Antecedent connector word models for interval type-2 fuzzy logic systems

We investigate ten compensatory operators and SOWA operators in the framework of Mamdani interval type-2 fuzzy logic systems (FLS) so that for the first time the uncertainties originating from descriptive words, connector words and data can be simultaneously modeled. Our investigations show that: 1) for a Mamdani singleton interval type-2 FLS all the ten operators can be implemented and optimized; and 2) for a Mamdani non-singleton interval type-2 FLS the multiplicative compensatory operator that uses the product t-norm and maximum t-conorm, Φ_p^MCA, can be implemented and optimized. We apply Φ_p^MCA to chaotic time-series prediction where the observations are corrupted by non-stationary noise. Our experimental results show that by incorporating Φ_p^MCA into a Mamdani interval type-2 FLS it may take less time to train an interval type-2 FLS to achieve a satisfactory performance, and the resulting system is more robust to noise.