T2-HyFIS-Yager: Type 2 Hybrid Neural Fuzzy Inference System
Chai Hiok Quek, Chenxiao Guan · 2009
The Hybrid neural Fuzzy Inference System (Hy- FIS) is a five layers adaptive neural fuzzy inference system, based on the Compositional Rule of Inference (CRI) scheme, for building and optimizing fuzzy models. To provide the HyFIS architecture with a firmer and more intuitive logical frame- work that emulates the human reasoning and decision-making mechanism, the fuzzy Yager inference scheme, together with the self-organizing gaussian Discrete Incremental Clustering (gDIC) technique , were integrated into the HyFIS network to produce the HyFIS-Yager-gDIC . This paper presents T2- HyFIS-Yager, a Type-2 Hybrid neural Fuzzy Inference System realizing Yager inference, for learning and reasoning with noise corrupted data. The proposed T2-HyFIS-Yager is used to perform time-series forecasting where a non-stationary time- series is corrupted by additive white noise of known and unknown SNR to demonstrate its superiority as an effective neuro-fuzzy modeling technique. I. INTRODUCTION Information uncertainties are inherent in everyday life, from the natural linguistic fuzziness at the cognitive level to the measurement inaccuracies at the empirical level. All of these uncertainties translate into uncertainties about the fuzzy set membership functions. Traditional Type-1 fuzzy logic systems are unable to directly model such uncertainties because crisp membership grades are used for the fuzzy membership functions in the systems. On the other hand, Type-2 fuzzy logic systems (1),(5) are able to handle in- formation uncertainties because the membership grades of the fuzzy membership functions used are also fuzzy. Such membership functions are fuzzy sets whose membership grades are Type-1 fuzzy sets, hence they are useful in incorporating information uncertainties in the systems. The Hybrid neural Fuzzy Inference System (HyFIS) (4) is a five layers adaptive Type-1 neural fuzzy network that is used to combine numerical and linguistic information into a common framework. It adopts a two phase learning scheme. In the first phase, a fuzzy technique by Wang and Mendel (14) is used to obtain the initial fuzzy rulebase and the initial structure of the neural fuzzy system. In the sec- ond phase, a parameter learning technique using a gradient descent approach is used to tune the memberships of the input and output dimensions. Subsequently, the fuzzy Yager inference scheme (3), which accounts for a firm and intuitive logical framework that emulates the human reasoning and decision-making mechanism, is integrated into the HyFIS network. Together with the implementation of the gaussian Discrete Incremental Clustering (gDIC) (10) technique in the initialization phase of the HyFIS network which allows for self-organization of the membership functions, a self- organizing Hybrid neural Fuzzy Inference System based on Yager inference (HyFIS-Yager-gDIC) (13) is produced. The realization of the fuzzy Yager inference scheme in the HyFIS network offers a firm and intuitive logical framework, and the use of gDIC is shown to be able to robustly handle noisy data when the noise level is low. This paper presents the Type-2 Hybrid neural Fuzzy In- ference System which implements the Yager inference (T2- HyFIS-Yager), a self-organizing hybrid neural fuzzy infer- ence system embedded with Type-2 fuzzy Yager inference. The proposed T2-HyFIS-Yager integrates the mathematical formalism of Type-2 fuzzy logic inference with the self- organizing Yager based HyFIS inference network, and allows for the robust learning and reasoning with noise corrupted data of known and unknown SNR. T2-HyFIS-Yager couples the Mamdani rule system (7) with Type-2 fuzzy inference to provide a clear interpretation to its knowledge-base and reasoning process for the comprehension of the human user. The rest of the paper is organized as follows: the HyFIS and HyFIS-Yager-gDIC networks are briefly described in Sect. II; the operations and learning process of the proposed T2-HyFIS-Yager network are presented in Sect. III; the application of T2-HyFIS-Yager on the forecasting of a non- stationary time-series corrupted with additive white noise is described in Sect. IV; and Sect. V concludes the paper.