New trapezoidal-triangular membership function in IT2FLS

What is it about?

The performance of Interval type-2 fuzzy logic system (IT2FLS) can be affected by many factors including the type of reduction methodology followed and the kind of membership function applied. Further, a particular membership function is influenced by its construction, the type of optimisation and adaptiveness applied, and the learning scheme adopted. The available literature lags in providing detailed information about such factors affecting the performance of IT2FLS.

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Photo by Codioful (Formerly Gradienta) on Unsplash

Photo by Codioful (Formerly Gradienta) on Unsplash

Why is it important?

➤A new MF has been introduced by combining trapezoidal and triangular MFs, and the results obtained confirm that the combined one, TTMF, yield better results compared to TrMF and TMF. ➤ Computation in IT2FLS using COS TR and "Wu-Mendel" uncertainty bounds has a different strategy, whereas the uncertainty bounds formulation has given the advantage of reduction of time delay in computation of IT2FLS. ➤ The MF having lesser parameters like GMF and SEMF has a higher accuracy rate than TrMF, TMF, and TTMF. ➤ Formulation of IT2FLS using uncertainty bounds can be replaced in place of type reductions, which proved as an equal substitution in place of type reduction. ➤ The results confirmed that the IT2FLS with GMF in both COS TR and "Wu-Mendel" uncertainty bounds has improved by 1% average error rate than the T1FLS [1]. ➤ In addition, the GMF, along with the "WuMendel" uncertainty bound and COS-TR method, is the best option compared to all others. ➤ The formulation of IT2FLS can be performed in two ways by using COS TR and "Wu-Mendel" uncertainty bounds. IT2FLS with "Wu-Mendel" uncertainty bounds has shown little better performance than COS TR. The future research directions are: ◆ The MFs can also be defined in terms of parameters associated with variable-gain nonlinear controller, which remains unexplored for SEMF and TTMF. ◆ The performance can be further studied based on the combination of MF, like trapezoidal with Gaussian, trapezoidal with semi-elliptic, and so on. Such a kind of membership may perform well in the prediction of uncertainties.

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