模糊資料模型的模糊多重值相依完備性之研究

Complete Axioms of Fuzzy Multivalued Dependencies in a Fuzzy Relational Data Model

陳惠君(Hui-Chun Chen)

指導教授 ： 龐金宗

元智大學/資訊學院/資訊管理學系/碩士(2004年)

摘要

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。

關鍵字

模糊關聯式資料庫 ； 模糊功能相依 ； 模糊多重值相依

並列摘要

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.

並列關鍵字

Fuzzy relational database ； Fuzzy functional dependency ； Fuzzy multivalued dependency

參考文獻

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