**7. Conclusion**

12 Will-be-set-by-IN-TECH

Table 9 shows diagnosis results. All values in the table are average. This result shows that associative TCNN could completely diagnose all learners. We next evaluate the validity of diagnosis result. For instance, learners in the cluster "A" should have higher understanding level in all levels. It has high accuracy and short time compared with averages of all in any level. Hence, the diagnosis result of cluster "A" is valid. Learners in cluster "C" should have high or higher understanding level in Standard and Easy (Level II and I), and low in Difficult (Level III). Learners in cluster "D" should have high or higher understanding level in Easy, and low in Difficult and Standard. Learners in cluster "E" should have low understanding level in all levels. We can similarly conclude that the diagnosis results of clusters C,D, and E

In order to evaluate the accuracy of our system, we make a comparison experiment. We use a

,where *Lt*, *La* are answer time and accuracy, respectively. *U* is understanding level. This equation is also based on our prior knowledge. It is appropriate as a comparison model with

1. All 38 questions are divided into two groups so that their difficulties will be the same. One

2. Accuracy and answer time are obtained from estimation part in order to be used in

3. Accuracy and answer time are obtained from evaluation part in order to be used in

5. Precision of associative TCNN and that of linear function are considered by comparing

In case of estimation by linear funcion, *k* is changed from 0.1 to 0.9, and the best is adopted as

Table 10 shows a comparison of precision. The precision of associative TCNN is superior to that of linear function. These results represent that synthetical diagnosis of associative TCNN

*U* = *kLt* + (1 − *k*)*La* (17)

linear function according to the related work (Sumada et al., 2007) as the following:

Table 9. Diagnosis results (Accuracy:%,Time:s)

Comparison experiment is performed as the following:

is estimation part, and the other is evaluation part.

estimating understanding level.

evaluating estimation results.

the estimation result.

4. True understanding level is obtained from 3.

with true understanding level obtained in 4.

is better than partial estimation of linear function.

**6.2 Experiment results and discussion**

are valid.

ours.

**6.3 Comparison experiment**

Level - A B C D E Others All - Numbers 3 0 3 3 11 0 20 I Accuracy 85.7 - 71.4 71.4 29.9 - 50.7 (Easy) Time 60.2 - 60.1 75.8 87.3 - 77.4 II Accuracy 81.0 - 71.4 19.0 15.6 - 34.3 (Standard) Time 98.3 - 133.9 68.2 89.0 - 94.0 III Accuracy 66.7 - 26.7 6.7 5.5 - 18.0 (Difficult) Time 134.1 - 261.8 45.1 60.2 - 99.3

The early half of chapter described a new diagnosis system of learner's understanding level by using associative Binary Cellular Neural Network (BCNN). The results obtained are as follows:


BCNN has an important problem with lack of representable understanding levels. Then, the latter half of chapter described an improved diagnosis system by using associative Tri-valued Cellular Neural Network (TCNN). The results obtained are as follows:


The diagnosis by associative TCNN plays a role in rough-classification in pattern recognition. Standard associative TCNN is used in the experiment. Hence, optimized associative TCNN will probably provide better results. Our future work is to improve diagnosis performance with optimized associative TCNN.
