在稀疏模糊規則庫系統中，模糊內插推論是一個很重要的研究課題。模糊內插推論不僅可以克服稀疏規則庫系統之缺點，而且可以降低模糊規則庫系統中之複雜度。在本論文中，我們根據Type-1模糊集合及粗糙模糊集合在稀疏規則庫系統中提出兩個新方法以作模糊內插推論。在本論文所提之第一個方法中，我們根據模糊集合之分段模糊熵提出一個新的加權式模糊內插推論方法，以處理多變數非線性迴歸問題、Mackey-Glass混沌時間序列預測問題、及時間序列預測問題。實驗結果顯示我們所提之加權式模糊內插推論方法比目前已存在之方法具有更高之預測準確率。在本論文所提之第二個方法中，我們根據粗糙模糊集合之分段模糊熵及粗糙模糊集合之模糊度比率提出一個新的模糊內插推論方法，其中在模糊規則中之前提變數及結論變數均以多邊形粗糙模糊集合表示。我們亦提出一個根據一組多邊形模糊集合以建構一個多邊形粗糙模糊集合之方法。實驗結果顯示我們所提之根據粗糙模糊集合的模糊內插推論方法比目前已存在之方法具有更合理的模糊內插推論結果。

Fuzzy interpolative reasoning is a very important research topic for sparse fuzzy rule-based systems. It can overcome the drawbacks of sparse fuzzy rule-based systems and can reduce the complexity of fuzzy rule bases for fuzzy rule-based systems. In this thesis, we propose two new fuzzy interpolative reasoning methods for sparse fuzzy rule-based systems based on type-1 fuzzy sets and rough-fuzzy sets, respectively. In the first method of our thesis, we propose a new method for weighted fuzzy interpolative reasoning based on piecewise fuzzy entropies of fuzzy sets. The experimental results show that the proposed weighted fuzzy interpolative reasoning method outperforms the existing methods for dealing with the multivariate regression problems, the Mackey-Glass chaotic time series prediction problem, and the time series prediction problems. In the second method of our thesis, we propose a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on piecewise fuzzy entropies and the ratios of fuzziness of polygonal rough-fuzzy sets, where the values of the antecedent variables and the consequence variables in the fuzzy rules are represented by polygonal rough-fuzzy sets. We also propose a method for constructing polygonal rough-fuzzy sets from a set of polygonal fuzzy sets. The experimental results show that the proposed fuzzy interpolative reasoning method based on rough-fuzzy sets gets more reasonable fuzzy interpolative reasoning results than the existing method.

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