使每一階層決策者都可接受。然而，此步驟必須耗費許多時間，若能夠在求解前，事先加入決策者之要求，則必能增加求解之效率。
　　因此，本研究針對上下階層之目標達成滿意度之限制進行探討，考慮決策者間之相對重要程度，提出一目標達成滿意度區間之建立方法，使得低階層之決策者能夠依據其與上階層決策者之相對關係，有限度的超越其目標達成滿意度，增加其決策彈性。在前置階段，分別建立各階層目標值與決策變數之歸屬度函數，以及各階層之目標達成滿意度區，為求解模型建立階段時之限制式。本研究提出權重模式及語意變數模式之模糊目標規劃模型對問題進行求解，決策者可根據問題之需求選擇合適之模型進行求解。模型建立完成後，套用數值範例實際演練，並將結果和過去學者之方法做比較，顯示本研究之方法能夠有效提升整體目標滿意度，並且降低總偏差值，使整體解的品質提升。並分析不同權重分布之決策群體，得出第一階層決策者權重遠高於其他階層權重之組織，使用本研究之方法目標滿意度結果會較好。最後對於本研究給予結論與建議，並提出未來可繼續研究之方向。

There are many hierarchical decision-making problems in daily life. The multi-level linear programming(MLLP) method was developed to solve these kinds of problems. Satisfaction level, which represents the degree of goal achievement includes uncertain information. Hence, the concept of fuzzy set theory is used to define the satisfaction level of each goal and decision variable through establishing their membership functions. However, there are some issues in multi-level decision making problems. When lower-level decision-makers (DMs) are making their decisions, they often need to consider the opinions of higher-level decision makers. Therefore, there might be a situation in which lower-level DMs can’t reach their ideal degree of satisfaction even if the goal is easy to achieve. To conquer the disadvantages of multi-level decision-making problems mentioned above, a more flexible method is proposed. The proposed method implies that the satisfaction-level of the lower-level DM can slightly surpass its higher-level DM’s within a specific range of tolerance. The exceeding ratio (β) is calculated by the weights of the adjacent DM. Hence, this method also considers the relationship between the neighboring DMs. Furthermore, linguistic variables are used to present the subjective opinions of DMs in order to restrict the satisfaction relationship between the adjacent level in the fuzzy goal programming model. By comparing the results of the proposed method and those of previous methods used to solve multi-level decision-making problems, the proposed method achieves a higher satisfaction level. This means that the proposed method enables lower-level DMs to have a more flexible decision space that can avoid restrictions by higher-level DMs, so these lower-level DMs can achieve higher satisfaction if the goal is easier to achieve. In addition, the proposed method also considers the structures of different organizations through the given weights of each DM.

蔡昭廷 (2015). "以模糊目標規劃求解多階層單目標之決策問題." 成功大學工業與資訊管理學系學位論文,1-68.

Arora, S. and R. Gupta (2009). "Interactive fuzzy goal programming approach for bilevel programming problem." European Journal of Operational Research, 194(2), 368-376.

Baky, I. A. (2010). "Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach." Applied Mathematical Modelling, 34(9),2377-2387.

Bard, J. F. (1983). "An algorithm for solving the general bilevel programming problem." Mathematics of Operations Research ,8(2), 260-272.

Ben-Ayed, O., et al. (1988). "A general bilevel linear programming formulation of the network design problem." Transportation Research Part B: Methodological, 22(4), 311-318.

Chang, C.-T. (2007). "Binary fuzzy goal programming." European Journal of Operational Research ,180(1), 29-37.

Charnes, A. and Cooper, W. W. , (1961). Management models and industrial applications of linear programming. Wiley, New York.

Chen, L.-H. and Chen, H.-H. (2013). "Considering decision decentralizations to solve bi-level multi-objective decision-making problems: A fuzzy approach." Applied Mathematical Modelling, 37(10-11), 6884-6898.

Chen, L.-H. and Chen, H.-H. (2015a). "A fuzzy approach with required minimum decision tolerances for multi-level multi-objective decision-making problems." Journal of Intelligent & Fuzzy Systems, 28(1), 217-224.

Chen, L.-H. and Chen, H.-H. (2015b). "A two-phase fuzzy approach for solving multi-level decision-making problems." Knowledge-Based Systems, 76, 189-199.

Chen, L.-H. and Tsai, F.-C. (2001). "Fuzzy goal programming with different importance and priorities." European Journal of Operational Research ,133(3), 548-556.

Delgado, M., et al. (1998). "Combining numerical and linguistic information in group decision making." Information sciences ,107(1), 177-194.

Dubois, D. and H. Prade (1978). "Operations on fuzzy numbers." International Journal of systems science, 9(6), 613-626.

George J, Klir. and Y. Bo (2008). "Fuzzy sets and fuzzy logic, theory and applications." Upper Saddle River, New Jersey.

Lai, Y.-J. (1996). "Hierarchical optimization: a satisfactory solution." Fuzzy Sets and Systems, 77(3), 321-335.
Mikhailov, L. (2004). "Group prioritization in the AHP by fuzzy preference programming method." Computers & Operations Research, 31(2),293-301.

Mohamed, R. H. (1997). "The relationship between goal programming and fuzzy programming." Fuzzy Sets and Systems ,89(2), 215-222.

Narasimhan, R. (1980). "Goal programming in a fuzzy environment." Decision sciences ,11(2), 325-336.

Pramanik, S. and Roy, T. K. (2007). "Fuzzy goal programming approach to multilevel programming problems." European Journal of Operational Research ,176(2), 1151-1166.

Romero, C. (2004). "A general structure of achievement function for a goal programming model." European Journal of Operational Research ,153(3), 675-686.

Sakawa, M., et al. (1998). "Interactive fuzzy programming for multilevel linear programming problems." Computers & Mathematics with Applications ,36(2), 71-86.

Sakawa, M., et al. (2000). "Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters." Fuzzy Sets and Systems ,115(1), 93-103.

Shih, H.-S., et al. (1996). "Fuzzy approach for multi-level programming problems." Computers & Operations Research ,23(1), 73-91.

Sinha, S. (2003). "Fuzzy mathematical programming applied to multi-level programming problems." Computers & Operations Research ,30(9),1259-1268.

Sinha, S. (2003). "Fuzzy programming approach to multi-level programming problems." Fuzzy Sets and Systems ,136(2), 189-202.

Xia, H.-C., et al. (2006). "Fuzzy LINMAP method for multiattribute decision making under fuzzy environments." Journal of Computer and System Sciences ,72(4), 741-759.

Zadeh, L. A. (1965). "Fuzzy sets." Information and control ,8(3), 338-353.

Zadeh, L. A. (1975). "The concept of a linguistic variable and its application to approximate reasoning—I." Information sciences, 8(3), 199-249.

Zhang, L. (2014). "A Fuzzy Algorithm for Solving a Class of Bi-Level Linear Programming Problem." Applied Mathematics & Information Sciences ,8(4), 1823-1828.

Zhang, Z., Zhang, G., Lu, J. & Guo, C. (2013). "A fuzzy tri-level decision making algorithm and its application in supply chain. " Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology.

Zimmermann, H.-J. (1978). "Fuzzy programming and linear programming with several objective functions." Fuzzy Sets and Systems ,1(1), 45-55.