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研究生:方翊嘉
研究生(外文):Yi Jia Fang
論文名稱:以模糊蘊含式進行模糊交集、聯集之有效性驗證
論文名稱(外文):Effectiveness examination of t-norms and t-conorms using fuzzy implication
指導教授:陳亭羽陳亭羽引用關係
指導教授(外文):T. Y. Chen
學位類別:碩士
校院名稱:長庚大學
系所名稱:企業管理研究所
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:2009
畢業學年度:97
論文頁數:140
中文關鍵詞:直覺模糊集合有效性模糊蘊含式模糊邏輯近似推理
外文關鍵詞:Intuitionistic fuzzy setEffectivenessFuzzy implicationFuzzy logicApproximate Reasoning
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模糊理論可以被應用於各種領域中,雖然領域有所不同,但其主要應用核心為模糊邏輯推理,構成模糊邏輯推理的是模糊蘊含式,而模糊蘊含式是由模糊交集、模糊聯集、模糊補集所組成的。但是模糊交集、聯集、補集並沒有一個唯一的運算方式,因此可以根據所需自行產生新的運算子。運算子可以透過產生器產生所需之運算子,因此也會造成模糊蘊含式的多樣化,而使用不同的模糊蘊含式,所推論之結果可能會有所差異。當選擇一個模糊蘊含式應要考慮其所造成的推論結果差異,因此本研究透過模擬運算的方式,來探討不同模糊蘊含式所造成的差異值。計算差異值之距離公式,分別使用標準化漢明距離及標準化歐幾理得距離。本研究使用最常被使用的4組(standard、algebraic、bounded、drastic)運算子、過去文獻常提及的參數型20組運算子,自行產生的28組運算子。分別與S蘊含式、QL1蘊含式及QL2蘊含式搭配產生新的模糊蘊含式。可得最常被使用模糊蘊含式12條、過去文獻參數型模糊蘊含式60條,及自行產生的蘊含式84條,最後總計會有156條模糊蘊含式會納入模擬運算中。邏輯推論的方式有很多種,本研究中所探討的模糊蘊含式,分別會進行廣義肯定前提式及廣義否定後論式這兩種較常被使用之推論方式的模擬運算。觀察最後運算結果是否有某些模糊蘊含式會因為推論方式的不同,而造成其結果有較大的差異。此外,每條模糊蘊含式將分別在廣義肯定前提式及廣義否定後論式中,進行15組不同的因素個數的模擬運算,每分組會進行30000次的模擬觸算,求其分組平均,之後再求15組的總平均值來與其他模糊蘊含式來進行比較。 最後從模擬運算的結果中可以得知,一些過去文獻常提及之模糊蘊含式及一些自行產生的模糊蘊含式,皆有表現較最常被使用的蘊含式為佳。
The fuzzy set theory has been applied in various fields. The core application of the fuzzy sets focuses on the fuzzy logic reasoning which is a function of fuzzy implication. The fuzzy implication consists of the fuzzy intersection, fuzzy union, and fuzzy complement. Because the fuzzy intersection, fuzzy union, and fuzzy complement have no constant types, these operators can become different molds by specific generators. Since the molds of fuzzy operators alter by generators, it results in the variation of fuzzy implications to accord with corresponding fuzzy operators. Considering the possible circumstance that using different fuzzy implications in the fuzzy logic reasoning would lead to distinct inferential outcomes, a simulate experiment implemented by the computer was utilized to examine the consequent difference caused by varied fuzzy implications. In order to calculate the consequent difference, the normalized Hamming distance and normalized Euclidean distance were employed to measure the difference. There were three species of implications, including S-implication, QL1-implication, and QL2-implication. We combined three implications with 52 types of operators in which there were 4 basic and well-known operators, 20 literature-based operators, and 28 developed operators yielded by the specific generators. That is, 156 implicators in total were used in the simulate experiment. Although the inference rules in the fuzzy logic reasoning had many different manners, this study mainly adopted the Generalized Modus Ponens and the Generalized Modus Tollens. In addition to the comparison among various implicators, we also observe the difference between the two inference rules. Every fuzzy implicator ran 15 different sets of simulation, which is the number of elements in the Generalized Modus Ponens and the Generalized Modus Tollens. Each set was carried out 30,000 times in the simulation, and was calculated its sub-average value. We calculated the average of 15 sub-average values, and compared it with other average generated by different implicators. The computational results indicate that some literature-based implicators and some developed implicators have better performance than the basic and well-known implicators.
目錄
指導教授推薦書
口試委員會審定書
授權書 iii
誌謝 iv
中文摘要 v
英文摘要 vi
目錄 vii
表目錄 viii
第一章 緒論 1
1.1研究背景與動機 1
1.2研究目的及內容 1
第二章 文獻回顧 3
2.1 模糊理論與模糊推論 3
2.2 直覺模糊集合及應用 5
第三章 模糊交集與模糊聯集 8
3.1 t-norm、t-conorm之基本概念 8
3.2 t-norm、t-conorm產生器 12
3.3 使用的t-norm、t-conorm 18
第四章 模擬實驗分析 22
4.1 二值邏輯推理與模糊邏輯推理 22
4.2 產生的模糊蘊含式 23
4.3 廣義肯定前提式模擬研究流程 39
4.4 廣義否定後論式模擬研究流程 51
第五章 結論與建議 64
附錄A T-norms與T-conorms之圖形 71
附錄B S-implication模擬研究分組數據 82
附錄C QL1-implication模擬研究分組數據 98
附錄D QL2-implication模擬研究分組數據 114

表目錄
表3.1 一些常見的模糊交集(t-norms) 10
表3.2 一些常見的模糊聯集(t-conorms) 11
表3.3 遞增、遞減產生器及其反函數列表 12
表3.4 搭配 產生出來的t-conorms 14
表3.5 搭配 產生出來的t-conorms 15
表3.6 搭配 產生出來的t-norms 16
表3.7 搭配 產生出來的t-norms q的參數為2 17
表3.8 t-norms、t-conorms彙總表 18
表4.1 模擬實驗使用之S-implication 24
表4.2 模擬實驗使用之QL1-Implication 28
表4.3 模擬實驗使用之QL2-Implication 33
表4.4 廣義肯定前提式下S-implication的模擬研究結果 41
表4.5 廣義肯定前提式下表現較佳之S蘊含式 43
表4.6 廣義肯定前提式下S蘊含式之距離分組 43
表4.7 廣義肯定前提式下S蘊含式的參數型蘊含式之比較 44
表4.8 廣義肯定前提式下QL1-implication的模擬研究結果 44
表4.9 廣義肯定前提式下表現較佳之QL1蘊含式 46
表4.10 廣義肯定前提式下QL1蘊含式的距離分組 46
表4.11 廣義肯定前提式下QL1蘊含式的參數型蘊含式之比較 47
表4.12 廣義肯定前提式下QL2-implication的模擬研究結果 47
表4.13 廣義肯定前提式下表現較佳之QL2蘊含式 49
表4.14 廣義肯定前提式下QL2蘊含式的距離分組 49
表4.15 廣義肯定前提式下QL2蘊含式的參數型蘊含式之比較 50
表4.16 廣義否定後論式下S-implication的模擬研究結果 52
表4.17 廣義否定後論式下表現較佳之S蘊含式 54
表4.18 廣義否定後論式下S蘊含式的距離分組 54
表4.19 廣義否定後論式下S蘊含式的參數型蘊含式之比較 55
表4.20 廣義否定後論式下QL1-implication的模擬研究結果 55
表4.21 廣義否定後論式下表現較佳之QL1蘊含式 57
表4.22 廣義否定後論式下QL1蘊含式的距離分組 57
表4.23 廣義否定後論式下QL1蘊含式的參數型蘊含式之比較 58
表4.24 廣義否定後論式下QL2-implication的模擬研究結果 59
表4.25 廣義否定後論式下表現較佳之QL2蘊含式 60
表4.26 廣義否定後論式下QL2蘊含式的距離分組 61
表4.27 廣義否定後論式下QL2蘊含式的參數型蘊含式之比較 61
表4.28 廣義肯定前提式與廣義否定後論式之蘊含式結果比較 62
表5.1 肯定前提式下可以產生表現良好之t-norms、t-conorms 64
表5.2 否定後論式下可以產生表現良好之t-norms、t-conorms 65
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