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Figure 1: The equivalent ANFIS structure Jang [20] proposed methods to update the ANFIS parameters involving gradient descent and Least Square Error (LSE). High complexity is one of these methods’ features. Several popular training algorithms for tuning parameters of ANFIS membership functions are compared in [21]. In this paper we use the hybrid learning algorithm proposed in [20] which is a combination of least square estimation and backpropagation algorithms.

Figure 1 The equivalent ANFIS structure Jang [20] proposed methods to update the ANFIS parameters involving gradient descent and Least Square Error (LSE). High complexity is one of these methods’ features. Several popular training algorithms for tuning parameters of ANFIS membership functions are compared in [21]. In this paper we use the hybrid learning algorithm proposed in [20] which is a combination of least square estimation and backpropagation algorithms.

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Table 2: Candidate Input Data
Table 2: Candidate Input Data
The corresponding RC values are shown in Fig. 2. Next, based on an introduced Cluster Validity Index, we determine that the optimum number of clusters is 7 (see Fig. 3). GK fuzzy clustering algorithm is applied for initialization of antecedent membership functions. Then ANFIS with hybrid learning algorithm (combination of least square estimation and backpropagation algorithms) is used for parameters tuning. We use Mamdani-style inference, min—max operators, and centroid defuzzification method. The rules that ANFIS generated make sense relative to the economics of the foreign exchange market, as shown in Fig. 4. Figure 2: Behavior of RC in proposed model
The corresponding RC values are shown in Fig. 2. Next, based on an introduced Cluster Validity Index, we determine that the optimum number of clusters is 7 (see Fig. 3). GK fuzzy clustering algorithm is applied for initialization of antecedent membership functions. Then ANFIS with hybrid learning algorithm (combination of least square estimation and backpropagation algorithms) is used for parameters tuning. We use Mamdani-style inference, min—max operators, and centroid defuzzification method. The rules that ANFIS generated make sense relative to the economics of the foreign exchange market, as shown in Fig. 4. Figure 2: Behavior of RC in proposed model
Figure 3: Identification of the optimum number of clusters
Figure 3: Identification of the optimum number of clusters
Figure 4: Fuzzy rule base of USD/JPY exchange rates forecasting To further validate this approach for currency exchange rates forecasting, the results were compared to the results with a) the Sugeno-Yasukawa [26] approach, b) a feedforward multi-layer neural network, and c) multiple regression. The comparison uses the root mean square of the prediction error (RMSE) and mean error of the prediction (BIAS). The comparison results for training and testing dataset are shown in Table 3, 4, 5, and 6. The characteristics of the mentioned test models are described next.
Figure 4: Fuzzy rule base of USD/JPY exchange rates forecasting To further validate this approach for currency exchange rates forecasting, the results were compared to the results with a) the Sugeno-Yasukawa [26] approach, b) a feedforward multi-layer neural network, and c) multiple regression. The comparison uses the root mean square of the prediction error (RMSE) and mean error of the prediction (BIAS). The comparison results for training and testing dataset are shown in Table 3, 4, 5, and 6. The characteristics of the mentioned test models are described next.
Table 6: BIAS of different models for testing set 5 Conclusions
Table 6: BIAS of different models for testing set 5 Conclusions
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Nonlinear identification
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