本論文之探討主題為模糊指派問題的敏感度分析，由於現實環境中的不確定因素，使得模糊指派問題於實際案例應用上更為廣泛。模糊指派問題如同指派問題一樣具有高度的退化現象，傳統敏感度分析(型I敏感度分析)只要求在目前最佳解之基底不變情況下的敏感度，對於模糊指派問題之最佳指派而言是不切實際的。因此我們利用型II 和型 III敏感度分析藉以克服此問題現象。
本論文提出了記演算法(the labeling algorithm) ，使其可延伸用來計算這另外兩種型態的敏感度分析，其中型II敏感度分析是在保持最佳指派不變情況下，計算細數可變動之範圍的敏感度分析；型III敏感度分析則是在保持目標函數斜率不變情況下，計算係數可變動之範圍的敏感度分析。本論文將標記演算法之演算過程分為兩個部份，分別是擾動(perturbation)發生在沒有被指派方格，或者是發生在有被指派的方格。兩者演算過程是利用相同觀念，因此有助學習。文中並提出數值範例說明計算模糊指派問題的型II和型III敏感度的步驟並顯示出標記演算法是可行的求解工具。

This thesis concentrates on sensitivity analysis of the fuzzy assignment problem(FAP). Since most real environment is uncertain, the FAP is more practical than the
assignment problem in application. Due to the high degeneracy of the FAP, as that of the assignment problem, traditional sensitivity analysis or Type I sensitivity analysis, which determines the range in which the current optimal basis remains optimal, is impractical. Hence, we attempt to perform practically other two types of sensitivity analysis-- Type II and Type III sensitivity analysis to overcome this problem.
We present the labeling algorithm, where to determine the two other types of sensitivity analysis, Type II sensitivity analysis is to determine the range of perturbation to keep the current optimal assignment remains optimal, and Type III sensitivity analysis is to determine the range for which the rate of change of optimal value function to keep unchanged. This study divided the procedure of the labeling algorithm into two parts: one is when the unassigned cell is perturbed, and the other is
when the assigned cell is perturbed. Both of them are base on the same concepts that make the procedure easy to learn. An example is presented in order to demonstrate that the labeling algorithm is an useful tool for determining the Type II and Type III sensitivity analysis of the FAP.

REFERENCES
[1] Arsham, H., Construction of the largest sensitivity region for general linear programs, Applied Mathematics and Computation 2007;189;1; 65-104.
[2] Avis, D., L. Devroye, An analysis of a decomposition heuristic for the assignment problem, Operations Research Letters 1985;3;6; 279-283.
[3] Bazaraa, M.S., H.D. Sherali, C.M. Shetty, Nonlinear programming—Theory and Algorithms, second ed., Wiley; New York; USA; 1993.
[4] Balinski, M.L., R.E. Gomory, A primal method for the assignment and transportation problems, Management Science 1967;10;3; 578–593.
[5] Bellman, R.E, L.A. Zadeh, Decision-making in a fuzzy environment, Management Science 1970;17B; 141–164.
[6] Captivo, M. E., J. Clímaco, J. Figueira, E. Martins, J.L. Santos, Solving bicriteria 0–1 knapsack problems using a labeling algorithm, Computers and Operations Research 2003;30; 1865–1886.
[7] Chanas, S., D. Kuchta, Fuzzy integer transportation problem, Fuzzy Sets and Systems 1998;98; 291-298.
[8] Chanas, S., D. Kuchta, A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, Fuzzy Sets and Systems 1996;82; 299-305.
[9] Chen, M.S., On a fuzzy assignment problem, Tamkang Journal 1985;22; 407-411.
[10] Chanas, S., W. Kolodziejczyk, A. Machaj, A fuzzy approach to the transportation problem, Fuzzy Sets and Systems 1984;13; 211-221.
[11] Charnes, A., W.W. Cooper, Programming with linear fractional functions, Naval Research Logistics Quarterly 1962;9; 181–186.
[12] Dijkstra, E. W., A note on two problems in connection with graphs, Numerische Mathematik 1959; 269-271.
[13] Dubois, D., P. Fortemps, Computing improved optimal solutions to max-min flexible constraint satisfaction problems, European Journal of Operational Research 1999;118; 95-126.
[14] Gal, T., Shadow prices and sensitivity analysis in linear programming under degeneracy-A state-of-the art survey, OR Spektrum 1986;8; 59-71.
[15] Gutiérrez, E., Andrés L. Medaglia, Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks, Annals of Operations Research 2008;157; 169-182.
[16] Hadigheh, A. G., T. Terlaky, Sensitivity analysis in linear optimization:Invariant support set intervals, European Journal of Operational Research 2006;169;4; 1158-1175.
[17] Haken, H., M. Schanz, J. Starke, Treatment of combinatorial optimal problems using selection equations with cost terms. Part I. Two-dimensional assignment problem, Physica D 1999;134; 227-241.
[18] Johnson, L.A., D.C. Montgomery, Operations research in production planning, in:Scheduling and Inventory Control, Wiley; New York; USA; 1974.
[19] Koltai, T., T. Terlaky, The difference between managerial and mathematical interpretation of sensitivity analysis results in linear programming, International Journal of Production Economics 2000;65; 257-274.
[20] Lin, C.J., U.P. Wen, Sensitivity analysis of the optimal assignment problem, European Journal of Operational Research 2003;149;1; 35-46.
[21] Lin, C.J., U.P. Wen, The labeling algorithm for the fuzzy assignment problem, Fuzzy Sets and Systems; 2004;142; 373-391.
[22] Lin, C.J., U.P. Wen, Sensitivity analysis of objective function coefficients of the assignment problem, Asia-Pacific Journal of Operational Research 2007;24;2; 203-221.
[23] Lotfi, V., A labeling algorithm to solve the assignment problem, Computers and Operations Research 1989;16;5; 397-408.
[24] Namkoong, S., J.-H. Rho, J.-U. Choi, Development of the tree-based link labeling algorithm for optimal path-finding in urban transportation networks, Mathematical and Computer modeling 1998;27; 51-65.
[25] Óh Éigeartaigh, M., A fuzzy transportation algorithm, Fuzzy Sets and Systems 1982;8; 235-243.
[26] Sakawa, M., I. Nishizaki, Y. Uemura, Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: a case study, European Journal of Operational Research 2001;135; 142-157.
[27] Schaible, S., T. Ibaraki, Fractional programming, European Journal of Operational Research 1983;12; 325–338.
[28] Shigeno, M., Y. Saruwatari, T. Matsui, An algorithm for fractional assignment problems, Discrete Applied Mathematics 1995;56; 333–343.
[29] Tada, M., H. Ishii, An integer fuzzy transportation problem, Computer Mathematical Application 1996;31; 71-87.
[30] Wang, X., Fuzzy optimal assignment problem, Fuzzy Mathematical 1987;3; 101-108.
[31] Werners, B., Interactive multiple objective programming subject to flexible constraints, European Journal of Operational Research 1987;31; 342-349.