Abstract

Conventional fuzzy time series approaches make use of type-1 or type-2 fuzzy models. Type-1 models with one index (membership grade) cannot fully handle the level of uncertainty inherent in many real world applications. The type-2 models with upper and lower membership functions do handle uncertainties in many applications better than its type-1 counterparts. This study proposes the use of interval type-2 intuitionistic fuzzy logic system of Takagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference that utilises more parameters than type-2 fuzzy models in time series forecasting. The IT2IFLS utilises more indexes namely upper and lower non-membership functions. These additional parameters of IT2IFLS serve to refine the fuzzy relationships obtained from type-2 fuzzy models and ultimately improve the forecasting performance. Evaluation is made on the proposed system using three real world benchmark time series problems namely: Santa Fe, tree ring and Canadian lynx datasets. The empirical analyses show improvements of prediction of IT2IFLS over other approaches on these datasets.

Highlights

  • TIME series forecasting is an important application area that has been extensively researched

  • Because fuzzy logic systems lack the learning capability, they are often hybridised with learning algorithms such as artificial neural networks (ANNs) - an approach that is adopted in this study

  • The performance criteria used for the experiments are the root mean square error (RMSE), the non-dimensional error index (NDEI) and the mean absolute error (MAE) as expressed in Equations (11) to (13) respectively

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Summary

INTRODUCTION

TIME series forecasting is an important application area that has been extensively researched. The use of soft computing methodologies such as fuzzy logic (type-1 and type-2), neural networks, simulated annealing and genetic algorithms have been reported in the literature for time series forecasting [1]–[4] These latter approaches have shown significant improvements over the traditional statistical methods because they are non-linear and are able to approximate any complex dynamical systems better than linear statistical models [5]. 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.

TYPE-1 AND TYPE-2 INTUITIONISTIC FUZZY SET
Fuzzification
EXPERIMENTS AND RESULTS
Example 1 - Santa Fe time series
Tree Ring Time Series
Canadian Lynx Time series
CONCLUSION
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