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研究生:陳怡如
研究生(外文):CHEN,YI-JU
論文名稱:模糊數的簡單折線形態逼近
論文名稱(外文):Approximations of Fuzzy Numbers by simply poly-lined fuzzy numbers
指導教授:葉啟村葉啟村引用關係
指導教授(外文):YEH,CHI-TSUEN
口試委員:陳東賢葉啟村黃印良
口試委員(外文):CHEN, TUNG-SHYANYEH,CHI-TSUENHUANG,YIN-LIANG
口試日期:2018-01-15
學位類別:碩士
校院名稱:國立臺南大學
系所名稱:應用數學系碩士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:42
中文關鍵詞:模糊數線性糢糊數計算公式模糊數的簡單折線形態逼近
外文關鍵詞:fuzzy numberstrapezoidal approximationsimply poly-lined fuzzy numbers
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  近年來有許多學者研究某此特定的模糊數的逼近方法。某些條件下,在模糊環境進行決策分析時,決策者給出的決策信息往往用模糊數來逼近保持線性計算公式。為降低模糊信息處理的困難度,需要用簡單模糊數來逼近模糊數。方案的優劣評價是決策過程的一個重要環節,需要用模糊數的排序方法解決。複雜模糊數的簡單模糊數逼近方法和模糊數的排序方法是解決複雜模糊多屬性決策問題的有效工具。
學者有對三角形逼近、對稱三角形逼近法,不對稱逼近法等圖形逼近、做出各種的解決方法。本論文的主要研究工作簡單折線形態逼近法的公式,提供給決策者解決問題參考。
In recent years, there are many scholars to study the approximation method of this particular fuzzy number. Under what conditions, when making the decision analysis in the fuzzy environment, the decision information given by the decision maker is often approximated by the fuzzy number to keep the linear formula. The difficulty of fuzzy information processing is reduced and the fuzzy number is needed to approximate the fuzzy number. The evaluation of the merits of the scheme is an important part of the decision-making process and needs to be solved by the sorting method of fuzzy numbers. The simple fuzzy number approximation method of complex fuzzy numbers and The method of ranking fuzzy numbers is an effective tool to solve the problem of complex fuzzy multi-attribute decision-making.
Scholars have a way to solve the problem of triangular approximation, symmetric triangulation approximation, asymmetric approximation, and so on. The main research work of this paper is to find a formula of the simple-lined approximation of fuzzy numbers.
Acknowledge I
Chinese abstract II
Abstract III
1 Introduction
1.1 The development of fuzzy theory 1
1.2 Fuzzy application 1
2 Preliminaries
2.1 The definition of fuzzy numbers 2
2.2 -cuts representation of fuzzy numbers 3
2.3 Approximations of fuzzy numbers 5
2.4 Karush-Kuhn-Tucker theorem 5
2.5 Chebyshev’s Inequality 6
3 Simply Poly-lined Approximations of Fuzzy Numbers
3.1 Definition of simply poly-lined fuzzy numbers 8
3.2 Nearest approximations by poly-lined fuzzy numbers 9
3.3 Proof 13
4 Example of simply poly-lined approximation of fuzzy numbers
5 Conclusion
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