Interval type-2 neuro-fuzzy system with implication-based inference mechanism

The system uses interval type-2 fuzzy sets in premises and consequences of rules.The system uses several interval type-2 fuzzy implications.The system applies logical interpretation to fuzzy rules.The paper is accompanied by numerical examples.The system can elaborate models with lower errors than type-1 and type-2 systems. Neuro-fuzzy systems have been proved to be an efficient tool for modelling real life systems. They are precise and have ability to generalise knowledge from presented data. Neuro-fuzzy systems use fuzzy sets most commonly type-1 fuzzy sets. Type-2 fuzzy sets model uncertainties better than type-1 fuzzy sets because of their fuzzy membership function. Unfortunately computational complexity of type reduction in general type-2 systems is high enough to hinder their practical application. This burden can be alleviated by application of interval type-2 fuzzy sets. The paper presents an interval type-2 neuro-fuzzy system with interval type-2 fuzzy sets both in premises (Gaussian interval type-2 fuzzy sets with uncertain fuzziness) and consequences (trapezoid interval type-2 fuzzy set). The inference mechanism is based on the interval type-2 fuzzy ukasiewicz, Reichenbach, Kleene-Dienes, or BrouwerGdel implications. The paper is accompanied by numerical examples. The system can elaborate models with lower error rate than type-1 neuro-fuzzy system with implication-based inference mechanism. The system outperforms some known type-2 neuro-fuzzy systems.

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