臺灣博碩士論文加值系統

從Butnariu(1978)研究兩人模糊非合作賽局開始，至今已有不少學者針對不同類型的模糊賽局，提出各種不同的求解模式，但綜觀目前相關的研究成果，發現下列幾點仍可做進一步的探討與改善：(1)在模糊非合作賽局的相關研究中，參與賽局的玩家數目大多只討論2人賽局，對於多人賽局較少研究，但在現實環境中，多人賽局是相當普遍的情況；(2)只針對零和賽局或非零和賽局進行研究，較少同時探討此兩類型賽局；(3)在目前的相關研究中，賽局矩陣中的報酬值絕大部份是直接給定，並沒有對於該報酬值的取得過程進行研究；(4)報酬值的型式，大都以模糊數表示，並無同時考慮明確數值或語意值。
針對上述幾點，本研究針對模糊非合作賽局發展完整的求解模式，各玩家根據可能採取的策略，與影響策略選擇的屬性因素，整合建立各玩家在不同策略組合下的綜合報酬值與完整的賽局矩陣，再發展一模糊線性規劃模式，運用數學規劃軟體，求出各玩家的最大期望報酬與混合策略機率值。
本研究所發展的模糊非合作賽局求解模式，將可完整考量下列狀況：兩人玩家至多人玩家、兩策略至多策略、零和與非零和賽局，除此亦考量影響各玩家策略的屬性因素與報酬值的型式等，以增加其完整性與實用性。
除以一數值範例說明整個模式的計算過程外，針對求解模糊線性規劃模式，本研究以明確報酬值及模糊報酬值之賽局進行驗證，最後，以某電信公司高雄地區之服務中心內設銷售據點的三家手機通路商為例，針對其所採取之行銷策略進行模糊非合作賽局分析，以驗證本研究之實用性。

Since Butnariu(1978) studied the two-person fuzzy noncooperative game, many researchers have been bringing up different solutions with the fuzzy game. There are some points can be conferred and improved in following results: (1) Most fuzzy noncooperative game focused on the game of two players; however, in general, the n-person game is common. (2) Previously studies seldom conferred with zero-sum game or non-zero-sum game simultaneously. (3) The game payoff was given directly by decision makers without explaining how to acquire it. (4) The type of payoff was showed by fuzzy number without thinking about crisp number and linguistic variables.
According to above viewpoints, this paper focuses on how the integrated model to solve the fuzzy noncooperative game. Players base on strategy and attributes of effect change to calculate payoff and establish game matrix. This study establishes a fuzzy linear programming model and applies mathematics programming software to find the maximum expected value and mixed strategy.
Therefore, the solution model of this study can be used on two-person or n-person, two strategy or n-strategy, and zero-sum game or non-zero-sum game. Besides, it confers types of payoff and attributes. It is not only more practical but also more complete.
In this study, it uses an example to explain the model of solution, and verify the fuzzy linear programming model by crisp payoff and fuzzy payoff game. Finally, the thesis uses three mobile stores that set up on telecom company in Kaohsiung area as an example to analyze the market strategy for evaluating practicability of the propose fuzzy noncooperative game.

謝誌………………………………………………………………….Ⅰ
摘要………………………………………………………………….Ⅱ
Abstract…………………………………………………………….Ⅲ
目錄………………………………………………………………….Ⅳ
表目錄……………………………………………………………….Ⅵ
圖目錄……………………………………………………………….Ⅶ
第一章 緒論
第一節 研究背景與動機…………………………………………………1
第二節 研究目的…………………………………………………………2
第三節 研究範圍與限制…………………………………………………3
第四節 本文架構…………………………………………………………3
第二章 文獻探討
第一節 模糊理論…………………………………………………………6
第二節 賽局理論…………………………………………………………9
第三節 模糊非合作賽局理論……………………………………………13
第四節 模糊線性規劃……………………………………………………16
第三章 研究方法與架構
第一節 符號定義…………………………………………………………22
第二節 研究架構…………………………………………………………23
第三節 建立模糊賽局矩陣………………………………………………25
第四節 求解混合策略機率………………………………………………32
第四章 數值範例與驗證
第一節 建立模糊賽局矩陣………………………………………………36
第二節 求解混合策略機率………………………………………………44
第三節 數值範例驗證……………………………………………………50
第五章 實例分析
第一節 背景說明…………………………………………………………57
第二節 實例研究…………………………………………………………57
第六章 結論與建議
第一節 結論………………………………………………………………66
第二節 建議………………………………………………………………66
參考文獻……………………………………………………………………68
附錄一………………………………………………………………………70
附錄二………………………………………………………………………87

一、中文參考文獻
1.施建生(1997)，賽局理論的要義，台灣經濟研究月刊，20(10)，pp6-8。
2..高孔廉、張緯良(1993)，作業研究(初版)，台北：五南圖書出版公司，pp19-54。
3.張浚威(1999)，模糊線性規劃方法之分析比較，台灣大學化學工程學研究所未出版 碩士論文
4.曾國雄、馮正民、陳郁文(1997)，模糊雙人競局應用於台灣地區小汽車市場競爭分 析，中國行政評論，6(3)，pp71-79。
5.楊蓉昌(1998)，管理數學(初版)，台北：五南圖書出版公司，pp272-274。
6.薄喬萍(1989)，作業研究決策分析(初版)，台南：復文書局，pp9-10
7.謝淑貞(1995)，賽局理論，台北：雙葉書廊，pp8-16。
二、英文參考文獻
1.Butnariu, D. (1978), Fuzzy Games; a Description of the Concept, Fuzzy Sets and Systems, 1, pp. 181-192.
2.Campos, L. (1989), Fuzzy Linear Programming Models to Solve Fuzzy Matrix Games, Fuzzy Sets and Systems, 32, pp. 275-289.
3.Dantzig, G.B. (1947), Programming in a Linear Structure, Washington, D. C. : U. S. Air Force.
4.Delgado, M., Verdegay, L. and Vila, M. A. (1989), A General model for Fuzzy Linear Programming, Fuzzy Sets and Systems, 29, pp. 21-29.
5.Lu, Y., Zhang, L., Guan, Z. and Shang, H. (2001), Fuzzy Mathematics Applied to Insurance Game, IFSA World Congress and 20th NAFIPS International Conference, 2, pp. 941-945.
6.Ramik, J. and Rimanek, J. (1985), Inequality Relation between Fuzzy Numbers and Its Use in Fuzzy Optimization, Fuzzy Sets and Systems, 16, pp. 123-138.
7.Ramik, J. and Rommelfanger, H. (1993), A Single- and Multi-valued Order on Fuzzy Numbers and Its Use in Linear Programming with Fuzzy Coefficients, Fuzzy Sets and Systems, 57, pp. 203-208.
8.Rommelfanger, H. (1989), Interactive Decision Making in Fuzzy Linear Optimization Problems, European Journal of Operational Research, 41, pp. 210-217.
9.Sakawa, M. and Nishizaki, I. (1994), Max-min Solution for Fuzzy Multi-objective Matrix Games, Fuzzy Sets and Systems, 67, pp. 53-69.
10.Song, Q. and Kandel, A (1999), A Fuzzy Approach to Strategic Games, IEEE Transactions on Fuzzy System, 7(6), pp. 634-641.
11.Tong, S. (1994), Interval Number and Fuzzy Number Linear Programming, Fuzzy Sets and Systems, 66, pp. 301-306.
12.Neumman, V. J. and Morgenstern, O.(1944), Theory of Games and Economic, Princeton: Princeton University Press.
13.Zadeh, L. A. (1965), Fuzzy Set, Information and Control, 8, pp. 338-353.
14.Zadeh, L. A. (1975), The Concept of A Linguistic Variable and Its Application to Approximate Ressoning I, II, III, Information Sciences, 8, pp. 199-251.
15.Zimmermann, H. J. (1975), Optimal Entscheibungen bei unscharfen Problembeschreibungen, Zeitschrift fur Betriebswirtschafiliche Forschung, 27, pp. 785-795.