Improving the accuracy of the Mamdani fuzzy rule base with double-consequent rules
DOI:
https://doi.org/10.31558/2786-9482.2023.1.5Keywords:
fuzzy inference, Mamdani-type fuzzy rules, double-consequent rule, rule selection, greedy algorithm, accuracy.Abstract
The paper considers the problem of modeling the multi-factor dependencies with a continuous output using fuzzy rule bases. One of the main competitive advantages of fuzzy modelling is the interpretability of the fuzzy rule base – it is quite easy for a user who is far from mathematical methods to understand what makes up a particular conclusion. For fuzzy modelling of dependency with continuous output, both Mamdani and Sugeno rule bases are most commonly used. The Sugeno rule base is more accurate but has low interpretability. Mamdani rule bases have high interpretability but low accuracy. It is problematic to increase the interpretability of Sugeno rule bases because this property is due to the rule format. The task of improving the accuracy of the Mamdani rule base is quite easy to formalize, so we can try to solve it in some algorithmic way. The goal of this article is to improve the accuracy of the Mamdani rule base. The way to improve the accuracy of the Mamdani rule base is to use double-consequent rules. A double-consequent rule is equivalent to two ordinal rules with the same antecedents and different consequents. The computational experiments carried out have shown that the use of double consequent rules by increasing the resolution of the linguistic description of the dependency provides better accuracy. The experiments were performed on three synthetic datasets and one real Auto MPG dataset. The selection of rules is done by a greedy algorithm. The use of double-consequent rules allows for to achievement of better accuracy and compactness of the model during the structural stage of fuzzy identification. It was also found that fuzzy inference on double-consequent rules can be implemented correctly and efficiently using the A-FATI scheme, while in previous studies a simplified B-FITA scheme was used.
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