摘要
這篇論文主要在討論如何在階層架構 (hierarchical structure) 下藉由決策者所提供的部分偏好資訊 (partial preference information) 來作決策。我們以二階層的架構來作討論並且提出一解法程序。此解法程序主要的觀念為利用第一階層的決策者所提供的部分偏好資訊來縮減非凌駕解集合 (non-dominated solution set)，並且由第二階層的決策者在被縮減過的非凌駕解集合當中選擇一妥協解 (compromise solution)。同時，為了提供更完整的資訊以作為決策的參考，我們針對成本以及資源來進行個別及整體的容忍度分析，並且求得縮減過的非凌駕解集合以及妥協解的容忍範圍。再者，我們針對以下二種情況提出以模糊規劃 (fuzzy programming) 的方法來找出一滿意解 (satisfactory solution) 的架構及求解程序，分別是 (1) 當決策者無法清楚表達目標權重的資訊時，(2) 當某些目標值，決策者認為約需大於或可能等於某一特定值時。

藉由文獻裡的觀念及方法論，我們有系統的說明如何在階層架構以及部分資訊下來進行決策及容忍度分析，進而考慮以上二種情況，我們在階層架構下發展出一找出滿意解的求解程序。

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ABSTRACT
This paper proposes a hierarchical procedure for solving multiple objective decision problems in which only partial information is given in the decision process. The procedure consists of two levels, a top-level and a base-level. The main idea is that the top-level provides partial preference information to reduce the non-dominated solution set；then the base-level determines a compromise solution from the reduced set. Furthermore, we also derive a procedure to find the tolerance regions of cost coefficients or RHS such that either the compromise solution or the final extreme solution set will maintain.

In this study we also consider that when DM is fuzzy about the tradeoff questions so that the DM may not be able to make exact tradeoffs among the objectives or sometimes, in a maximization (minimization) problem there exists some objectives for which DM may state to achieve substantially more (less) than or equal to some values. In such cases, we consider a fuzzy programming structure and construct an interactive fuzzy programming to find a satisfactory solution.

CHAPTER 2 LITERATURE REVIEW . . . . 5

CHAPTER 3 MULTI-OBJECTIVE ANALYSIS WITH PARTIAL

PREFERENCE INFORMATION . . . 8

3.1 Preference Presentation . . . . 8

3.2 Properties Derived From the Partial Information . 10

3.3 Conclusion . . . . . 12

CHAPTER 4 THE INTERACTIVE PROCEDURE FOR HIERARCHICAL DECISION

MAKING . . . . . 13

4.1 The Zionts-Wallenius Algorithm . . . 13

4.2 The Interactive Procedure for Hierarchical Decision

Makers . . . . . 14

4.3 Conclusion . . . . . 23

CHAPTER 5 TOLERANCE ANALYSIS OF AN MOLP WITH HIERARCHICAL

DECISION MAKERS . . . . 25

5.1 The Revised Algorithm for Perturbation Analysis . 35

5.2 Tolerance Analysis of the Cost Coefficients for

Hierarchical Decision Makers . . . 43

5.3 Tolerance Analysis of the RHS . . . 52

5.4 Tolerance Analysis of Both the Cost Coefficients

and RHS . . . . . 53

5.5 Conclusion . . . . . 54

CHAPTER 6 INTERACTIVE FUZZY PROGRAMMING . . 55

6.1 Problem Formulation . . . . 55

6.2 An Interactive Fuzzy Programming for Hierarchical

Decision Makers . . . . 58

6.3 Conclusion . . . . . 64

CHAPTER 7 SUMMARY AND CONCLUSIONS . . . 65

REFERENCES . . . . . 67

REFERENCES
[1] C. H. Antunes and J. N. Climaco, “Sensitivity analysis in MCDM using the weight space,” Operations Research Letters vol.12, pp.187-196, 1992.
[2] R. E. Bellman and L. A. Zadeh, “Decision Making in a Fuzzy Environment,” Management Science, vol.17, pp.141-164, 1970.
[3] E. Carrizosa, E. Conde, F. R. Fernandez and J. Puerto, “Multi-criteria analysis with partial information about the weighting coefficients,” European Journal of Operational Research vol.81, pp.291-301, 1995.
[4] W. J. Davis and J. Talavage, “Three-level models for hierarchical coordination,” Omega vol.5, pp.709-720, 1977.
[5] D. Deshpande and S. Zionts, “Sensitivity analysis in multiple objective linear programming : changes in the objective function matrix,” in : G. Fandel and T. Gal, Multiple Criteria Decision Making- Theory and application, Springer- Verlag, Berlin, pp.26-39, 1980.
[6] T. Gal and K. Wolf, “Stability in vector maximization-A survey,” European Journal of Operations Research vol.25, pp.169-182, 1986.
[7] C. Homburg, “Hierarchical multi-objective decision making,” European Journal of Operational Research vol.105, pp.155-161, 1998.
[8] R. L. Keeney and H. Raiffa, “Decisions with multiple objectives,” John Wiley & Sons, New York. 1976.
[9] J. Kornbluth, “Duality, indifference and sensitivity analysis in multiple objective linear programming,” Operation Research Quarter vol.25, pp.599-614, 1974.
[10] A. M. Marmol, J. Puerto and F. R. Fernandez, “The Use of Partial Information on Weights in Multicriteria Decision Problems,” J. Multi-Crit. Decis. Anal. vol.7, pp.322-329, 1998.
[11] M. Sakawa, “Fuzzy Set and Interactive Multiobjective Optimization”, New York：Plenum Press, 1993.
[12] M. Sakawa, I. Nishizaki and Y. Oka, “Interactive Fuzzy Programming for Multiobjective Two-Level Linear Programming Problems With Partial Information of Preference,” International Journal of Fuzzy Systems, vol.2, pp.79-86, June 2000.
[13] L. Seiford and P. L. Yu, “Potential solution of linear system : the multicriteria, mul-tiple constraint level program,” Journal of Mathematical Analysis and Applications vol.69, pp.283-303, 1979.
[14] R. E. Steuer, “Multiple Criteria Optimization : Theory, Computation and Application,” Wiley, New York, 1986.
[15] J. Telgen, “Minimal representation of convex polyhedral sets,” Journal of Optimization Theory and Applications vol.38, pp.1-24, 1982.
[16] H. F. Wang and Ou-Yang, H., “Tolerance analysis of a nondominated set in MOLP,” Technical Report, Department of Industrial Engineering and Engineering Management, National Tsing Hua University, 1994
[17] H. F. Wang and M. L. Wang, “Inter-parametric tolerance of a multiobjective linear programming,” Journal of Mathematical Analysis and Applications vol.179, pp.275-296, 1993.
[18] U. P. Wen and S. T. Hsu, “Linear Bi-level Programming Problems- A Review,” Journal of Operational Research Society, vol.42, pp.125-133, 1991.
[19] H.-J. Zimmermann, “Fuzzy Programming and Linear Programming with Several Objective Function,” Fuzzy Set and Systems, vol.1, pp.45-55, 1978.
[20] S. Zionts and J. Wallenius, “An interactive programming method for solving the multiple criteria problem,” Management Science vol.22, pp.652-663, 1976.
[21] S. Zionts and J. Wallenius, “An interactive Multiple objective linear programming method for a class of underlying nonlinear utility function,” Management Science vol.29, pp.519-529, 1983.

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