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

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