臺灣博碩士論文加值系統

這論文致力於使用一致的方法以偏序集（尤其是在絡(Lattice)）上當做是機器學習時的論域。絡(Lattice)理論已經應用在釵h的領域裡如邏輯、離散數學和資訊科學裡。絡理論被應用在規則學習(rule learning)。這論文的工作在於建立絡理論的術語、產生新的理論結果和利用實驗結果對絡理論有新的了解。近年來語意網（Semantic Web）蓬勃發展，其中語意網的核心──本體論（Ontology）即是一種絡的結構。我們預計我們的研究結果將可用在本體論上的自動類別學習。
第一級衍推(Frist Degree Entailment(FDE))是一種四值邏輯。在我們的研究中，我們延伸了FDE並且設計了兩種絡值模糊集(L-Fuzzy Set)：FDE集和fFDE集。模糊絡(Fuzzy Lattice)是一種傳統絡論理論的模糊化。我們合併了fFDE集和模糊絡，提出了一種新的模糊絡：fFDE模糊絡。這種新的模糊絡有更好的能力描述在絡中任兩元素的關係。採用fDE模糊絡我們可以解決資訊遺失(Information Loss)的問題。我們了利用了fDE模糊絡設計了一種新的分類器（classifier），採用了fDE模糊絡為核心的分類器有快速學習和高準確率的特性。

We approached learning in a unified manner by considering partly ordered sets and, in particular mathematical lattices, as the learning domain. Lattice theory has been employed practically in the past in various contexts including logic, discrete mathematics, and computer science. Lattice theory is also employed for rule learning. The work here maintains an established lattice theory terminology, produces new theoretical results, and gains new insights while demonstrating pilot experimental results. Recently, the semantic web is developing rapidly. The kernel of the semantic web has been an ontology which is also a lattice structure, and we expect that our results would be useful for automatically learning the classes of this ontology.
First Degree Entailment (FDE) is a kind of 4-valued logic. We extend (FDE) and design two kinds of L-fuzzy sets, FDE sets and fFDE sets. The notion of a fuzzy lattice extends traditional lattice theory by using fuzzy sets. We propose fFDE lattices by combining fFDE sets and fuzzy lattices. This new kind of fuzzy lattice has higher ability to describe membership. Using this framework, we can solve the problem information loss. We also designed a learning scheme combined with the fFDE lattice framework. This new classifier has features of rapid learning and good performance.

1 Introduction
2 Theoretical Background
2.1 Lattice
2.2 First Degree Entailment
2.3 Fuzzy Sets and L-Fuzzy Sets
2.4 Fuzzy Lattice
2.5 Intervals and Families
3 Contribution
3.1 FDE sets
3.2 FDE fuzzy poset
3.3 Fuzzy FDE Sets
3.4 fFDE Lattice
3.5 Membership Tuples
3.6 Inclusion Function and Activity Function
4 The Fuzzy FDE Lattice Learning Scheme
4.1 Learning Phase
4.2 Testing Phase
5 Experiments and Results
5.1 VOWEL Benchmark Data Set
6 Conclusion

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