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博碩士論文 etd-0729115-120206 詳細資訊
Title page for etd-0729115-120206
論文名稱
Title
一般第二型模糊集合的型態降階方法
The Type-Reduction Method for General Type-2 Fuzzy Sets
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
53
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2015-08-27
繳交日期
Date of Submission
2015-08-31
關鍵字
Keywords
α平面、區間第二型模糊集合、第二型模糊集合、型態降階、Karnik-Mendel演算法
interval type-2 fuzzy set, α-plane, type-2 fuzzy set, Karnik-Mendel algorithm, type-reduction
統計
Statistics
本論文已被瀏覽 5715 次,被下載 43
The thesis/dissertation has been browsed 5715 times, has been downloaded 43 times.
中文摘要
型態降階在第二型模糊系統中是一項非常重要的過程,其主要概念是計算出第二型模糊集合的質心。Liu介紹了α平面的概念,即是一種水平切面的表示法,並以此概念為基礎提出了對第二型模糊集合的型態降階方法,主要做法是將第二型模糊集合透過α切面的方式,以不同的α值將原本的第二型模糊集合解構成多個區間第二型模糊集合,也就是α平面,再綜合這些α平面的結果來得知原先第二型模糊集合的質心。但是Liu所提出的降階方法並無法適用在特定的第二型模糊集合上,假若次要歸屬函數為凹函數時,獲得的α平面未必會是區間第二型模糊集合,因此我們擴展Liu的型態降階方法,基於α平面的概念,將其遇到的問題轉換成多個子問題,藉由解決這多個子問題來得到原本問題的結果。我們用數學的式子證明我們所提出的方法是正確且有效的。
Abstract
A centroid type-reduction strategy for type-2 fuzzy sets based on decomposed α-planes was proposed by Liu. However, it cannot be applied to deriving the centroid of a type-2 fuzzy set with concave secondary membership functions. In this paper, we extend the Liu’s method so that the centroid of a type-2 fuzzy set with concave secondary membership functions can be derived. For each decomposed α-plane, we convert it into a group of interval type-2 fuzzy sets. The union of the centroids of its member interval type-2 fuzzy sets constitutes the centroid of theα-plane. Then the weighted union of the centroids of the decomposed α-planes becomes the centroid type-reduced set of the original type-2 fuzzy set. When dealing with a type-2 fuzzy set with convex secondary membership functions, our proposed method is reduced to the Liu’s method.
目次 Table of Contents
論文審定書+i
致謝+iii
摘要+iv
Abstract+v
圖目錄+viii
表目錄+x
第一章 導論+1
2.1. 研究背景與目的+1
2.2. 論文架構+3
第二章 文獻探討+4
3.1. 模糊集合+4
3.2. 第二型模糊集合+4
3.3. 區間第二型模糊集合+5
3.4. 模糊系統+7
3.5. 型態降階+8
3.6. Karnik-Mendel演算法+8
3.7. 增強型Karnik-Mendel演算法+9
第三章 Liu的型態降階方法+11
4.1. α平面表示法+11
4.2. 第二型模糊集合的降階方法+11
第四章 研究方法 +13
5.1. Liu的型態降階方法缺陷+13
5.2. 我們的型態降階方法+14
5.3. 範例+17
5.3.1. 第二型模糊集合範例+17
5.3.2. 實驗流程+18
第五章 實驗結果 +27
6.1. 實驗一+27
6.2. 實驗二+30
6.3. 實驗三+33
第六章 結論與未來展望+37
參考文獻+38
參考文獻 References
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