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Fuzzy interpolative reasoning is a very important research topic in sparse fuzzy rule-based systems. In this thesis, we propose two new fuzzy interpolative reasoning methods for sparse fuzzy rule-based systems. In the first method, we propose a new transformation-based weighted fuzzy interpolative reasoning method based on the ranking values of polygonal fuzzy sets and the proposed scale and move transformation techniques. The proposed weighted fuzzy interpolative reasoning method is based on the multiple fuzzy rules and multiple antecedent variables fuzzy interpolative reasoning scheme, which can automatically calculate the weight of each fuzzy rule and can automatically calculate the weight of each antecedent variable of the fuzzy rules. The proposed scale and move transformation techniques can deal with singleton fuzzy sets and polygonal fuzzy sets. In the second method, we propose a new adaptive fuzzy interpolative reasoning method based on general representative values of polygonal fuzzy sets and the proposed shift and modification techniques. The proposed adaptive fuzzy interpolative reasoning method includes a new contradiction solving method to get a higher similarity degree between polygonal fuzzy sets of the adaptive fuzzy interpolative reasoning results. The experimental results show that the proposed weighted fuzzy interpolative reasoning method and the proposed adaptive fuzzy interpolation for sparse fuzzy rule-based systems outperforms the existing methods

Fuzzy interpolative reasoning is a very important research topic in sparse fuzzy rule-based systems. In this thesis, we propose two new fuzzy interpolative reasoning methods for sparse fuzzy rule-based systems. In the first method, we propose a new transformation-based weighted fuzzy interpolative reasoning method based on the ranking values of polygonal fuzzy sets and the proposed scale and move transformation techniques. The proposed weighted fuzzy interpolative reasoning method is based on the multiple fuzzy rules and multiple antecedent variables fuzzy interpolative reasoning scheme, which can automatically calculate the weight of each fuzzy rule and can automatically calculate the weight of each antecedent variable of the fuzzy rules. The proposed scale and move transformation techniques can deal with singleton fuzzy sets and polygonal fuzzy sets. In the second method, we propose a new adaptive fuzzy interpolative reasoning method based on general representative values of polygonal fuzzy sets and the proposed shift and modification techniques. The proposed adaptive fuzzy interpolative reasoning method includes a new contradiction solving method to get a higher similarity degree between polygonal fuzzy sets of the adaptive fuzzy interpolative reasoning results. The experimental results show that the proposed weighted fuzzy interpolative reasoning method and the proposed adaptive fuzzy interpolation for sparse fuzzy rule-based systems outperforms the existing methods

Abstract i
Acknowledgements ii
Contents iii
List of Figures and Tables v
Chapter 1 Introduction 1
1.1 Motivation 1
1.2 Related Literature 6
1.3 Organization of This Thesis 11
Chapter 2 Preliminaries 12
2.1 Basic Concepts of Fuzzy Sets 12
2.2 Characteristic Points of Polygonal Fuzzy Sets 12
2.3 Summary 13
Chapter 3 Weighted Fuzzy Interpolated Reasoning Based on Ranking Values of Polygonal Fuzzy Sets and Scale and Move Transformation Techniques 15
3.1 Ranking Values of Polygonal Fuzzy Sets 15
3.2 A New Weighted Fuzzy Interpolated Reasoning Based on Ranking Values of Polygonal Fuzzy Sets and Scale and Move Transformation Techniques 16
3.3 A Comparison of Fuzzy Interpolative Reasoning Results for the Proposed Method and the Existing Methods 28
3.4 Summary 81
Chapter 4 Adaptive Fuzzy Interpolation Based on General Representative Values of Polygonal Fuzzy Sets and the Shift and Modification Techniques 82
4.1 Preliminaries 82
4.2 A New Adaptive Fuzzy Interpolation Based on General Representative Values of Polygonal Fuzzy Sets and the Shift and Modification Techniques 83
4.3 A Comparison of the Proposed Adaptive Fuzzy Interpolation Method and the Existing Methods 95
4.4 Summary 100
Chapter 5 Conclusions 102
5.1 Contributions of This Thesis 102
5.2 Future Research 102
References 104

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- Adaptive Fuzzy Interpolative Reasoning Based on Polygonal Fuzzy Sets and Adaptive Weighted Fuzzy Interpolative Reasoning Based on Interval Type-2 Fuzzy Sets
- New Fuzzy Interpolative Reasoning Methods Based on Ranking Values of Polygonal Fuzzy Sets, Automatically Generated Weights of Fuzzy Rules and Similarity Measures Between Polygonal Fuzzy Sets
- New Fuzzy Interpolative Reasoning Methods for Sparse Fuzzy Rule-Based Systems
- New Fuzzy Interpolative Reasoning Methods for Sparse Fuzzy Rule-Based System
- Fuzzy Interpolative Reasoning Based on the Slopes of Fuzzy Sets and PSO-Based Weights-Learning Techniques