胡承方952221E214043

胡承方952221E214043

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1 行政院國家科學委員會補助專題研究計畫成果報告 ※※※※※※※※※※※※※※※※※※※※※※※※ 模糊變分不等式之求解 ※※※※※※※※※※※※※※※※※※※※※※※※ 計畫類別:■個別型計畫 □整合型計畫 計畫編號: NSC 95 2221 E 214 043 執行期間: 95 8 1 日至 96 7 31 計畫主持人:胡承方 本成果報告包括以下應繳交之附件: □赴國外出差或研習心得報告一份 □赴大陸地區出差或研習心得報告一份 ▇出席國際學術會議心得報告及發表之論文各一份 □國際合作研究計畫國外研究報告書一份 執行單位:義守大學 工業工程與管理學系 96 7 12
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2 行政院國家科學委員會專題研究計畫成果報告 模糊變分不等式之求解 Solving Fuzzy Variational Inequations 計畫編號:NSC 95-2221-E-214-043 執行期限:95 年 8 月 1 日至 96 年 7 月 31 日 主持人: 胡承方 義守大學 工業工程與管理學系 計畫參與人員:蔡佩紋 元智大學 工業工程與管理學系 陳昱達 義守大學 工業工程與管理學系 一、中文摘要 本計畫擬探討具模糊定義域 (fuzzy domain) 及模糊映射 (fuzzy mapping) 之變 分不等式 (variational inequalities) 問題。我 們將證明此一問題可以藉由模糊理論的 分析轉化為傳統雙層規劃問題 (bilevel programming problem) 。有關此問題解的 存在性質及最佳解的充要條件將被討 論。此外,我們提出以“加權函數 (penalty function) ”觀念為理論基礎的求解演算 法,並證明此演算法的收斂性。最後,我 們將以數值實例來驗證所提之方法的可 行性及有效性。 關鍵詞 :變分不等式,模糊最佳化問題, 數學規劃 Abstract This work studies variational inequalities for fuzzy mappings over a fuzzy domain. It is shown that such problem can be reduced to a regular bilevel programming problem. Some basic analysis of the solution optimality conditions is presented. A penalty function algorithm is introduced with a convergence proof, and numerical examples are included to illustrate the theory and solution procedure. Keywords : Variational Inequalities, Fuzzy Optimization, Mathematical Programming 二、緣由與目的 Variational inequalities have been widely used as a mathematical programming tool in modeling many optimization and decision making problems. However, facing uncertainty is a constant challenge for optimization and decision making. Treating uncertainty by fuzzy mathematics results in the study of fuzzy optimization and decision making. Recently, Chang and Zhu [4] introduced the concepts of the variational inequalities for fuzzy mappings and later developed by Noor [13,14,15], Chang and Huang[3], and Lee et al . [11]. Inspired and motivated by the recent research works on
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This note was uploaded on 11/27/2009 for the course IM MA420 taught by Professor Mar,lee during the Spring '09 term at National Taiwan University.

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胡承方952221E214043

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