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研究生:蘇耀瓏
研究生(外文):Yao-Lung Su
論文名稱:一個第二型模糊集合降階的改良式演算法
論文名稱(外文):An Improved Type Reduction Algorithm for Type-2 Fuzzy Sets
指導教授:李錫智李錫智引用關係
指導教授(外文):Shie-Jue Lee
學位類別:碩士
校院名稱:國立中山大學
系所名稱:電機工程學系研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:61
中文關鍵詞:Karnik-Mendel 演算法增強型 Karnik-Mendel 演算法區間第二型模糊集合型態降階第二型模糊系統
外文關鍵詞:Karnik-Mendel algorithmEnhanced Karnik-Mendel algorithmtype reductionType-2 fuzzy systeminterval type-2 fuzzy set
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所謂型態降階即是計算出在第二型模糊集合的質心。經由解模糊化的過程,可以得到在第一型態集合相對應的明確數值結果。型態降階在第二型模糊推論中已經是一項非常重要的過程,因此在第二型模糊系統的應用上,使得型態降階更有效率的執行是一件非常有意義的事情。Liu介紹了α平面的概念,就是一種水平切面表示法,並且提出了對於第二型模糊集合的型態降階方法。其中我們於一些型態降階的有效特性,藉著探索α平面表示法和區間第二型模糊集合的,開發出一個更快速的方法去計算第二型模糊集合的質心,在計算次數和比較次數上有效的減少了,根據結果,型態降階可以更有效率的完成計算和比較次數上的減少。我們將會以數學分析和實驗結果來證明我們所提出的方法是很有效率的。
Type reduction does the work of computing the centroid of a type-2 fuzzy set. The result is a type-1 fuzzy set from which a corresponding crisp number can then be obtained through defuzzification. Type reduction is one of the major operations involved in type-2 fuzzy inference. Therefore, making type reduction efficient is a significant task in the application of type-2 fuzzy systems. Liu introduced a horizontal slice representation, called the α-plane representation, and proposed a type reduction method for a type-2 fuzzy set. By exploring some useful properties of the α-plane representation and of the type reduction for interval type-2 fuzzy sets, we develop a fast method for computing the centroid of a type-2 fuzzy set. The number of computations and comparisons involved is greatly reduced. As a result, type reduction can be done much more efficiently. The effectiveness of the proposed method is analyzed mathematically and demonstrated by experimental results.
摘 要 i
Abstract ii
圖 次 v
表 次 vi
第一章 緒論 1
第一節 研究動機 1
第二節 論文架構 3
第二章 文獻探討 4
第一節 概述 4
第二節 第二型模糊集合 4
第三節 區間第二型模糊集合 6
第四節 增強型Karnik-Mendel演算法 8
第三章 Liu的型態降階方法 11
第一節 α平面表示法 11
第二節 Liu的方法 12
第四章 我們的改良式方法 14
第一節 觀察增強型Karnik-Mendel演算法 14
第二節 觀察Liu的方法 18
第三節 我們的方法 20
第四節 複雜度比較 26
第五章 範例 28
第六章 實驗結果 37
第一節 環境介紹 37
第二節 實驗一 37
第三節 實驗二 43
第七章 結論與未來展望 49
參考文獻 50
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