esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Discussion  
Fourier analysis, carried out in conjunction with the expansion of the wavefront in terms of Zernike polynomials, makes it possible to determine the statistical characteristics for each aberration corresponding to a particular polynomial. This could be useful when designing adaptive optical systems, particularly when choosing the system speed and spatial resolution of the wavefront correct actuators. For example, if the system can correct for the aberrations of the first 15 Zernike polynomials, then up to 90% of the WF distortions introduced by turbulence will be compensated. In that case, probably, it would be useful to apply the low-cost bimorph deformable mirror that can successfully reproduce the first 25 Zernike modes [23; 24]. It can also be noted that the created mathematical apparatus will make it possible to analyze the parameters of real atmospheric turbulence.  
Conceptualization, A.K., A.R.; methodology, A.K., A.R.; software, V.B., A.R.; validation, A.K., A.N., J.S.; formal analysis, A.N., A.R., V.T.; investigation, A.R., A.N., V.B.; resources, A.K.; data curation, A.R., V.T.; writing--original draft preparation, A.R.; writing--review and editing, A.N., J.S., V.T.; visualization, A.N., A.R.; supervision, A.K.; project administration, A.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the RUSSIAN SCIENCE FOUNDATION, grant number 19-19-00706.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The work is supported by the Russian Science Foundation under grant #19-19-00706.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
## 4 Case Study: AQM Implementation
### Verification and Assessment for the CNS
#### 4.3.3 The RVQA Process at the Agent Content Level of the CNS  
Figure 11 shows the agent content-sharing activities and the RVQA implementation to check the agent data confidentiality disclosure status during the execution. The agent content-sharing activities include the stage when the agent's account becomes active, contents are shared, and finally the stage when agent's account becomes inactive.  
Algorithm 3 shows the RVQA data confidentiality violations detection for the agent content level of the CNS. As defined by the checking rules for the content level [51], the agent account active state is an agent critical state, while the shared content types determine the agent's content-disclosure status. Shared content types that are \"public\" or \"private\" determine whether the shared contents are \"disclosed\" or \"protected,\" respectively.  
Figure 11: The RVQA implementation at the agent content level of the CNS.  
These verification and assessment processes are performed continuously for all levels whenever the defined critical states are reached. The numbers of detected violations, i.e., noDisclosedIdentity, noDisclosedLocation, noDisclosedSocialInformation and noDisclosedContent, are increased every time the data disclosures are detected. It is followed by keeping track of the total number of confidentiality disclosures detected to indicate the overall confidentiality disclosure level at that particular time. The total number of detected violations, noDisclosures, is calculated and reported. An increased number of detected disclosures means that the agent confidentiality violation level is high (low agent quality) and fewer detected disclosures means that the agent confidentiality violation level is low (high agent quality).
# Comparison of Machine Learning Models for Sentiment Analysis of Big Turkish Web-Based Data +
## 4 Results
When the success of the SVM model is evaluated with the confusion matrix, it is seen that the model's success in classifying positive examples is relatively high. While 50,829 (98.7%) data were correctly predicted in the positive class, 666 (1.3%) were incorrectly predicted in other classes. In neutral samples, 870 (32.6%) data were predicted in the correct class, while 3133 (67.4%) were in the wrong class, indicating a \begin{table}
\begin{tabular}{c c} \hline \hline
**Word/Phrase** & **Normalized Word/Phrase** \\ \hline güzl & güzel (beautiful) \\ begen & begen (like) \\ hizli & hzli (fast) \\ ba yl ddm & bayldldm (I loved) \\ hacimli bir urün degil & hacim vermedi (didn’t give volume) \\ basarli bir urüni diyemem & basanszürün (unsuccessful product) \\ surekli & surekli (consistently) \\ kullandim & kullandim (used it) \\ puruzsuz & purürizsuz (smooth) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Word and phrase normalization list. low success rate. Finally, 7270 (86%) negative samples were identified in the correct class, while 1182 (14%) samples were mispredicted. This shows that the SVM model does not show added success while working successfully on positive and negative classes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classifier**} & \multirow{2}{*}{**Product Group**} & \multirow{2}{*}{**Predicted**} & \multicolumn{3}{c}{**Actual**} \\ \cline{5-6}  & & & **Positive** & **Neutral** & **Negative** \\ \hline K-Nearest Neighbor & Skin Make-Up & Positive & 8541 (95.7\%) & 256 (2.9\%) & 128 (1.4\%) \\  & & Neutral & 264 (63.2\%) & 106 (25.3\%) & 48 (11.5\%) \\  & & Negative & 918 (58.3\%) & 190 (12.1\%) & 465 (29.6\%) \\  & Eye Make-Up & Positive & 12,476 (97.9\%) & 132 (1\%) & 137 (1.1\%) \\  & & Neutral & 354 (70.6\%) & 101 (20.2\%) & 46 (9.2\%) \\  & & Negative & 1449 (59.8\%) & 63 (2.6\%) & 912 (37.6\%) \\  & Lip Make-Up & Positive & 10,093 (97.8\%) & 116 (1.1\%) & 113 (1.1\%) \\  & & Neutral & 359 (75.1\%) & 69 (14.4\%) & 50 (10.5\%) \\  & & Negative & 1136 (65.1\%) & 61 (3.5\%) & 549 (31.4\%) \\  & Skin Care & Positive & 49,878 (96.9\%) & 781 (1.5\%) & 836 (1.6\%) \\  & & Neutral & 1644 (61.6\%) & 784 (29.4\%) & 241 (9\%) \\  & & Negative & 4632 (54.8\%) & 236 (2.8\%) & 3584 (42.4\%) \\ Hair Care & Positive & 20,278 (75.8\%) & 6184 (23.1\%) & 298 (1.1\%) \\  & & Neutral & 367 (29.9\%) & 769 (62.6\%) & 93 (7.5\%) \\  & & Negative & 386 (10.4\%) & 1700 (45.8\%) & 1626 (43.8\%) \\ Body Care & Positive & 26,622 (83\%) & 5180 (16\%) & 321 (1\%) \\  & & Neutral & 476 (39.6\%) & 633 (52.6\%) & 94 (7.8\%) \\  & & Negative & 418 (14.2\%) & 1368 (46.8\%) & 1140 (39\%) \\ Perfume & Positive & 4274 (98.3\%) & 30 (0.7\%) & 45 (1\%) \\  & & Neutral & 123 (82\%) & 22 (14.7\%) & 5 (3.3\%) \\  & & Negative & 588 (69.9\%) & 10 (1.2\%) & 243 (28.9\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: K-NN confusion matrix results for each product group.
# Span-Based Fine-Grained Entity-Relation Extraction via Sub-Prompts Combination
## 4 Experiments
### \(\langle S,R\rangle\) and \(\langle R,O\rangle\) Extraction Inspection  
Since our model can extract more fine-grained elements \(\langle S,R\rangle\) and \(\langle R,O\rangle\), we also observed their extraction results on the ADE dataset. The experimental results are shown in Table 6. The _Precision_ of \(\langle Effect,\)\(Adverse-Effect\rangle\) extraction reaches 85.27%, the _Recall_ reaches 86.72%, and the \(F\)1 reaches 85.99%; the _Precision_ of \(\langle Adverse-Effect,Drug\rangle\) extraction reaches 96.05%, the _Recall_ reaches 95.92%, and the \(F\)1 reaches 95.99%. By analyzing the results, we can make the following observations. Firstly, SSPC can not only complete the entity recognition task, but also achieve more fine-grained extraction by integrating entity and relation information, which is critical for subsequent tasks. Secondly, SSPC has a solid ability to capture _Drug_-type entities. However, the extraction ability of \(Effect\)-type entities is unsatisfactory. We speculate that the pre-trained model has more and better knowledge of drugs.  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{
\begin{tabular}{c} **Standard** \\ **Setting** \\ **All** \\ **Data** \\ \end{tabular} } & \multirow{2}{*}{**8**} & \multirow{2}{*}{**TACRED**} & & \multicolumn{3}{c}{**TACREV**} \\  & & & & & & **Standard** & & **Few-Shot Setting** & \\  & & & & & & **All** & & **8** & **16** & **32** & **Mean** \\ \hline ENT & \multirow{2}{*}{69.4} & \multirow{2}{*}{27.0} & \multirow{2}{*}{31.3} & \multirow{2}{*}{31.9} & \multirow{2}{*}{30.1} & \multirow{2}{*}{79.8} & \multirow{2}{*}{27.4} & \multirow{2}{*}{31.2} & \multirow{2}{*}{32.0} & \multirow{2}{*}{30.2} \\ MARKER & & & & & & & & & & \\ \hline YP & \multirow{2}{*}{71.0} & \multirow{2}{*}{28.9} & \multirow{2}{*}{32.0} & \multirow{2}{*}{32.4} & \multirow{2}{*}{31.1} & \multirow{2}{*}{80.8} & \multirow{2}{*}{27.6} & \multirow{2}{*}{31.2} & \multirow{2}{*}{32.0} & \multirow{2}{*}{30.3} \\ MARKER & & & & & & & & & \\ \hline PTR [3] & 72.4 & 28.1 & 30.7 & 32.1 & 30.3 & 81.4 & 28.7 & 31.4 & 32.4 & 30.8 \\ \hline KnowPrompt [35] & 72.4 & 32.0 & **35.4** & 36.5 & 34.6 & 82.4 & 32.1 & 33.1 & 34.7 & 33.3 \\ \hline SSPC (ours) & **72.7** & **32.7** & 34.9 & **37.0** & **34.9** & **83.1** & **32.7** & **34.2** & **37.7** & **34.9** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Our experimental results on the datasets TACRED and TACREV. \(F\)1 scores of various models with different sizes of training instances.The best results are bold.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Precision** & **Recall** & **F1** \\ \hline Full & 80.79 & 82.86 & 81.79 \\ w/o (3-2) & 68.33 & 80.18 & 73.78 \\ w/o (3-1) & 73.84 & 81.25 & 77.37 \\ w/o (3-1) and (3-2) & 60.40 & 87.79 & 71.56 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Ablations on the ADE dataset.
## 4 Results and Discussion
### Comparative Experiments of Different Models on our Own Dataset
#### 4.1.3 Comparison Experiments of Accuracy for Each Category  
To further validate the advantages of the integrated model, the accuracy of each category is compared in this section. According to the above experiments, ResNet152 and SE-ResNeXt101, which achieve the highest test accuracy in the corresponding structures, were compared. The confusion matrix is used to compare the accuracy for each category of the two models.  
Figure 8: Variations of train accuracy with epoch changes (lr = 0.01). (**a**) The number of layers is 50; (**b**) The number of layers is 101; (**c**) The number of layers is 152.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Layers** & \multicolumn{2}{c}{**50**} & \multicolumn{2}{c}{**101**} & \multicolumn{2}{c}{**152**} \\ \hline
**Model** & **ResNet [10]** & **SE-ResNeXt** & **ResNet [10]** & **SE-ResNeXt** & **ResNet [10]** & **SE-ResNeXt** \\ \hline lr = 0.01 & 0.906 & 0.935 & 0.898 & 0.935 & 0.908 & 0.921 \\ lr = 0.1 & 0.879 & 0.919 & 0.899 & 0.929 & 0.881 & 0.925 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Test accuracy of six models.  
Figure 7: Variations of train accuracy with epoch changes (lr = 0.1). (**a**) The number of layers is 50; (**b**) The number of layers is 101; (**c**) The number of layers is 152.  
Figure 9a,b are the confusion matrices of test sets for ResNet152 and SE-ResNeXt101, respectively. The values on the diagonal represent the accuracy of the model for recognizing Goral, Badger, Lynx, Red Deer, and Roe Deer. The more yellow the color of the matrix, the better the model recognizes the corresponding species.  
SE-ResNeXt101 has higher recognition accuracy for five species than ResNet152 and the maximum difference is 4.4%. For the two models, the performance of recognizing Roe Deer is worse than other categories. This is because Roe Deer resembles Red Deer, but the number of Roe Deer images is only half the number of Red Deer and the image quality is lower than that of Red Deer. When identifying Red Deer, with the help of so many high-quality images, the accuracy of SE-ResNeXt101 is much higher than that of ResNet152. The results prove that SE-ResNeXt can achieve better performance in recognition tasks on our own dataset.
## 3 Results and Discussion
### Correlations among Different Parameters
#### 3.3.2. Thyme  
Pearson's correlation coefficients (r) among the main phenolic compounds and the antioxidant capacity of the thyme extracts are given in Figure 5.  
All of the samples of _T. mastichiua_ showed a high antioxidant capacity and a high TPC; however, not all of the samples with the highest rosmarinic acid content were amongst the samples that presented the highest values of the TPC or antioxidant capacity. The results showed no significant correlation between the Total Phenol Content and antioxidant assays, and no significant correlation between those assays and individual phenolic compounds. Contrary to our results, [PERSON] et al. [29] found that rosmarinic acid influenced the DPPH radical activity, as well as the FRAP assay, when analyzing methanolic extracts of _T. mastichiua_ from Spain, indicating that rosmarinic acid is responsible for the antioxidant capacity of thyme. Moreover, [PERSON] et al. [42] also reported a highly significant correlation between the TPC and DPPH assay.  
Nevertheless, some correlations were found among the phenolic compounds. For instance, the content of luteolin was strongly correlated with the apigenin (r = 0.780, \(p\) < 0.01), since they are compounds from the same flavonoid class. Also, a strong correlation between quercetin and genistein (r = 0.708, \(p\) <0.01) was presented despite the fact that they belong to different flavonoid classes.
## 6 Performance Evaluation
### Simulation Results
#### 6.4.1 Sensor Network Density Test (First Simulated Scenario)  
In this scenario, we set the number of source communicating nodes to ten, varied the network density from 100 to 1000 nodes in step of 100 nodes, and observed the routing performance. As observed from Figure 4a-e, the success rate drops to less than 100% between 100 to 1000 nodes by SSR and SHR protocols. However, ASAART maintain a 100% success rate between 500 to 1000 nodes compared with SSR and SHR protocols. This is attributed to the fewest number of communicating source nodes. There are fewer packets that reach the destination. However, the ASAART protocol slightly outperforms both SHR and SSR in terms of successful number of delivered network packets.  
Figure 4: _Cont._Figure 4: Sensor network density test (first simulated scenario) with source node = 10: (**a**) Average packet delivery rate (success rate); (**b**) End-to-end delay; (**c**) Energy consumption; (**d**) Transmitted MAC layer packets; (**e**) Packets error rate.  
In Figure 4b, ASAART end-to-end network delays show a slight reduction compared with SSR and SHR protocols, which means better reduction in the end-to-end delay. In Figure 4c,d, we can observe that ASAART protocol shows better energy consumption and a total number of reduced MAC layer packets delivery compared with the SSR and SHR protocols. This is attributed to its enhanced route repair mechanism that tries to control flooding at the MAC layer. In Figure 4e we can observe that ASAART packet error rate (PER) is lower at higher network densities compared with the SSR and SHR protocols. Showing a zero percent of error in packet delivery between the network of sizes 500 to 1000 nodes.
# FEA for Optimizing Design and Fabrication of Frame Structure of Elevating Work Platforms
## 3 Results
### Criteria Analisys for Evaluation
#### 3.1.2 Stress and Factor of Safety (FOS)  
Analyzing the results, it must be considered that the expected design loads are already increased with coefficients imposed by the current Uni EN 280 standard.  
Analyzing the model created with Aluminum Alloy (EN-AW 1200), the Maximum Stress value of 219.8 MPa and the very low FOS value determine the inadequacy of this material for the intended use [18].  
The models simulated with Aluminum Alloy (EN-AW 2014), HSLA Steel (700), and HSLA Steel (Fe275 JR) present good strength and safety values, well within their yield strength. The high FOS indicates that the material can withstand unexpected dynamic loads or overloading conditions, a key advantage for agricultural applications.  
Aluminum Alloy (EN-AW 2014) exhibited slightly higher stress (220.9 MPa) but maintained an FOS of 1.2. Due to the lower density value of aluminum, the entire system will be lighter.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Maximum Stress** & **Maximum** & **Factor of Safety** \\  & **(N m\({}^{-2}\))** & **Deformation (mm)** & **Factor of Safety** \\ \hline Aluminium Alloy (EN-AW 1200) & 219,800,000 & 231.8 & 0.1 \\ Aluminium Alloy (EN-AW 2014) & 220,900,000 & 225.3 & 1.2 \\ High-Strength Low-Alloy Steel (Fe275 JR) & 197,400,000 & 82.5 & 1.4 \\ High-Strength Low-Alloy Steel (S700) & 179,400,000 & 79.5 & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Behavior of materials with applied loads.  
HSLA Steel (Fe275 JR) allowed FOS to increase up to 1.4, reducing the maximum stress (197.4 MPa) but increasing the structure weight, similarly to HSLA Steel (700), where the maximum stress is lower (179.4 MPa) and FOS is higher, 1.5.  
Figure 5 compares the four different materials and the simulated Stress diagrams; similarly, Figure 6 compares the FOS calculated.
## 2 Obtaining Maximum Inlet Spacing (Methods)
### Determining Inlet Spacing
#### 2.3.1 Analysis of \(z\) in Equation (5)  
Two potentially unknown parameters are in Equation (5): inlet spacing \(x\) and flow depth at the curb \(z\). The focus here is to obtain inlet spacing with its maximum allowable values, and if \(x\) poses the maximum possible inlet spacing, it is safe to assume that \(z\) also takes its maximum values. Considering over-lane flow depths stay within an acceptable range (because otherwise the design should be reconsidered), there are two scenarios for determining flow depth. Either it must be restricted by maximum spread criteria, the intruding flow into the lanes, or by maximum allowable depths at the curb. Contribution of the over-lane flow depth to the overall depth at the curb could be neglected as their orders of magnitude differ. Based on this and the uniform transverse slope assumption, potential water depth at the curb face for a uniformly sloped surface becomes:  
\[z=T_{\text{max}}S_{x} \tag{6}\]  
where \(z\) is in m or ft., \(T_{\text{max}}\) is maximum allowable flow spread in m or ft. (taken equal to \(W\) here to prevent intrusion into the lanes), and \(S_{x}\) is cross slope. Any \(z\) value calculated using Equation (6) that is equal to or less than \(z_{\text{max}}\) is valid for use in Equation (5). However, if \(z>z_{\text{max}}\), then \(z\) in Equation (5) must be replaced with \(z_{\text{max}}\) and Equation (6) should be disregarded, as in no case should the depth overtop the set criteria. Again, as long as \(z_{r}<4\) mm (Equation (1)), and \(z=T_{\text{max}}S_{x}\leq z_{\text{max}}\) (Equation (6)), inlet spacing in Equation (5) is solved using the \(z\) value in Equation (6), but if \(z=T_{\text{max}}S_{x}>z_{\text{max}}\), then Equation (5) is solved for \(z=z_{\text{max}}\). Now being left with a single unknown \(x\), Equation (5) can be solved for inlet spacing.  
Figure 2: Working from the last inlet to the first.
# An IP Multimedia Subsystem Services Proxy Gateway Based on a JAVA Dynamic Module System
## 2 Background  
### IP Multimedia Subsystem (IMS)  
The IMS Network, i.e., IP Multimedia Subsystem Network, which is the control layer of the Next Generation Network (NGN) and was formulated by the 3 GPP (3 rd Generation Partnership Project) and 3 GPP [1; 2; 3; 4], is used to access different network technologies such as Wi-Fi, LTE, 3G/3.5G and wired network and depends on SIP (Session Initiation Protocol) [18] as the communications protocol to control SIP signals by the Call Session Control Function (CSCF). The brief network architecture of IMS is shown in Figure 1.  
* P-CSCF (Proxy-CSCF): As the first IMS network server faced by one user, P-CSCF forwards a user's messages into IMS, SIP messages to I-CSCF for further processing, and any SIP signal response to a user.
* I-CSCF (Interrogating-CSCF): I-CSCF is a query server that relies on a user's SIP requests or information brought by P-CSCF to find an appropriate S-CSCF for relevant services and saves the information in Home Subscriber Server (HSS) for other queries later.
* S-CSCF (Serving-CSCF): S-CSCF is a service server which is particularly used in processing a user's service requests and depends on the requests to find a corresponding application server.
* HSS (Home Subscriber Server): HSS in IMS is particularly used in storing users' data such as e-mail, phone number and user's authority to access services.
* Application Server (AS): As a top-layer application server such as a multimedia streaming and monitoring system, AS depends on S-CSCF to give user services.
## 3 Our Model
### The Algorithm  
The algorithm adopted in the proposed model is shown in Algorithm 1, and Figure 4 shows the working flowchart of the TMV-TSK-FC model.  
Figure 4: TMV-TSK-FC structure diagram.  
Figure 3: Membership function value selecting under the joint view.  
```
Input: The training set \(\mathbf{X}_{v_{1}}=[x_{1},x_{2},\ldots,x_{N}]^{T}\), \(\mathbf{X}_{v_{2}}=[\mathbf{x}_{1}^{\prime},\mathbf{x}_{2}^{\prime},\ldots, \mathbf{x}_{N}^{\prime}]^{T}\);  The corresponding class label set \(\mathbf{T}=(t_{1},t_{2},\ldots,t_{N})^{T}\)
```  
**Step 1: Compute the values of Gaussian membership functions**  
Step 1(a): Compute the values of Gaussian membership functions for each view  
\[u=\exp(-(x_{ij}-a_{k})^{2}/2\sigma_{k}^{2})\]  
Step 1(b): Compute the maximum Gaussian membership functions for each view and the mix view  
\[\begin{split}\mu_{v_{1}}(i,j)&=\prod\limits_{r_{1} =1}^{C_{1}}u_{v_{1}-}\underset{j_{1}}{\text{max}}(x_{ij})\\ \mu_{v_{2}}(i,j)&=\prod\limits_{r_{2}=1}^{C_{1}}u_{v_ {2}-}\underset{j_{2}}{\text{max}}(x_{ij}^{\prime})\\ \mu_{v_{1}v_{2}}(i,j)&=\sqrt{\prod\limits_{r_{1}=1}^ {C_{1}}u_{v_{1}-}\underset{j_{1}}{\text{max}}(x_{ij})\cdot\prod\limits_{r_{2}=1 }^{C_{2}}u_{v_{2}-}\underset{j_{2}}{\text{max}}(x_{ij}^{\prime})}\\ \end{split}\]  
**Step2: Compute the projection matrix**  
\[\boldsymbol{\varphi}_{v_{1}v_{2}}=\left(\begin{matrix}\boldsymbol{\varphi}_{v_ {1}}(1,1)\otimes\boldsymbol{\varphi}_{v_{2}}(1,1)&\cdots&\boldsymbol{\varphi}_{v_ {1}}(1,K)\otimes\boldsymbol{\varphi}_{v_{2}}(1,K)\\ \vdots&\ddots&\vdots\\ \boldsymbol{\varphi}_{v_{1}}(D,1)\otimes\boldsymbol{\varphi}_{v_{2}}(D,1)& \cdots&\boldsymbol{\varphi}_{v_{1}}(D,K)\otimes\boldsymbol{\varphi}_{v_{ 1}}(D,K)\end{matrix}\right)_{D\times K}\]  
**Step 3: For \(i\gets 1\,to\,n\)**  
**Choose optimized membership functions to compute the following value of the premise of each fuzzy rule**  
\[\boldsymbol{W}_{ik}=\prod\limits_{j=1}^{D}\boldsymbol{\mu}_{v_{1}v_{2}}(i,j) \boldsymbol{\cdot}\boldsymbol{\varphi}_{v_{1}v_{2}}(j,k)\]  
Step 3(a): If \(\mu_{v_{1}}(i,j)\)\(>\)\(\mu_{v_{1}v_{2}}(i,j)\)\(>\)\(\mu_{v_{2}}(i,j)\), Then \(\boldsymbol{W}_{ik}=\prod\limits_{j=1}^{D}\boldsymbol{\mu}_{v_{1}}(i,j)\boldsymbol{ \cdot}\boldsymbol{\varphi}_{v_{1}v_{2}}(j,k)\)  
Step 3(b): If \(\mu_{v_{2}}(i,j)\)\(>\)\(\mu_{v_{1}v_{2}}(i,j)\)\(>\)\(\mu_{v_{1}}(i,j)\), Then \(\boldsymbol{W}_{ik}=\prod\limits_{j=1}^{D}\boldsymbol{\mu}_{v_{2}}(i,j)\boldsymbol{ \cdot}\boldsymbol{\varphi}_{v_{1}v_{2}}(j,k)\)  
Step 3(c): If \(\mu_{v_{1}}(i,j)\)\(>\)\(\mu_{v_{1}v_{2}}(i,j)\), \(\mu_{v_{2}}(i,j)\)\(>\)\(\mu_{v_{2}v_{2}}(i,j)\), Then \(\boldsymbol{W}_{ik}=\prod\limits_{j=1}^{D}\frac{\boldsymbol{\mu}_{v_{1}}(i,j) \boldsymbol{\cdot}\boldsymbol{\varphi}_{v_{1}v_{2}}}{2}\)\(\cdot\)\(\boldsymbol{\varphi}_{v_{1}v_{2