臺灣博碩士論文加值系統

模糊關聯式資料模型是傳統關聯式資料模型的擴展。傳統關聯式資料庫，主要在處理精確的資訊；但在現實生活中，存在許多不確定、不精確(imprecise)的資訊，因此Zadeh於1965年基於數學的理論架構下提出模糊集合理論(fuzzy set theory)，用模楜集合來表達現實生活中不精確的資訊。而在模糊關聯式資料模型中，針對資料庫之需求加入不同的整合限制(integrity constraints)，例如：模糊功能相依(fuzzy functional dependency)、模糊多重值相依(fuzzy multivalued dependency) 、模糊合併相依(fuzzy join dependency)…等等，用來規範模糊關聯表中的資料。
本文採用延伸可能性分佈模型(Extended-possibility-based)之近似關聯(Proximity Relation)來描述模糊資料，以Conformance定義為基礎，以二筆值組的關係及子關係(two-tuple relations and its subrelations)觀點，重新定義模糊功能相依及模楜多重值相依，並針對模糊功能相依及模糊多重值相依提出一套具有健全性及完備性的推導規則（sound and complete inference rules），以做為模糊關聯式資料庫正規化之依據。

A fuzzy relational data model is an extension of the traditional relational data model that is mainly to process precise data. However, in the real world, there are a lot of uncertain and imprecise data. In order to deal with imprecise data, Zadeh introduced the theory of fuzzy sets based on the mathematical framework in 1965. In the fuzzy relational data model, different kinds of integrity constraints, such as fuzzy functional dependency, fuzzy multivalued dependency, fuzzy join dependency, etc., were added to relational database to filter and constrain its data according to the requirements of database.
This thesis utilizes the proximity relation of extended-possibility-based model to describe fuzzy data. It proposes a new conception of fuzzy functional dependency and fuzzy multivalued dependency based on conformance and from the point of view of two-tuple relations and its subrelations. In addition, sound and complete inference rules for fuzzy functional dependencies and fuzzy multivalued dependencies presented here can serve as the normalized criteria of fuzzy relational database.

第一章　緒論..................................................1
1.1 研究背景................................................1
1.2 研究動機................................................1
1.3 研究目的及重要性........................................2
1.4 論文架構................................................3
第二章　文獻探討..............................................4
2.1 模糊集合(Fuzzy Set)的基本概念...........................4
2.1.1 明確集合(Crisp Set)...................................4
2.1.2 模糊集合(Fuzzy Set)...................................5
2.1.3 模糊集合的表示方法....................................6
2.1.4 模糊集合基本運算......................................8
2.2 關聯式資料模型(Relational Data Model)...................9
2.2.1 關聯式資料模型...................................10
2.2.2 鍵值(Key)之介紹..................................12
2.2.3 關聯式代數(Relational Algebra)...................12
2.3 正規化(Normalization)..................................14
2.4 模糊關聯式資料模型(Fuzzy Relational Data Model)........18
2.4.1 相似關係為主之模型(Similarity-Relation-Based)....19
2.4.2 可能性分佈為主之模型(Possibility-Distribution-
Based)...........................................20
2.4.3 延伸可能性分佈之模型(Extended-Possibility-
Based)...........................................21
2.4.4 模糊關聯為主之模型(Fuzzy-Relation-Based).........22
第三章 研究方法.............................................24
3.1 以EQUAL為基礎的模糊近似關係............................24
3.2 以Conformance為基礎的模糊近似關係......................26
3.3 模糊功能相依(Fuzzy Functional Dependency)..............29
3.3.1 以EQUAL近似關聯為基礎的模糊功能相依..............29
3.3.2 以Conformance近似關聯為基礎的模糊功能相依........30
第四章　模糊功能相依(Fuzzy Functional Dependency)............34
4.1 模糊功能相依...........................................34
4.2 模糊功能相依的推導規則.................................34
第五章　模糊多重值相依(Fuzzy Multivalued Dependencies).......38
5.1 模糊多重值相依.........................................38
5.1.1 以傳統多重值相依概念擴展至模糊多重值功能相依.....38
5.1.2 模糊多重值相依定理及二筆值組之間的關聯...........41
5.2模糊多重值相依的推導規則................................42
第六章　結論及未來研究方向...................................51
6.1 結論...................................................51
6.2 研究貢獻...............................................51
6.3 後續發展及建議.........................................52
參考文獻.....................................................53

[1] W.W. Armstrong,”Dependency structures of Database relationships,” Proceedings of the IFIP Congress(1974), pp.580-583.
[2] J.F. Baldwin and S.Q.Zhou , “A fuzzy relational inference language”, Fuzzy Sets and Systems 14 (1984), pp.155-174.
[3] C. Beeri, R. Fagin, and J.H. Howard, “A Complete Axiomatization for Function and Multivalued Dependencies”, Proc. ACM SIGMOD-ACM International conference on Management of Data (1977), pp.47-61.
[4] Tapan K.Bhattacharjee and Arun K. Mazumdar, “Axiomatisation of fuzzy multivalued dependencies in a fuzzy relational data model,” Fuzzy Set and Systems (1998), pp.343-352.
[5] B.P. Buckles and F.E, Petry, “A fuzzy representation of data for relational databases, “ Fuzzy Set and Systems(1982), pp.213-226.
[6] B.P. Buckles and F.E, Petry,”Fuzzy database and their applications,” Fuzzy inform. Decision process(1982), pp.361-371.
[7] C.J Date, An introduction to database systems, Addison-Wesley Publishing Company, Inc (1995).
[8] Ramez Elmasri and Shamkant B. Navathe, Fundamentals Of Database Systems(Third Edition) (2000).
[9] George J.klir and Bo Yuan. Fuzzy Set and Fuzzy Logic Theory and Applications(2002).
[10] Z.M Ma, W.J. Zhang and W.Y. Ma, ”Semantic Measure of Fuzzy Data in Extended Possibility-Based Fuzzy Relational Databases,” Information Sciences 34 (2000), pp.121-143.
[11] D. Maier, The Theory of Relational Databases, Computer Science Press, Rockville, MD (1983).
[12] Raju and A.K. Mazumdar, “Functional dependencies and lossless join decomposition of fuzzy relational database system,” ACM trans.Database System 13 (1988), pp.129-166.
[13] H. Prade and C. Testemale, “Generalizing Database Relational Algebra for the treatment of incomplete or Uncertain Information,” Information Sciences 34 (1984), pp.115-143.
[14] S.Shenoi and A. Melton, “Proximity Relations in the fuzzy Relational Database Model,” Fuzzy Sets and Systems 31 (1989), pp.287-296.
[15] S.Shenoi and A Melton,” Functional dependencies and normal forms in the fuzzy relational database model,” Information Sciences 60 (1992), pp.1-28.
[16] Mustafa Ilker Sozat and Adnan Yazici, ”A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations, ” Fuzzy Sets and Systems117 (2001), pp.161-181.
[17] L.A Zadeh, Fuzzy set, Inform and control 8 (1965), pp.338-353.
[18] 王文俊，認識Fuzzy，全華圖書，民92.
[19] 李允中，王小璠，蘇木春，模糊理論及其應用，全華圖書，民92.
[20] 曾守正，周韻寰，資料庫系統之理論與實務，華泰出版社，民92.