線性規劃問題(linear programming problem)是對所有資源進行有效率的規劃，其中參數與變數都必須明確定義，並從各種限制條件中求得最佳結果。然而，現實生活中，由於資訊的不完整與不足，導致參數與決策變數無法明確定義，所以越來越多學者進行模糊線性規劃的探討，以模糊歸屬函數的概念表達資訊的不確定性問題，而當資訊不足時，變數與參數皆為模糊數之完全模糊線性規劃比起模糊線性規劃考量更多的不確定性。直覺模糊的概念允許人對資訊存在著猶豫性，以歸屬程度、非歸屬程度與猶豫程度來表達資訊。過去的學者在研究完全直覺模糊線性規劃大部分採用排序函數與字典排序，這些方法可以將過於複雜的完全直覺模糊線性規劃模型進行轉換成一般的線性規劃模型再進行求解，但求解的答案會根據決策者所使用的排序方法而有所不同。
本研究提出兩個以 截集概念直接求解直覺模糊數之完全模糊線性規劃模型，在模型Ⅰ與模型Ⅱ之中，以歸屬程度與非歸屬程度表達資訊的正向關係與負向關係，本研究模式Ⅰ主要分為四個步驟，首先建立出完全直覺模糊線性規劃的基本模型，第二步則將模型轉換為 截集的區間模型，第三步則轉換為 截集端點的模型，並將目標整合為單目標，最後則進行求解。而模型Ⅱ考量模型限制式兩邊值為關係模糊，多加入風險敏感度使決策者調整數值的大小關係。
套用數值範例與應用案例，顯示本研究提出兩個模型的可行性，並針對各種情境進行分析與探討。模型Ⅱ能夠提供決策者選擇其風險態度，並根據風險態度提供不同的結果，結果顯示本研究所提出模型Ⅱ可以給予風險趨避者模糊性較低的解決方案，而給予風險追求者模糊性較高的解決方案，而使用 截集也可以避免不同的方法所產生的不同結果，直接進行模型上的求解。最後，針對本研究給予結論與建議，並提出未來之研究方向。

Linear programming involves efficient planning of all resources, in which parameters and variables must be clearly defined, and the best results can be obtained from various constraints. However, in a real environment, due to incomplete and insufficient information, parameters and decision variables cannot be clearly defined. Scholars have discussed fuzzy linear programming as a method by which to express the uncertainty of information with the concept of fuzzy membership function. When the information is insufficient, fully fuzzy linear programming problems, in which all of the variables and parameters are stated as fuzzy numbers, consider more uncertainty than fuzzy linear programming. In the past, scholars studying fully intuitionistic fuzzy linear programming mostly used ranking function or lexicographic ranking methods. These methods can be used to convert the fully intuitionistic fuzzy linear programming model into a general linear programming model, but the results tend to vary depending on the ranking method used by the decision maker.
This study proposes two fully fuzzy linear programming models that directly solve the intuitionistic fuzzy numbers using the concept of -cut. Mode I is divided into four steps. First, a basic model of fully intuitionistic fuzzy linear programming is built. Second, the model is converted into an interval model. In the third step, the model is converted into an endpoint model, and finally the model is solved. Model II considers the constraints in the numerical relationship on both sides to be fuzzy, and risk sensitivity degree is added to allow the decision maker to adjust the value.
Numerical examples and application cases reveal the feasibility of the two models proposed in this study. Model II can provide decision makers with their level of risk and provide different results based on their attitude toward risk. The results show that Model II proposed in this study can provide solutions with a lower degree of ambiguity for risk avoiders and a higher degree of ambiguity for decision-makers who are less risk averse.

Arana‐Jiménez, M. (2018). Nondominated solutions in a fully fuzzy linear programming problem. Mathematical Methods in the Applied Sciences, 41(17), 7421-7430.
Atanassov, K. T. (1986), Intuitionistic fuzzy sets.Fuzzy Sets and Systems, 20 (1), 87-96.
Buckley, J. J., & Feuring, T. (2000). Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy Sets and Systems, 109(1), 35-53.
Baykasoğlu, A., & Subulan, K. (2015). An analysis of fully fuzzy linear programmimg with fuzzy decision variables through logistics network design problem. Knowledge-Based Systems, 90,165-184.
Bhardwaj, B., & Kumar, A. (2015). A note on “A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem”. Applied Mathematical Modelling, 39(19), 5982-5985.
Das, S. K., Mandal, T., & Edalatpanah, S. A. (2017). A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Applied Intelligence, 46(3), 509-519.
Dubois, D. and H. Prade (1978). Operations on fuzzy numbers. International Journal of Systems Science, 9(6), 613-626.
Dubey, D., Chandra, S., & Mehra, A. (2012). Fuzzy linear programming under interval uncertainty based on IFS representation. Fuzzy Sets and Systems, 188(1), 68-87.
Ebrahimnejad, A. (2019). An effective computational attempt for solving fully fuzzy linear programming using MOLP problem. Journal of Industrial and Production Engineering, 36(2), 59-69.
Ebrahimnejad, A., & Verdegay, J. L. (2018). A new approach for solving fully intuitionistic fuzzy transportation problems. Fuzzy Optimization and Decision Making, 17(4), 447-474.
Ezzati, R., Khorram, E., & Enayati, R. (2015). A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Applied Mathematical Modelling, 39(12), 3183-3193.
Mahapatra, G. S., & Roy, T. K. (2009). Reliability evaluation using triangular intuitionistic fuzzy numbers arithmetic operations. World Academy of Science, Engineering and Technology, 3(2), 350-357.
Guha, D., & Chakraborty, D. (2010). A theoretical development of distance measure for intuitionistic fuzzy numbers. International Journal of Mathematics and Mathematical Sciences, 2010.
Hamadameen, A. O., & Hassan, N. (2018). A compromise solution for the fully fuzzy multiobjective linear programming problems. IEEE Access, 6, 43696-43711.
Hashemi, S. M., Modarres, M., Nasrabadi, E., & Nasrabadi, M. M. (2006). Fully fuzzified linear programming, solution and duality. Journal of Intelligent & Fuzzy Systems, 17(3), 253-261.
Hosseinzadeh, A., & Edalatpanah, S. A. (2016). A new approach for solving fully fuzzy linear programming by using the lexicography method. Advances in Fuzzy Systems, 2016, 4.
Jeevaraj, S., & Dhanasekaran, P. (2016). A linear ordering on the class of trapezoidal intuitionistic fuzzy numbers. Expert Systems with Applications, 60, 269-279.
Kaur, J., & Kumar, A. (2012). Exact fuzzy optimal solution of fully fuzzy linear programming problems with unrestricted fuzzy variables. Applied Intelligence, 37(1), 145-154.
Khan, I. U., Ahmad, T., & Maan, N. (2013). A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2), 536-546.
Kumar, A., & Kaur, J. (2013). General form of linear programming problems with fuzzy parameters. Journal of Applied Research and Technology, 11(5), 629-635.
Kumar, A., Kaur, J., & Singh, P. (2011). A new method for solving fully fuzzy linear programming problems. Applied Mathematical Modelling, 35(2), 817-823.
Lotfi, F. H., Allahviranloo, T., Jondabeh, M. A., & Alizadeh, L. (2009). Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Applied Mathematical Modelling, 33(7), 3151-3156.
Nagoorgani, A., & Ponnalagu, K. (2012). A new approach on solving intuitionistic fuzzy linear programming problem. Applied Mathematical Sciences, 6(70), 3467-3474.
Ozkok, B. A., Albayrak, I., Kocken, H. G., & Ahlatcioglu, M. (2016). An approach for finding fuzzy optimal and approximate fuzzy optimal solution of fully fuzzy linear programming problems with mixed constraints. Journal of Intelligent & Fuzzy Systems, 31(1), 623-632.
Pérez-Cañedo, B., & Concepción-Morales, E. R. (2019). A method to find the unique optimal fuzzy value of fully fuzzy linear programming problems with inequality constraints having unrestricted LR fuzzy parameters and decision variables. Expert Systems with Applications, 123, 256-269.
Pérez-Cañedo, B., & Concepción-Morales, E. R. (2019). On LR-type fully intuitionistic fuzzy linear programming with inequality constraints: Solutions with unique optimal values. Expert Systems with Applications, 128, 246-255.
Razmi, J., Jafarian, E., & Amin, S. H. (2016). An intuitionistic fuzzy goal programming approach for finding pareto-optimal solutions to multi-objective programming problems. Expert Systems with Applications, 65, 181-193.
Tanaka, H., & Asai, K. (1984). Fuzzy solution in fuzzy linear programming problems. IEEE Transactions on Systems, Man, and Cybernetics, (2), 325-328.

Wan, S. P., Wang, F., Lin, L. L., & Dong, J. Y. (2015). An intuitionistic fuzzy linear programming method for logistics outsourcing provider selection. Knowledge-Based Systems, 82, 80-94.
Wang, G., & Peng, J. (2019). Fuzzy optimal solution of fuzzy number linear programming problems. International Journal of Fuzzy Systems, 21(3), 865-881.
Wu, H. C. (2019). Solving fuzzy linear programming problems with fuzzy decision vvariables. Mathematics, 7(7), 569.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control ,8(3), 338-353.
Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55.