由語意近似於模糊功能相依性之研究

Semantic Proximity on Fuzzy Relational Databases

李尉瑄(Wei-Hsuan Lee)

指導教授 ： 龐金宗

元智大學/資訊學院/資訊管理學系/碩士(2007年)

https://doi.org/10.6838/YZU.2007.00230

摘要

語意近似(Semantic Proximity) 是用來測量兩個模糊集合的接近程度, 因此, 我們可以用來定義模糊功能相依性(Fuzzy Functional Dependency), 以達成資料正規化, 及減少資料重覆(data redundancy) 與更新異常(anormal updating)。
1997年W. Y. Liu 利用區間的表示方法, 提出語意近似的概念, 並用來定義模糊功能相依性。本論文則是利用模糊數的表示方法, 推廣語意近似, 及模糊功能相依性的定義。並結合1999年Liao, Wang, 與Liu 所提出的推導規則(Inference Rules), 用語意近似的概念, 證明與傳統關聯式的推導規則類似。根據模糊功能相依性的概念, 我們能將模糊數壓縮, 使隸屬函數變得更精確。而語意近似的概念, 還可以計算出兩個值組的接近程度, 進而定義出模糊重覆值組, 以用來探討模糊關聯式代數(Fuzzy Relational Algebra) 的特性。

關鍵字

語意近似 ； 模糊功能相依性 ； 模糊關聯式代數

並列摘要

Semantic proximity is a method to measure the proximity degrees of two fuzzy sets. Based on the concepts of semantic proximity, we propose a definition of the fuzzy functional dependency (FFD) in order to normalize a relational table, eliminate the redundancy of data, and avoid anormal updating.
W. Y. Liu proposed the idea of semantic proximity and fuzzy functional dependency using interval number in 1997. In this thesis, we extend the idea of semantic proximity and fuzzy functional dependency using fuzzy numbers. We prove that the related inference rules, which are similar to those of the
Armstrong’s Axioms for the classical case, are sound and complete. By using the fuzzy functional dependencies, we can compress the range of a fuzzy value and make this fuzzy value ”clear”. Furthmore, we discuss the results of fuzzy relational algebra by using the definition of duplicate tuples.

並列關鍵字

Semantic Proximity ； Fuzzy Functional Dependency ； Fuzzy Relational Algebra

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