Interval type-2 intuitionistic fuzzy logic system for non-linear system prediction

Abstract

Abstract-This paper presents an approach to prediction based on a new interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi-Sugeno-Kang (TSK) fuzzy inference. The gradient descent algorithm (GDA) is used to adapt the parameters of the IT2IFLS. The empirical comparison is made on the designed system using two synthetic datasets. Analysis of our results reveal that the presence of additional degrees of freedom in terms of non-membership functions and hesitation indexes in IT2IFLS tend to reduce the root mean square error (RMSE) of the system compared to a type-1 fuzzy logic approach and some interval type-2 fuzzy systems.

Time series forecasting with interval type-2 intuitionistic fuzzy logic systems

“…A T2IFS [12] denoted byà * has a type-2 membership function µÃ * (x, u), and a type-2 non-membership function νà * (x, u), i.e.,…”

“…As defined above, an IT2IFSà * is made up of interval type-2 membership function, µÃ * (x, u) and interval type-2 nonmembership function, νà * (x, u) for every x ∈ X expressed as in Eqn (1) [12].…”

“…Intuitionistic fuzzy sets of type-1 have been successfully employed in time series forecasting [10], [11]. However, because type-1 intuitionistic fuzzy sets (T1IFS) have membership and non-membership grades that are precise, they may not handle uncertainty well in many applications (see [12]). …”

“…To this end, we propose an application of the recently developed interval type-2 intuitionistic fuzzy logic system (IT2IFLS) [12] framework for time series analysis. The IT2IFLS utilises extra degrees of freedom in terms of interval non-membership functions.…”

Interval Type-2 Intuitionistic Fuzzy Logic Systems - A Comparative Evaluation

“…Recently, in Eyoh et al [12], IFS is fused with IT2FS and an interval type-2 intuitionistic FS (IT2IFS) is obtained with artificial neural network learning capability. The uncertainties in IT2IFLS that utilises IT2IFS in the IF-THEN rules are captured by the footprints of uncertainties (FOUs) of both MFs and NMFs.…”