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研究生:蔡昭廷
研究生(外文):Chao-TingTsai
論文名稱:以模糊目標規劃求解多階層單目標之決策問題
論文名稱(外文):Solving Multi-level Single-objective Decision Making Problems using Fuzzy Goal Programming
指導教授:陳梁軒陳梁軒引用關係
指導教授(外文):Liang-Hsuan Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工業與資訊管理學系
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:68
中文關鍵詞:多階層規劃問題模糊集合理論模糊目標規劃滿意度區間
外文關鍵詞:Multi-level programmingFuzzy goal programmingSatisfaction interval
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多階層規劃問題(Multi-level programming)描述問題中之決策者間存在著階層架構,且決策過程須依此階級次序進行決策。且為評估對於求解結果之滿意度,可利用模糊歸屬度函數概念表達其達成度,藉以求解。而由於多階層規劃問題中,存在多個欲達成之目標,故可利用模糊目標規劃之方式,以同時求取達成之解與設定目標值間差距最小化。然而在多階層規劃問題中,「領導權力」與「目標達成困難」會使得決策過程趨於複雜。有些決策傾向保有上階決策者之領導權力,以限制下階決策者之達成滿意度;但倘若上階決策者之目標達成相當困難,在欲保留其領導權力之條件下,便有可能壓抑下階決策者之達成度。除此之外,多階層規劃之決策過程中,上階決策者可依據自己的想法,對於下階決策所求得之解進行調整。但此調整過程通常必須反覆進行,而造成整個決策過程過於繁複,求解較無效率。
因此,本研究提出滿意度區間之概念,使滿意度落於此區間範圍內。此滿意度區間可依據決策者之意願,容忍其下階決策者有限度的超越上階決策者可能達成之滿意度,以此避免下階決策者之達成度過於壓抑,但又可部分保留上階決策者之領導權力。除此之外,本研究另考量決策者調整求解結果之原因,事先列入限制式中進行求解。本研究可分為兩階段,第一階段建立各階層滿意度歸屬度函數,再依建立步驟決定各階層目標之滿意度區間範圍。第二階段將此歸屬度函數及滿意度區間範圍,納入模糊目標規劃之模式中,進行求解。並利用兩數值例說明本研究所提出模式之可行性,並且與先前文獻做比較,以顯示本研究較為優越之處。而後針對區間下界值與超越比例值進行敏感度分析,說明其對本數值例求解結果之影響,以提供決策者求解問題時之參考。最後對整份研究給予結論與建議,除總結本研究所提出方法與分析外,並對於未來可以研究之方向進行說明。
Multi-level linear programming (MLLP) is an approach that can be used to solve decision problems based on hierarchical decision structures. Satisfactions that represent the judgement of solutions obtained for a decision-maker (DM) include uncertain information. Hence, the concept of fuzzy sets is used to define the satisfaction of the corresponding value by building membership functions. This study develops a method for interpreting the relationships of satisfaction between different levels by using satisfaction intervals. To overcome the shortcomings of methods that strictly restricts the satisfaction of lower-level DMs by higher-level DMs, a more flexible decision space is proposed. The proposed model implies that satisfaction obtained of lower-level transcending the one of higher-level is allowed. An exceeding ratio (α) is proposed to provide an exceeding tolerance for lower-level DMs under some limited conditions. Moreover, linguistic variables are used to express the extra requirements of DMs that restrict the relation between adjacent levels. After integrating all constraints, fuzzy goal programming is applied. A comparison of the proposed method with other fuzzy goal programming approaches in solving multi-level programming problems shows that the proposed method achieves higher satisfaction when the middle level is difficult to satisfy. This study provides a method for interpreting the satisfaction between different levels by giving a more flexible decision space for lower-level DMs to reach higher satisfaction.
摘要 I
Abstract II
誌謝 V
目錄 VI
表目錄 VIII
圖目錄 IX
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目標 2
第三節 研究範圍與限制 3
第四節 研究流程 3
第五節 論文架構 4
第二章 文獻探討 6
第一節 模糊集合理論 6
第二節 模糊目標規劃 9
第三節 多階層規劃決策 12
第四節 小結 24
第三章 多階層單目標之模糊目標模式構建 25
第一節 研究構想 25
第二節 模式建構 28
第三節 小結 43
第四章 模式應用與分析 44
第一節 數值例演算 44
第二節 求解結果比較與分析 52
第三節 特殊數值例討論 59
第四節 數值例分析結論 63
第五章 結論與建議 64
第一節 研究成果 64
第二節 未來方向 65
參考文獻 66
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