esa-sceva/satcom-chunk-collection huggingface dataset:
# A Target Detection Method of Distributed Passive Radar without Direct-Path Signal
## 3 GLRT Detection Algorithm
### Detection Algorithm
Similarly, let \(l_{0}(s)=\log p_{0}(s)\) represent the log-likelihood function under \(H_{0}\), GLRT can be written as  
\[\underset{\{\gamma,\mathbf{u}\}}{\text{max}}l_{1}(\gamma,\mathbf{u}|s)-l_{0} (s)\underset{H_{0}}{\gtrless}\xi, \tag{8}\]  
where \(\xi\) is the threshold, ignoring the additive constant, which \(l_{1}(\gamma,\mathbf{u}|s)\) can be written as  
\[l_{1}(\gamma,\mathbf{u}|s)=-\frac{1}{\sigma^{2}}\sum_{j=1}^{N_{t}}\left\|s_{j} -\gamma_{j}\Big{(}D_{j}\otimes\mathbf{a}_{j}\Big{)}\mathbf{u}\right\|^{2}. \tag{9}\]According to Equation (7), the maximum likelihood estimate (MLE) of \(\gamma\) is  
\[\hat{\gamma}=\frac{\left(\left(D_{j}\otimes\mathbf{a}_{j}\right)\mathbf{u} \right)^{H}\!\!s_{j}}{\left\|\left(D_{j}\otimes\mathbf{a}_{j}\right)\mathbf{u} \right\|^{2}}, \tag{10}\]  
where \(\left[\cdot\right]^{H}\) is the Hermitian transpose of \(\left[\cdot\right]\), Equation (10) can be simplified to  
\[\hat{\gamma}=\frac{\left(\left(D_{j}\otimes\mathbf{a}_{j}\right)\mathbf{u} \right)^{H}\!\!s_{j}}{\left\|\left(D_{j}\otimes\mathbf{a}_{j}\right)\mathbf{u} \right\|^{2}}, \tag{11}\]  
where \(\left\|\mathbf{u}\right\|^{2}=L\), \(\widetilde{s}_{sj}=\left(D_{j}\right)^{H}\!\!s_{j}\), \(s_{j}\) is the echo signal received by the \(j\)th receiver, \(\widetilde{s}_{sj}\) is the signal after removing the delay and Doppler shift, substitute \(\gamma\) into Equation (6) can be obtained  
\[l_{1}(\hat{\gamma},\mathbf{u}|s)=-\frac{1}{\sigma^{2}}\left(\left\|s\right\|^ {2}-\frac{\left(\mathbf{u}\right)^{H}\!\!\Phi(\Phi)^{H}\mathbf{u}}{\left\| \mathbf{u}\right\|^{2}}\right), \tag{12}\]  
where \(\Phi=[\widetilde{s}_{s1},\cdots,\widetilde{s}_{sNr}]\in\mathbb{C}^{ML\ast N_{ r}}\), let \(\lambda_{1}(\cdot)\) denote the maximum eigenvalue of the matrix and let \(\mathbf{v}_{1}(\cdot)\) denotes its associated eigenvector, then the maximization of Equation (10) is equivalent to maximizing the Rayleigh quotient, and when \(\lambda_{1}(\Phi\Phi^{H})\) taking and its associated eigenvector \(\mathbf{u}=\mathbf{v}_{1}\!\left(\Phi\Phi^{H}\right)\), the Rayleigh quotient reaches its maximum value so \(\overset{\boldsymbol{\wedge}}{\mathbf{u}}=\mathbf{v}_{1}(\Phi\Phi^{H})\)[25], so \(l_{1}(\hat{\gamma},\overset{\boldsymbol{\wedge}}{\mathbf{u}}|s)\) can be written as  
\[H_{1}:s_{j} =\gamma_{j}\Big{(}D_{j}\otimes\mathbf{a}_{j}\Big{)}\mathbf{u}+ \mathbf{n}_{j} \tag{5}\]0  
where \(P=\Phi\Phi^{H}\!\lambda_{1}(\Phi\Phi^{H})=\lambda_{1}(\Phi^{H}\Phi)\!\!,\!N_{ r}\ll L\), and for more efficient calculations, Equation (13) can be simplified to  
\[H_{1}:s_{j} =\gamma_{j}\Big{(}D_{j}\otimes\mathbf{a}_{j}\Big{)}\mathbf{u}+ \mathbf{n}_{j} \tag{5}\]1  
Similarly, under \(H_{0}\) conditions
## 3 QZS Analysis  
QZS isolators perform excellently in the field of low-frequency vibration isolation, thus warranting research into their construction and distribution. Using a stiffness analysis, this section describes in detail the main parameters that directly influence QZS and the four linear spring configuration schemes used to build QZS systems.
## 2 Materials and Methods
### Implemented Gestures  
The gestures used in the study were selected with an intention for intuitive control of a contactless interface that can be used by any member of the public. The following list of 12 gestures was compiled for the study, all illustrated in Figure 3: (G1) arm to left--full swipe of an arm from right to left, (G2) arm to right--full swipe of an arm from left to right, (G3) hand away--taking a hand away from radar, (G4) hand closer--taking a hand closer to the radar, (G5) arm up--an arm movement from bottom to top, (G6) arm down--an arm movement from top to bottom, (G7) palm up--rotating a palm upwards, (G8) palm down--rotating a palm downwards, (G9) hand to the left--a hand movement to the left (without an arm movement), (G10) hand to the right--a hand movement to the right, (G11) closing a fist horizontally, (G12) closing a fist vertically. All gestures are simple to perform, easily explainable to subjects without prior training, and can intuitively be assigned to different actions of the interface.  
Four subjects were involved in collection of the data samples: three females and one male. Overall, 4600 samples were collected, with the detailed distribution between subjects shown in Table 2.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Antenna configuration & 2 TX, 4 RX \\ Azimuth resolution & 15 \\ Range resolution & 0.039 m \\ Radial velocity resolution & 0.13 m/s \\ Frame duration & 33 ms \\ Range detection threshold: 30 dB & 30 dB \\ Doppler detection threshold: 30 dB & 30 dB \\ \hline \hline RX—receiver, TX—transmitter. \\ \end{tabular}
\end{table}
Table 1: AWR1642 parameters.  
Figure 3: Gestures: (**G1**) arm to left, (**G2**) arm to right, (**G3**) hand away, (**G4**) hand closer, (**G5**) arm up, (**G6**) arm down, (**G7**) palm up, (**G8**) palm down—rotating palm down, (**G9**) hand to the left, (**G10**) hand to the right, (**G11**) closing a fist horizontally, (**G12**) closing a fist vertically.
## 4 Experiments Analysis and Discussion
### Impact of Different Weight \(\alpha,\beta\)  
In TSNN, the weighted average strategy is adopted to fuse the long-term and short-term prediction results, so as to achieve the goal of bias mitigating. The forecasting result outputs from the two long-term models with encoder-only and encoder-decoder architecture are treated as having equal importance. Figure 5 displays the performance of different combinations of long-term weight \(\alpha\) and short-term weight \(\beta\). Specifically, we fixed the input sequence time step to 96 and the prediction step to 96. At the same time, we respectively discussed the prediction effect of the weight ratio of 1:5 to 5:1 in the fields  
Figure 3: Performance of long-term bias mitigating.  
of energy, finance, and weather (i.e., ECL, Exchange, and Weather datasets). If the weight \(\alpha\) for long-term predictions is set too large, it may fail to serve its intended purpose of bias correction. Conversely, it may be ineffective in capturing long-standing relationships when short-term weights are set too large. As recommended, the best performance on the Exchange dataset is achieved when the ratio of a to b is 2:1, that is, a = 0.67 and b = 0.33. In the ECL and Weather datasets, the ratio is set to 1:1, that is, the best effect is obtained when a = 0.5 and b = 0.5.
## 3 Results and Discussion
### Crystalline Structure Assessment  
The crystallinity and molecular arrangement of a polymer can significantly impact the rate of water penetration, influencing its subsequent erosion or degradation and, ultimately, the drug release profile. To assess the crystal structure of the synthesized copolyesters, XRD analysis was conducted, following melt crystallization, similar to the second scan in DSC analysis (using quenched samples). As shown in Figure 5, the results confirm the semi-crystalline nature of all materials, as indicated by the shape of the peaks and curves. A small number of distinct crystal diffraction peaks were observed across all samples. For neat PLA, the strongest diffraction peak was recorded at 20 = 17\({}^{\circ}\), with two additional peaks at 15.3\({}^{\circ}\) and 19.25\({}^{\circ}\). The PLA-sorbitol sample exhibited peaks at 20 = 15.45\({}^{\circ}\), 17\({}^{\circ}\), and 19.35\({}^{\circ}\), while the PLA-glycerol sample displayed peaks at 20 = 15.75\({}^{\circ}\), 17.45\({}^{\circ}\), and 19.75\({}^{\circ}\). Similarly, the PLA-pentaerythnitol sample showed peaks at 20 = 16.2\({}^{\circ}\), 17.9\({}^{\circ}\), and 20.25\({}^{\circ}\). These findings highlight the preserved semi-crystalline structure across all copolyesters, with slight variations in diffraction patterns depending on the branching agent used. As a result, the peaks are slightly shifted toward higher 20 values, indicating differences in the crystal structure among the various materials compared to previously reported XRD data for PLA [54; 55]. In this study, the limited number of diffraction peaks observed at specific 20 positions, along with the fact that crystallization occurred at relatively low temperatures (88-101 \({}^{\circ}\)C), suggests the presence of the \(\alpha^{\prime}\) crystal form in both the linear PLA and the'star-like' PLA copolyesters [54; 55]. The dominance of the \(\alpha^{\prime}\) crystal form, which is less ordered and more flexible than the \(\alpha\) form, may facilitate water absorption and accelerate polymer degradation, potentially leading to faster drug dissolution. Consequently, the increased branching and the associated decrease in crystallinity--evidenced by the broadening or shifting of XRD peaks--indicate a more amorphous-like behavior within the polymer matrix, which is expected to enhance the drug release rate [56].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **T\({}_{\text{m}}\) (\({}^{\circ}\)C)** & **T\({}_{\text{g}}\) (\({}^{\circ}\)C)** & **T\({}_{\text{c}}\) (\({}^{\circ}\)C)** \\ \hline PLA neat & 175.9 & 57 & 116 \\ PLA glycerol & 161.4 & 50 & 123 \\ PLA sorbitol & 160.1 & 52 & 127 \\ PLA pentaerythnitol & 150 & 51 & 118 \\ \hline \hline \end{tabular}
\end{table}
Table 2: List of values for melting temperatures: T\({}_{\text{m}}\), glass transition temperatures, T\({}_{\text{g}}\), melt/hot crystallization temperatures, T\({}_{\text{c}}\), of the samples under investigation, recorded by conventional DSC.  
Figure 5: XRD patterns of the prepared neat PLA and its copolymers.
## 2 Cold-Sky Calibration Simulator
### Effect of Antenna Thermal Distortion  
In order to improve the fidelity of the simulation for cold-sky calibration design, a parameter that can depict the effect of the space environment, especially the thermal conditions, should be introduced into the procedure of the cold-sky calibration strategy. The beta angle (\(\beta\)), which is the angle between the solar vector and the orbital plane, is usually used to perform thermal analysis and design. Thereby, it can be used as the parameter that depicts the thermal environment variation around the orbit. The worst thermal environments happen at higher beta angles when the sun is more fully incident on the feed horn, and the mutation of the thermal environment happens at the red dot area, as shown in Figure 6. The thermal analysis results of the radiometer antenna can be obtained from the material properties of the antenna and the thermal model, which is traditionally modeled by the beta angle [16]. The spaceborne radiometer antenna's gain is affected by the variation in the physical temperature, whose effect on cold-sky calibration can be very large. When the temperatures of the antennas change periodically as the satellite flies, geometrical errors of the antennas are generated periodically. The red dots in Figure 6 show both the inflection point of the beta angle curve and the moment when the eclipse seasons begin and end, where the temperature changes extensively, and the worst-case thermal stability [16]. By being combined with the thermal expansion coefficient of the antenna material and antenna temperatures, the antenna deformation can be quantitatively established, and the relationship between the beta angle and the gain variation of the antenna can be modeled as a look-up table before launch. In-orbit antenna pattern verification is based on the flat target response of the cold-sky scene during external observation [1]. The antenna pattern errors due to thermal distortion will reduce the effect of flat target transformations. Therefore, the space environment of the satellite operating on should be paid attention to when choosing opportunities for cold-sky calibration. The beta angle can be used as a parameter depicting the space environment's impact.  
Figure 6: The beta angle of the SMAP satellite is shown for one year with the eclipse duration.
## 4 Q1 Synth Networks for Group Performance  
This section introduces the setup developed for a performance entitled _Spinnings_, with three Q1 Synth units. A MIDI gesture controller is used to rotate the qubit with hand movements.  
Three Q1 Synth instruments are networked in a star topology with an additional machine acting as a hub (Figure 7). As each player rotates the spheres, the instruments produce their respective sounds, which are mixed and relayed to the speakers (Figure 7c). The hub tracks the state vectors of each instrument and simulates a combined three-qubit quantum state dynamically (Figure 7b).  
The hub is programmed to recognise the thumbs-up gesture as a command for measurement (Figure 7b). When a player makes a thumbs-up, the hub stops tracking the instruments and builds a quantum circuit expressing the current status of the simulated state vector. Then, it sends the circuit to the quantum computer for measuring (Figure 7d,e).  
The measurement, which in this case will be three digits long (\([c_{2},c_{1},c_{0}]\)), is relayed back to the hub. The hub informs each instrument of its respective outcome and synthesises the'measurement sound'. This sound lasts for the period it takes for the vectors (i.e., red dots) to move to the north or sound poles of the respective instruments. It is programmed to take five seconds by default, but this is customisable. As soon as the sound ends, the players gain back control of the spheres and another cycle commences.  
Figure 6: A screenshot of the Q1 Synth in ‘Advanced’ mode. In contrast to the ‘Simple’ mode, in ‘Advanced’ mode the system provides options to adjust the range of the synthesis parameters.  
Even though each player has control over their own sound as they rotate the sphere, the measurement sound will be surprising: it depends on the measurement of the combined quantum state.  
_Spinnings_ was premiered on 8 November 2022. The concert took place at the Goethe-Institut in London, during a _Living in a Quantum State_ event [17] to launch the book _Quantum Computer Music_, edited by [PERSON]. [5]. The event was organised with Meth Quantum [18].  
The instruments and the hub were projected on a cinema screen, which enabled the audience to follow the actions of the performers (Figure 8). A live recording of the performance is available [19].  
Figure 8: Premiere of _Spinnings_ at the Goethe-Institut, starring [PERSON]. (on the **left**), [PERSON] (in the **middle**), and [PERSON]. (on the **right**).  
Figure 7: Three networked Q1 Synth instruments for the performance _Spinnings_. Three Q1 Synth units (**a**) are networked in a star topology with an additional machine (**b**) acting as a hub. The hub builds a quantum circuit expressing the current status of the simulated state vector (**c**) and sends the circuit to the quantum computer (**d**) for measuring. The hub informs each instrument of its respective outcome and synthesises the ‘measurement sound’ (**e**).
###### Abstract  
Waste management is becoming one of the most challenging tasks for developing countries in order to ensure good human health, as well as a healthy environment. Rajshahi City Corporation (RCC) is one of the 12 city corporations in Bangladesh. Various environmental and human health problems have arisen due to a lack of proper knowledge of waste management. Thus, the aim of this work is to illustrate the present status of MSW generation and management in Rajshahi City Corporation, Bangladesh. Fifty households were selected throughout RCC for waste collection, which represent approximately all types of households in RCC. From the qualitative and quantitative analysis, it is estimated that the approximate MSW generation in RCC is 358.19 t/d (tons/day) at an approximate rate of 0.4214 kg/person/d. Calorific values of the wastes have also been determined using the ultimate analysis results of the MSW. A higher calorific value of the dry MSW has been calculated as 14.9 MJ/kg. Moisture content of the MSW has been found to be 48.28%. It is also estimated that the possible power generation (steam energy to electrical power) from MSW generated in RCC is 159.40 MWh/d. Lastly, future scopes of MSW management and different waste management measures that need to be taken are illustrated. Waste-to-energy (WTE) conversion has been given priority and anaerobic digestion (AD) has been found to be an interesting prospect in this sector. Techno-economic analysis of the AD has been conducted. Energy potential from the proposed plant has been calculated as 3.85 MW and the payback period has been found to be 4.9 years. It has been observed that employing AD on a large scale can not only reduce the waste, but also meet a large portion of the energy demand of this city.  
municipal solid waste; waste management; waste-to-energy; sustainable environment; energy harvesting +
Footnote †: journal: Applied Sciences
# Progress in THz Rectifier Technology: Research and Perspectives
### THz Diode Technology: I-V Characteristics and Figures of Merit (FOM) for MIM Diode
#### 2.2.2 Transmission Probability D  
If an insulator layer is less than 3 nm thick, an electron may tunnel through it and appear almost instantly on the other side. This condition, indicated as transmission probability \(D\), is given by Equation (3) [7; 23; 27; 28; 29]:  
\[D=e^{\left(-2d\sqrt{\frac{2m(V-E)}{H^{2}}}\right)} \tag{3}\]  
where \(V\) is the barrier height, \(E\) is the energy of electron, and \(d\) is the thickness of the insulator.  
The probability of an electron to pass through the insulator bandgap depends on \(V\) and \(d\); in fact, as \(d\) and \(V\) increase, \(D\) decreases.
## 3 Results and Discussion
### Crude Oil Tankers
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Engine Load**} & \multicolumn{2}{c}{**Strain Gauge**} & \multicolumn{2}{c}{**Optical**} \\  & & **(Speed Trial/Model Test)** & \multicolumn{2}{c}{**(Speed Trial/Model Test)**} \\ \cline{3-5}  & & **Thrust** & **Torque** & **Thrust** & **Torque** \\ \hline \multirow{4}{*}{65\%} & 1 st & 99.4\% & 98.4\% & 104.6\% & 94.0\% \\  & 2 nd & 101.0\% & 99.3\% & 106.3\% & 95.1\% \\ \cline{2-5}  & Avg. & 100.2\% & 98.9\% & 105.5\% & 94.6\% \\ \hline \multirow{4}{*}{75\%} & 1 st & 99.5\% & 98.3\% & 104.8\% & 94.0\% \\  & 2 nd & 101.1\% & 99.7\% & 106.6\% & 95.0\% \\ \cline{2-5}  & Avg. & 100.3\% & 99.0\% & 105.7\% & 94.5\% \\ \hline \multirow{4}{*}{75\%} & 3 rd & 100.2\% & 99.2\% & 105.9\% & 94.3\% \\  & 4 th & 98.0\% & 97.7\% & 104.1\% & 92.8\% \\ \cline{2-5}  & Avg. & 99.1\% & 98.5\% & 105.0\% & 93.6\% \\ \hline \multirow{4}{*}{90\%} & 1 st & 101.3\% & 99.4\% & 105.9\% & 95.0\% \\  & 2 nd & 97.1\% & 96.3\% & 102.5\% & 92.2\% \\ \cline{2-5}  & Avg. & 99.2\% & 97.9\% & 104.2\% & 93.6\% \\ \hline \multirow{4}{*}{100\%} & 1 st & 104.0\% & 102.2\% & 102.2\% & 104.1\% \\  & 2 nd & 99.2\% & 98.3\% & 98.1\% & 100.4\% \\ \cline{2-5}  & Avg. & 101.6\% & 100.3\% & 100.2\% & 102.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Difference ratio between speed trial measurement and prediction results based on model test of the first vessel. Figure 7: Comparison of thrust and torque between speed trials and prediction results based on model test of the first vessel.
## 4 Synthesis and Characterizations of Ball Milled Variants
### Synthesis of Non-Magnetic Metallic Nanocomposites  
[PERSON] et al. [88] fabricated Al/CNT nanocomposite using a planetary ball milling followed by sintering. The dispersion of CNT in Al and the mechanical behavior and hardness of the composite nanostructures were evaluated. Milling was carried out at 100 and 150 rpm rotating speed for 5 and 15 min with a 10:1 ball to powder ratio using zirconia balls. The milled composite was then subjected to calcination at 500 \({}^{\circ}\)C for 5 h and was cooled at room temperature. CNT was well-dispersed homogenously into the Al surface and resulted in enhanced mechanical strength and hardness. As inevitably demonstrated in Figure 9, the mechanical hardness increased at least 40-60 HV values for the Al/CNT nanocomposite ball milled when compared to un-milled or milled Al samples.  
[PERSON] and co-workers [89, 90] aimed to investigate the effect on the properties of ball milling ZrO\({}_{2}\) nanomaterial in the Cu matrix. Cu and ZrO\({}_{2}\) powders were ball milled at a rotating speed of 250 rpm and were cold-welded and calcined at 950 \({}^{\circ}\)C for 2 h. The microhardness increased up to 288%, the compressive strength increased with the decrease in crystalline size, and the electrical conductivity decreased with higher ZrO\({}_{2}\) contents.  
[PERSON] et al. [91] embedded Cu particles onto Al\({}_{2}\)O\({}_{3}\) nanocomposite using a planetary ball mill. Process controlling agent was added to avoid agglomeration during the milling process. Uniform dispersion of Cu over Al\({}_{2}\)O\({}_{3}\) was obtained with higher fracture strength. These studies show that the nanocomposites between materials that have very different chemical and physical identity can be successfully synthesized using ball milling technique.
# Hybrid Fuzzy Regression Analysis Using the \(F\)-Transform
## 3 Fuzzy Regression Based on the \(F\)-Transform and Discriminant Analysis
In the fuzzy regression model, if the number of spreads of a given dependent variable is small due to iterations, it converts the dependent variable to a categorical variable. To do this, we use the \(F\)-transform. In this paper, we propose  
* Estimate the left spread of the dependent variable using F-transform and [PERSON]'s linear discriminant analysis. * Define the universe of discourse \(S^{l}\): \(S_{l_{Y}}=\{s_{l_{Y_{i}}}:i=1,2,...n\}\) is the set of spreads of dependent variable. Let \(s_{l_{Y_{i}(1)}}\) and \(s_{l_{Y_{i}(n)}}\) be the minimum and the maximum value of \(S_{l_{Y}}\). Then the universe of discourse \(S^{l}\) is defined by \(S^{l}=[max\{0,s_{l_{Y_{i}(1)}}-c_{1}\},s_{l_{Y_{i}(n)}}+c_{2}\ ]\), where \(c_{1}\) and \(c_{2}\) are two proper positive real numbers. The values \(c_{1}\) and \(c_{2}\) are predefined by researcher or can be considered to be the tuning parameters. * Define the basic function on \(S^{l}\) and obtain F-transform: The \(F\)-transform \(F_{k}[S_{l_{Y}}]=[F^{l}_{1},F^{l}_{2},\cdots,F^{l}_{k}]\) is obtained by \[F^{l}_{j}=\frac{\sum_{i=1}^{n}s_{l_{Y_{i}}}A_{j}(s_{l_{Y_{i}}})}{\sum_{i=1}^{ n}A_{j}(s_{l_{Y_{i}}})},\ \ \ \ j=1,\cdots,k,\] (2) where the function \(A_{j}(x)\) is the basic function on the universe \(S^{l}\). * Classify the given data by using the [PERSON]'s linear discriminant analysis: Each of the data is grouped q times which is the number of overlapped basic functions of corresponding data. In Figure 1, the number of overlapped basic functions \(q=2\) in (a,b) and \(q=3\) in (c). If \(s_{l_{Y_{i}}}\) is included in the support of \(A_{j}\) then \(s_{l_{Y_{i}}}\) is assigned to group \(g_{j}\). Since the basic functions are overlapped, \(s_{l_{Y_{i}}}\) can be assigned to more than one group. Using the assigned group and independent variables, we construct the [PERSON]'s linear discriminant function and predict the assigned group based on the discriminant score. The predicted group is represented by \(\hat{g_{j}}\), \(j=1,2,\cdots,q\). * Predict the left spread of dependent variable using the inverse F-transform: Using the F-transform obtained by the previous step 2-2 and the inverse F-transform, the spread \(s_{l_{Y_{i}}}\) is predicted. Let \(F_{k}[S_{l_{Y}}]=[F^{l}_{1},F^{l}_{2},\cdots,F^{l}_{k}]\) be the F-transform of the left spread with respect to \(A_{1}(x),\cdots,A_{k}(x)\). Then the predicted left spread is given by \[\hat{s}_{l_{Y_{i}}}=\frac{\sum_{j=1}^{k}F^{*}_{j}A_{j}(s_{l_{Y_{i}}})}{\sum_{j =1}^{k}A_{j}(s_{l_{Y_{i}}})},\ \ \ \ i=1,\cdots,n,\] (3) where \(F^{*}_{j}\) represents the F-transform corresponding to the predicted group \(\hat{g_{j}}\). * Predict the right spread \(s_{r_{Y_{i}}}\) by the step 2. By this hybrid algorithm, we predict the values of dependent variable. Our overall method is summarized in Algorithm 1. Figure 1: Examples of basic functions. (**a**) Triangular function, (**b**) sinusoidal function, (**c**) trapezoidal function.