Academia.eduAcademia.edu

Figure 3 – uploaded by QUEST JOURNALS

See full PDFdownloadDownload figure
The COCOMO software cost model measures effort in calendar months of 152 hours (development and management hours included). COCOMO assumes that the effort grows more than linearly on software size; that is:

Table 3 The COCOMO software cost model measures effort in calendar months of 152 hours (development and management hours included). COCOMO assumes that the effort grows more than linearly on software size; that is:

Related Figures (27)

The fuzzy logic model for software development effort evaluation, shown in Figure 1, contains a knowledge base and processing stage. The knowledge base provides membership functions and the fuzzy rules needed for the process. Numerical crisp variables are the input of the system in the processing stage. These variables are passed through a fuzzification stage where they are transformed into linguistic variables, which become the fuzzy input of the inference engine. This fuzzy input is transformed by rules of the inference engine to fuzzy output. These linguistic results are then changed by a defuzzification stage into numerical values that becomes the output of the system. Figure 1: Fuzzy Logic Model for Software Development Effort Evaluation
The fuzzy logic model for software development effort evaluation, shown in Figure 1, contains a knowledge base and processing stage. The knowledge base provides membership functions and the fuzzy rules needed for the process. Numerical crisp variables are the input of the system in the processing stage. These variables are passed through a fuzzification stage where they are transformed into linguistic variables, which become the fuzzy input of the inference engine. This fuzzy input is transformed by rules of the inference engine to fuzzy output. These linguistic results are then changed by a defuzzification stage into numerical values that becomes the output of the system. Figure 1: Fuzzy Logic Model for Software Development Effort Evaluation
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. Table 3: Modes of Development Constants
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. Table 3: Modes of Development Constants
Table 4 shows the ratings (numeric values) of the COCOMO effort attributes (multipliers) and their correlation with more effort.
Table 4 shows the ratings (numeric values) of the COCOMO effort attributes (multipliers) and their correlation with more effort.
Table 5: 15 COCOMO II sample for PCA *Corresponding Author: Edward N. Udo
Table 5: 15 COCOMO II sample for PCA *Corresponding Author: Edward N. Udo
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. After the calculation of the mean of the 15 cost drivers, the transpose matrix of the dataset, the estimation of the covariance and the correlation set matrix, the Eigen vector is shown in Table 6.
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. After the calculation of the mean of the 15 cost drivers, the transpose matrix of the dataset, the estimation of the covariance and the correlation set matrix, the Eigen vector is shown in Table 6.
Table 6: Eigen Vector of the Correlation Matrix The coefficients of the eigenvectors serve as the regression coefficients of the 15 principal components (PC). For example, the first PC can be expressed by:
Table 6: Eigen Vector of the Correlation Matrix The coefficients of the eigenvectors serve as the regression coefficients of the 15 principal components (PC). For example, the first PC can be expressed by:
Table 7: Eigen value summary The corresponding bar chart for the data in Table 7 is depicted in Figure 2.
Table 7: Eigen value summary The corresponding bar chart for the data in Table 7 is depicted in Figure 2.
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And . From the above chart, it can seen that the principal component determinant, which is the Eigen vector favors only RELY, DATA, CPLX, TIME and AEXP based on their percentage composition. For design’s sake, PCA is used to reduce 15 dimensions in the original COCOMO II file to 5 dimensions for flawless computations; however, in the implementation using MATLAB, the 23 inputs is reduced to 6.
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And . From the above chart, it can seen that the principal component determinant, which is the Eigen vector favors only RELY, DATA, CPLX, TIME and AEXP based on their percentage composition. For design’s sake, PCA is used to reduce 15 dimensions in the original COCOMO II file to 5 dimensions for flawless computations; however, in the implementation using MATLAB, the 23 inputs is reduced to 6.
The model was trained with 70% of the entire dataset and tested with 30% of the dataset. Figure 3 shows the distribution of training dataset. The model training was carried out on different number of epochs: 10 epoch, 20 epoch, 25 epoch, 30 epoch, 50 epoch, 70 epoch and 100 epoch. The ANFIS training result with different epoch values are presented in Figures 4 — 9. Figure 4 shows the ANFIS training error result at 10 epoch with a training error of 0.5732 and 0.0079 for Back Propagation and Hybrid algorithm respectively.
The model was trained with 70% of the entire dataset and tested with 30% of the dataset. Figure 3 shows the distribution of training dataset. The model training was carried out on different number of epochs: 10 epoch, 20 epoch, 25 epoch, 30 epoch, 50 epoch, 70 epoch and 100 epoch. The ANFIS training result with different epoch values are presented in Figures 4 — 9. Figure 4 shows the ANFIS training error result at 10 epoch with a training error of 0.5732 and 0.0079 for Back Propagation and Hybrid algorithm respectively.
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. Figure 4: Training Results for Epoch 10 (Back Propagation vs Hybrid)
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. Figure 4: Training Results for Epoch 10 (Back Propagation vs Hybrid)
Figure 5: Training result with 20 Epochs (Back Propagation vs Hybrid) Figure 5 shows the ANFIS training with 20 epoch giving a training error of 0.5305 and 0.0063for Back Propagation and Hybrid algorithm respectively.
Figure 5: Training result with 20 Epochs (Back Propagation vs Hybrid) Figure 5 shows the ANFIS training with 20 epoch giving a training error of 0.5305 and 0.0063for Back Propagation and Hybrid algorithm respectively.
Figure 6: Training result with 50 Epoch (Back Propagation vs Hybrid) Figure 6 is the ANFIS training result with 50 epochs giving a training error of 0.4966 and 0.0050 for Back Propagation and Hybrid algorithm respectively.
Figure 6: Training result with 50 Epoch (Back Propagation vs Hybrid) Figure 6 is the ANFIS training result with 50 epochs giving a training error of 0.4966 and 0.0050 for Back Propagation and Hybrid algorithm respectively.
Figure 7: Training result with 60 Epoch (Back Propagation vs Hybrid) Figure 7 presents the training results at epoch of 60 with a training error of 0.4867 and 0.0048 for Back propagation and Hybrid algorithm respectively. At Epoch 60, BP algorithm converges while the Hybrid experienced a premature convergence.
Figure 7: Training result with 60 Epoch (Back Propagation vs Hybrid) Figure 7 presents the training results at epoch of 60 with a training error of 0.4867 and 0.0048 for Back propagation and Hybrid algorithm respectively. At Epoch 60, BP algorithm converges while the Hybrid experienced a premature convergence.
Figure 8: Training result with 70 epochs (Back Propagation vs Hybrid) Figure 8 presents the training results at epoch of 70 with a training error of 0.4773 and 0.0045 for Back propagation and Hybrid algorithm respectively. Figure 9 shows the training results at Epoch 100. At Epoch 70, BP algorithm had converged already with some little divergence difference of 0.0094 but the Hybrid experienced a proper convergence from Epoch 70.
Figure 8: Training result with 70 epochs (Back Propagation vs Hybrid) Figure 8 presents the training results at epoch of 70 with a training error of 0.4773 and 0.0045 for Back propagation and Hybrid algorithm respectively. Figure 9 shows the training results at Epoch 100. At Epoch 70, BP algorithm had converged already with some little divergence difference of 0.0094 but the Hybrid experienced a proper convergence from Epoch 70.
Figure 9: Training result with 100 epochs (Back Propagation (BP) vs Hybrid (HB))
Figure 9: Training result with 100 epochs (Back Propagation (BP) vs Hybrid (HB))
Figure 10: ANFIS Training Error Plot The ANFIS training error plot is shown in Figure 10.
Figure 10: ANFIS Training Error Plot The ANFIS training error plot is shown in Figure 10.
Figure 11: Training Error and Validation Error Plots In order to test the accuracy of the ANFIS model, 30% of the reduced dataset was used for model testing. The training error and validation error for each of the epoch is shown in Figure 11.
Figure 11: Training Error and Validation Error Plots In order to test the accuracy of the ANFIS model, 30% of the reduced dataset was used for model testing. The training error and validation error for each of the epoch is shown in Figure 11.
Table 8: ANFIS Training Errors
Table 8: ANFIS Training Errors
Figure 12: ANFIS Output and Real Output The graph in Figure 12 compares the ANFIS model output and COCOMO output which is the actual effort (number of person-hours) required to develop software.
Figure 12: ANFIS Output and Real Output The graph in Figure 12 compares the ANFIS model output and COCOMO output which is the actual effort (number of person-hours) required to develop software.
Table 9: ANFIS Testing Error
Table 9: ANFIS Testing Error
Table 10: Comparison of Predictions and COCOMO Model *Corresponding Author: Edward N. Udo
Table 10: Comparison of Predictions and COCOMO Model *Corresponding Author: Edward N. Udo
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. *Corresponding Author: Edward N. Udo
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. *Corresponding Author: Edward N. Udo
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. vu. PENPUNRNVIANUR BVALUALLUIN Based on the conducted experiments, ANFIS model using Hybrid Training Model with six (6) inputs reduced by PCA gave better estimate than the Back Propagation Model with six (6) inputs reduced by PCA. The result of performance measures using MMRE and MSE for each of the training is shown in Table 11.
A Comparative Analysis Of Adaptive Neuro-Fuzzy Inference System Back Propagation And .. vu. PENPUNRNVIANUR BVALUALLUIN Based on the conducted experiments, ANFIS model using Hybrid Training Model with six (6) inputs reduced by PCA gave better estimate than the Back Propagation Model with six (6) inputs reduced by PCA. The result of performance measures using MMRE and MSE for each of the training is shown in Table 11.
Table 11: Performance Evaluation Results
Table 11: Performance Evaluation Results
Figure 13: MRE Plot ANFIS BP The MRE Performance Measure of Hybrid and Back Propagation were plotted. The plot shows that the Hybrid training guaranteed convergence more than BP training. In Figure 13, the high shoots between Epoch 10 and Epoch 20, Epoch 60 and 90 were responsible for negative predictions. In some cases, the predictions appeared to be meaningful why others were not. This is where the least square method complements the back propagation algorithm to prevent large learning rate that may have occurred at the early epochs.
Figure 13: MRE Plot ANFIS BP The MRE Performance Measure of Hybrid and Back Propagation were plotted. The plot shows that the Hybrid training guaranteed convergence more than BP training. In Figure 13, the high shoots between Epoch 10 and Epoch 20, Epoch 60 and 90 were responsible for negative predictions. In some cases, the predictions appeared to be meaningful why others were not. This is where the least square method complements the back propagation algorithm to prevent large learning rate that may have occurred at the early epochs.
In Figure 14, the least square method complements the large learning rate that occurred between epoch 10 and 20. These learning rates, if large, affect the weights of neuron, so the least square updates parameters by minimizing the squared difference between observed data and desired data. At Epoch 20 the large learning rate was reduced by least-square hence ensuring convergence at Epoch 70.
In Figure 14, the least square method complements the large learning rate that occurred between epoch 10 and 20. These learning rates, if large, affect the weights of neuron, so the least square updates parameters by minimizing the squared difference between observed data and desired data. At Epoch 20 the large learning rate was reduced by least-square hence ensuring convergence at Epoch 70.
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved