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Fig. 6. Average error obtained (a) by training and checking data set (b) to develop the optimal model. Fig. 5. The error of each observation for checking and training data.

Figure 6 Average error obtained (a) by training and checking data set (b) to develop the optimal model. Fig. 5. The error of each observation for checking and training data.

Related Figures (10)

Fig. 1. Control action surface after training (a), and comparison of output (SAP) surfaces constructed by the five MFs, after (b) normalization for inputs (Major and Quiz).
Fig. 1. Control action surface after training (a), and comparison of output (SAP) surfaces constructed by the five MFs, after (b) normalization for inputs (Major and Quiz).
La(X), where x is the mark to represent an achievement of a stu- dent in set A. Fuzzy rules are mathematical relationships mapping
La(X), where x is the mark to represent an achievement of a stu- dent in set A. Fuzzy rules are mathematical relationships mapping
Fig. 3. Fine tuned membership functions of ‘Final exam (a), Major exam (b)’ as input variables. The rule set in Eq. (3) illustrates the reasoning mechanism and the corresponding equivalent ANFIS architecture where the nodes of the same layer have similar functions. difference between actual and desired outputs). The parameters associated with the MFs will change through the learning process.
Fig. 3. Fine tuned membership functions of ‘Final exam (a), Major exam (b)’ as input variables. The rule set in Eq. (3) illustrates the reasoning mechanism and the corresponding equivalent ANFIS architecture where the nodes of the same layer have similar functions. difference between actual and desired outputs). The parameters associated with the MFs will change through the learning process.
Fig. 4. ANFIS architecture for a six input single-output Sugeno fuzzy model. Fig. 4 shows the architecture of the neural network structure. The computation of MFs parameters (or their adjustment) is facilitated by a gradient vector, which provides a measure of how well the AN- FIS is modeled with the input/output data for a given set of para- meters. Once the MFs are constituted, any of several optimization routines can be applied in order to adjust the parameters to reduce the error measure (usually defined by the sum of the squared
Fig. 4. ANFIS architecture for a six input single-output Sugeno fuzzy model. Fig. 4 shows the architecture of the neural network structure. The computation of MFs parameters (or their adjustment) is facilitated by a gradient vector, which provides a measure of how well the AN- FIS is modeled with the input/output data for a given set of para- meters. Once the MFs are constituted, any of several optimization routines can be applied in order to adjust the parameters to reduce the error measure (usually defined by the sum of the squared
Training and checking data and the errors of ANFIS outputs versus the classical statistical method. Table 1
Training and checking data and the errors of ANFIS outputs versus the classical statistical method. Table 1
Outcomes of the SAP for statistical and ANFIS model; their linguistic values based on different inputs. Table 2
Outcomes of the SAP for statistical and ANFIS model; their linguistic values based on different inputs. Table 2
ANFIS SAP outcomes with subclustering and grid partitioning methods, their error versus statistical SAP outcomes Table 3
ANFIS SAP outcomes with subclustering and grid partitioning methods, their error versus statistical SAP outcomes Table 3
Fig. 7. The outcomes of SAP versus Statistical and ANFIS for different observations.
Fig. 7. The outcomes of SAP versus Statistical and ANFIS for different observations.
Fig. 8. The outcomes of ANFIS model and their linguistic values. (uaA(55) = 0.5). This is the flexibility of fuzzy linguistic variables and their labels.
Fig. 8. The outcomes of ANFIS model and their linguistic values. (uaA(55) = 0.5). This is the flexibility of fuzzy linguistic variables and their labels.
Related topics:
Engineeringadaptive neuro fuzzy inference system (ANFIS)Fuzzy System
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