在模糊規則庫系統中，模糊內插推理是一個很重要的研究課題。模糊內插推理不但可以克服稀疏模糊規則庫系統產生不合理推理結論之缺點，更可以幫助簡化模糊規則庫系統之複雜度。在本論文中，我們根據Type-1模糊集合及區間Type-2模糊集合在稀疏模糊規則庫系統中提出五個新方法以作模糊內插推理。在本論文的第一個方法中，我們根據Type-1模糊集合之面積比例關係提出一個新的模糊內插推理方法。結果顯示我們所提之方法比目前已存在之方法更具有彈性且產生更合理之模糊內插推理結果。在本論文的第二個方法中，我們以模糊分群技術及模糊內插推理技術為基礎提出一個新的模糊預測方法以多變數模糊預測問題，其中我們應用我們所提之方法以處理溫度預測問題及台灣股價加權指數之預測問題，我們所提之方法比目前已存在之模糊預測方法具有更高的預測準確率。在本論文的第三個方法中，我們根據Type-1模糊集合之模糊比例關係及遺傳演算法提出一個新的加權模糊內插推理方法，我們所提之方法可以處理模糊規則具有不同權重之前提變數的模糊內插推理，且可以處理以多邊形模糊集合及鐘形模糊集合為基礎之模糊內插推理。我們也根據遺傳演算法提出一個自動權重學習方法。我們並應用我們所提之模糊內插推理方法及自動權重學習方法於自動倒車入庫問題、多變數非線性回歸問題及時間序列預測問題。根據統計分析之實驗結果，我們所提之方法比目前已存在之方法具有更高的準確率。在本論文的第四個方法中，我們根據區間Type-2模糊集合之模糊度提出一個新的模糊內插推理方法，此方法可以處理以區間Type-2多邊形模糊集合及區間Type-2鐘形模糊集合為基礎之模糊內插推理。對於不同之觀察模糊集合，我們所提之方法可以產生不同之結論模糊集合。實驗結果顯示我們所提的方法比目前已存在之方法具有更合理的模糊內插推理結果。在本論文的第五個方法中，我們提出一個可以處理區間Type-2高斯模糊集合之模糊內插推理新方法，我們也根據遺傳演算法提出一個區間Type-2高斯歸屬函數自動學習方法。我們並應用我們所提之方法處理多變數非線性回歸問題及時間序列預測問題，實驗結果顯示我們所提之方法得到比目前已存在之方法具有更高的預測準確率。

Fuzzy interpolative reasoning is an important research topic for sparse fuzzy rule-based systems. It not only can overcome the drawback of sparse fuzzy rule-based systems, but also can help to reduce the complexity of large fuzzy rule bases for fuzzy rule-based systems. In this dissertation, we present five new fuzzy interpolative reasoning methods for sparse fuzzy rule-based systems based on type-1 fuzzy sets and interval type-2 fuzzy sets, respectively. In the first method of our dissertation, we present a new fuzzy interpolative reasoning method for sparse fuzzy rule-based system based on the areas of fuzzy sets. The proposed method uses the weighted average method to infer the fuzzy interpolative reasoning results. In terms of the six evaluation indices, the experimental results show the proposed method performs more reasonably than the existing methods. In the second method of our dissertation, we present a new method for multi-variables fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques. We apply the proposed method to the temperature prediction problem and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) data. The experimental results show that the proposed method produces better forecasting results than existing methods. In the third method of our dissertation, we present a new weighted fuzzy interpolative reasoning method for sparse fuzzy rule-based systems. It is based on genetic algorithm (GA)-based weight-learning techniques. The proposed method can deal with fuzzy rule interpolation with weighted antecedent variables. We also present a GA-based weight-learning algorithm to automatically learn the optimal weights of the antecedent variables of the fuzzy rules. We also apply the proposed weighted fuzzy interpolative reasoning method and the proposed GA-based weight-learning algorithm to deal with the truck backer-upper control problem, multivariate regression problems and time series prediction problems. Based on statistical analysis techniques, the experimental results show that the proposed weighted fuzzy interpolative reasoning method using the optimally learned weights obtained by the proposed GA-based weight-learning algorithm has statistically significantly smaller error rates than the existing methods. In the fourth method of our dissertation, we present a new method for fuzzy rule interpolation for sparse fuzzy rule-based systems based on the ratios of fuzziness of interval type-2 fuzzy sets. The proposed method can deal with fuzzy rule interpolation based on polygonal interval type-2 fuzzy sets and bell-shaped interval type-2 fuzzy sets. The experimental results show that the proposed method gets more reasonable results than the existing methods. In the fifth method of our dissertation, we present a new method for fuzzy rule interpolation with interval type-2 Gaussian fuzzy sets for sparse fuzzy rule-based systems. We also present a learning algorithm to learn the optimal interval type-2 Gaussian fuzzy sets for sparse fuzzy rule-based systems based on genetic algorithms. We also apply the proposed fuzzy rule interpolation method and the proposed learning algorithm to deal with multivariate regression problems and time series prediction problems. The experimental results show that the proposed fuzzy rule interpolation method using the optimally learned interval type-2 Gaussian fuzzy sets produces higher accuracy than the existing methods.

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