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研究生:曾莉惠
研究生(外文):Tseng Li-Huei
論文名稱:利用約略集合理論於不完全資料之學習
論文名稱(外文):Learning Rules from Incomplete Data Based on the Rough Set Theory
指導教授:洪宗貝洪宗貝引用關係王學亮
指導教授(外文):Tzung-Pei HongShyue-Liang Wang
學位類別:碩士
校院名稱:義守大學
系所名稱:資訊工程學系
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:2002
畢業學年度:90
語文別:英文
論文頁數:86
中文關鍵詞:模糊集合約略集合不完全資料不完全數量型資料較低近似集合較高近似集合
外文關鍵詞:fuzzy setrough setincomplete dataincomplete quantitative datalower approximationupper approximation
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機器學習或資料挖掘可以從現有的資料庫或訓練例子中擷取所需的知識以減輕建置專家系統時之發展瓶頸或提供決策者決策參考。以往大部分的學習或挖掘方法多著重在處理明確離散型的資料,然而實際應用上不完全的資料也相當常見。在1982年Pawlak首先提出約略集合理論,該理論採用等價類別的概念來分割訓練例子,作為處理資料分類問題的一種數學工具。由於我們發現等價類別的觀念可輕易解決不完全資料的分類問題,因此在本論文中,將採用約略理論作為我們的發展方法以從不完全資料學習規則。此外,由於模糊集合概念簡單且類似人類的推論方式,因此在智慧型系統中常用語意名詞與隸屬函數來表示數量型的資料。因此本論文中也將利用模糊理論的觀念以擴展約略理論來處理不完全的數量型資料,並從不完全的數量型資料中學習規則。本論文共提出三種學習規則的方法,第一種方法是改良約略集合理論中的較低近似集合及較高近似集合之定義,以從不完全資料中同時推導出所有最泛化規則並推估出不完全資料的合適數值。第二種方法是結合模糊理論的概念以從不完全數量型資料中同時推導出所有最泛化模糊規則及推估出不完全數量型資料中合適的未知數值。而第三種方法主要是擴充上述之第一種方法,以涵蓋(coverage)的觀點從不完全資料中去挖掘分類知識。涵蓋的觀點指的是不需要將所有的規則找出,而只要將可正確涵蓋所給定例子的規則求出即可。在上述三種方法中對於不完全資料中的未知值首先先假設成在不完全資料中任何可能出現的值,再根據由訓練例子中所計算出的較低近似集合及較高近似集合,逐漸的推估出未知值。最後,利用例子與近似集合間彼此交互作用的關係來推導出所有確定性規則和可能性的規則。由上述方法所推導出的規則將可作為發展專家系統時知識庫建立之雛型。

Machine learning and data mining techniques can extract desirable knowledge from existing databases or training instances to ease the development bottleneck in building expert systems or help supervisors make decisions. In the past, most learning or mining methods deal with complete data sets. Real applications are, however, full of incomplete data sets. The rough-set theory, proposed by Pawlak in 1982, can serve as a new mathematical tool to deal with data classification problems. It adopts the concepts of equivalence classes to partition the training instances according to some criteria. Since we find that the concept of equivalence classes can easily solve classification problems of incomplete data, the rough set theory is thus adopted in this thesis as the mining tool. Also, the fuzzy set concepts have often been used in intelligent systems to represent quantitative data by linguistic terms and membership functions because of their simplicity and similarity to human reasoning. They are thus used in this thesis to deal with incomplete quantitative data. We propose three new methods to learning rules. The first method modifies the original rough-set definitions of lower approximation and upper approximation, and simultaneously derives all general rules from incomplete data and estimates the unknown values. The second method combines the fuzzy-set concepts and the rough-set theory to simultaneously derive all general fuzzy rules from incomplete quantitative data and to estimate the unknown quantitative values. The third method further extends the first method to mining coverage rules, instead of all possible rules, from incomplete data. All the coverage rules gathered together can cover all the given training examples. In all the above three methods, unknown values in incomplete data sets are first assumed to be any possible values and are gradually refined according to the incomplete lower and upper approximations derived from the given incomplete training examples. The training instances and the approximations then interact on each other to derive certain and possible rules and to estimate appropriate unknown values. The rules derived can then be used to build a prototype knowledge base.

CHINESE ABSTRACT III
ENGLISH ABSTRACT V
ACKNOWLEDGEMENTS VII
LIST OF FIGURES IX
LIST OF TABLES IX
CHAPTER 1 INTRODUCTION 1
1.1 PROBLEM DEFINITION AND MOTIVATION 1
1.2 CONTRIBUTIONS 3
1.3 READER'S GUIDE 4
CHAPTER 2 REVIEW OF RELATED WORKS 5
2.1 ROUGH SET THEORY 5
2.2 FUZZY SET THEORY 8
2.3 INCOMPLETE DATA SETS 10
CHAPTER 3 MINING ALL GENERAL RULES FROM INCOMPLETE DATA 13
3.1 NOTATION 13
3.2 INCOMPLETE ROUGH SETS 14
3.3 A ROUGH-SET-BASED APPROACH TO SIMULTANEOUSLY ESTIMATE MISSING VALUES AND DERIVE RULES 17
3.4 AN EXAMPLE 22
CHAPTER 4 LEARNING ALL FUZZY RULES FROM INCOMPLETE QUANTITATIVE DATA 32
4.1 NOTATION 32
4.2 FUZZY INCOMPLETE ROUGH SETS 34
4.3 THE PROPOSED ALGORITHM FOR INCOMPLETE QUANTITATIVE DATA SETS 38
4.4 AN EXAMPLE 44
CHAPTER 5 LEARNING A COVERGAGE SET OF GENERAL RULES 58
5.1 NOTATION 58
5.2 THE ALGORITHM FOR LEARNING MAXIMALLY GENERAL COVERAGE RULES FROM INCOMPLETE DATA ....59
5.3 AN EXAMPLE 63
5.4 DISCUSSION 71
CHAPTER 6 CONCLUSIONS AND FUTURE WORKS 73
REFERENCES 75

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