Naturaleza cognitiva de la percepción visual

The dataset used in this section is collected from all the identified sources for creating the qualitative taxonomy as described in Chapter 5. The data consist of the final composite scores given originally by the six used composite indicators: the ITU-IDI, WB-KEI, WEF-GCI, INS-GII, WEF-NRI and IMD-WCY for 51 economies for three years periods 2009, 2010 and 2011. These final scores values were used to predict each of the used indicators in a multi-fold or permutation order.

To train the presented model, the dataset were separated into two parts: train- ing set (51 economies final scores for 2009 and 2010) and testing set (51 economies final scores for 2011). To allow ANFIS to learn all probable states, so the inference system could generate high predictability rules input, it is suggested to shuffle the data in a random order so the datasets would have a good mix. ANFIS training is an iterative process, which calculates and minimises the sum of the squared differences between predictions and training instances. For the analysis, MAT- LAB fuzzy toolbox is employed. Using the collected data as input/output data set, Fuzzy Inference Systems (FIS) are constructed where membership function parameters are automatically tuned using either a backpropagation algorithm alone or in combination with a least squares type of method. This Hybrid ad- justment allows the proposed fuzzy system to learn from the data and propose the rules to guide the proposed model and hence the desired aggregated and pre- dicted output. Many trials were carried to achieve the most accurate prediction results. Parameters of the Knowledge Based Prediction (KBP) model are setup as follows: For the membership function, the Gaussian-bell shaped were used. To train the FIS, the hybrid learning algorithm were used and the sub clustering partition were utilised in order to generate the FIS method. Given separate sets of input and output data, the sub clustering function were modified to generate the FIS using FCM clustering. The function achieves this by attaining a set of

6. Unified Macro-Knowledge Competitiveness Framework

Figure 6.12: The inner-structure of IMD-WCY fuzzy sub-model.

rules that models the data behaviour. The rule attaining method first uses the FCM function to establish the number of rules and membership functions for the antecedents and consequents.

Figure6.12, shows the details for the IMD-WCY fuzzy sub-model to illustrate the inputs data behaviour and the inner structure for one of these generated fuzzy inference systems, which is capable of predicting the IMD-WCY scores from the other indices using the ANFIS generated rules.

Sample of these rules which was created to give the decision for the IMD-WCY predicted scores are listed below.

Rule 1. If (IDI is cluster1) and (KEI is cluster1) and (GCI is cluster1) and (GII is cluster1) and (NRI is cluster1) then (IMD-WCY is cluster1)

Rule 2. If (IDI is cluster2) and (KEI is cluster2) and (GCI is cluster2) and (GII is cluster2) and (NRI is cluster2) then (IMD-WCY is cluster2)

Rule 3. If (IDI is cluster3) and (KEI is cluster3) and (GCI is cluster3) and (GII is cluster3) and (NRI is cluster3) then (IMD-WCY is cluster3)

.. .. .. ..

Rule 26. If (IDI is cluster26) and (KEI is cluster26) and (GCI is cluster26) and (GII is cluster26) and (NRI is cluster26) then (IMD-WCY is cluster26).

The full IMD-WCY fuzzy rule sub-model is presented in Figure 6.13 which depicts how the above rules are applied in order to generate a certain predicted IMD-WCY score.

6. Unified Macro-Knowledge Competitiveness Framework

Figure 6.13: Fuzzy rules to construct the predicted IMD-WCY scores.

bine the knowledge and competitiveness indices into a new single meaningful index using the fuzzy clustering model which reflects the rate of knowledge com- petitiveness and progress in a nation; each sub-model represents a non-linear expression presented in a fuzzy rule-based format of the following form:

In= f

X Ii



, i = [1, 2, 3, 4, 5, 6], i 6= n (6.4) where In is the predicted value for an index based on other indices Ii i =

[1, 2, 3, 4, 5, 6], i 6= n. These Sub-models are trained to minimise the total er- ror. Root Mean Square (RMS) error is used to measure the error of prediction for each index. The goal is to minimise the total error as indicated below:

RM SE =r P e

2

IDI+ e2KEI + e2GCI + e2GII + e2N RI+ e2W CY

6. Unified Macro-Knowledge Competitiveness Framework

Table 6.9: UKCI overall predicted errors.

Predicted Knowledge Indicators

Input Predicted RMSE IDI, KEI, GII, NRI, WCY GCI 0.168 KEI, GCI, GII, NRI, WCY IDI 0.191 IDI, GCI, GII, NRI, WCY KEI 0.201 IDI, KEI, GCI, NRI, WCY GII 0.397 IDI, KEI, GCI, GII, WCY NRI 0.368 IDI, KEI, GCI, NRI, GII WCY 0.311

Predicted UKCI Root Mean Sq. Error

IDI, KEI, GCI, GII, NRI, WCY UKCI 0.2725

where eIDI, eKEI, eGCI, eGII, eN RI, and eW CY are the average prediction error for

each fuzzy sub-model. Using ANFIS for the six sub-models, where sub-clustering technique is used to generate the initial rules.

6.4.1.6 ANFIS Predictions and Validation Results

The aggregated error is first summed up for the final output using the RMSE measure. Table 6.9 summarizes the average errors obtained by the model and the overall error is calculated using expression 6.5. Therefore by aggregating the indices the new model would predict an aggregated value which will form the proposed UKCI with a margin of combined error = 0.2725. The overall fit is good for all indices, but the best fit is achieved for the WEF-GCI score with an average error of 0.168 as shown in Figure 6.14(a). The second best result was achieved for predicting the ITU-IDI score as Figure6.14(b) shows. The third best result was achieved for the WB-KEI as Figure6.14(c) shows. The worst predicted value by the model is presented in Figure Figure 6.15(a) for the INS-GII with an average error of 0.397. This is due to the nature of formation as it depends on “soft variables” to form its final score and its innovation focused. Figure 6.15(b) and (c) show the plot for the predicted scores for the WEF-NRI and IMD-WCY respectively.

6. Unified Macro-Knowledge Competitiveness Framework

(a) GCI

(b) IDI

(c) KEI

Figure 6.14: Predicted vs. 2011 real scores. (a) WEF-GCI , (b) ITU-IDI, (c) WB-KEI.

6. Unified Macro-Knowledge Competitiveness Framework

(a) GII

(b) NRI

(c) WCY

Figure 6.15: Predicted vs. 2011 real scores. (a) INS-GII, (b) WEF-NRI, (c) IMD-WCY.

6. Unified Macro-Knowledge Competitiveness Framework

Figure 6.16: Schematic diagram of the UKCI fuzzy inference model.