 Why is it still giving triangle as an output? It seems like the roll activation showing square and this centroid is also overlaid over square The issue you're encountering where the system identifies the input as a triangle wave despite the roll activation and centroid indicating a square wave Could be due to several reasons Centroid calculation issue the centroid appears to be correctly located within the range that should indicate a square wave as per the aggregated output fuzzy set with centroid graph However, the final classification output is a triangle wave This suggests there might be a problem with how the centroid value is being interpreted or mapped to the output classification Defuzzification process the defuzzification process translates the fuzzy values into a single crisp output There could be a bargain logical error in the defuzzification code that interprets the centroid value Output classification logic the logic that takes the centroid value and determines the output wave classification might be incorrectly implemented It's possible that the thresholds for classifying the centroid value into a square triangle or trapezoid wave are not set correctly Front-end back-end mismatch there might be a mismatch between the back-end processing and the front-end display It's essential to ensure that the front-end correctly receives and interprets the back-end's response To divide this issue Check the back-end logic verify the logic in your flask application that maps the centroid to the output classification Given the provided centroid value of 0.53 in the classification logic The output wave should indeed be classified as a triangle because 0.53 is less than two-thirds But greater than one-third the classification logic seems to be functioning as programmed according to the conditions you set up However, if the visualizations in your understanding of the system indicate that the waveform should be classified as a square rather than a triangle Then you may need to adjust your classification thresholds based on the centroid value The current thresholds might not be correctly aligned with the characteristics of the waveforms you're analyzing Here are some steps you can take Re-evaluate thresholds reconsider the centroid thresholds for classifying waveforms It might be that the boundary is a too strict or too lenient You might need to analyze a variety of waveforms and see where the centroid is usually lied to adjust these thresholds better Waveform feature analysis analyze the features of your waveforms, especially the symmetry and sharpness values that contribute to the centroid calculation The features that lead to the centroid being calculated as 0.53 for a square wave might need to be investigated to ensure they're being calculated correctly Visualizations use the visualizations to confirm the centroid calculation is consistent with the rule activations If the rule activation clearly shows a higher activation for the square rule yet the centroid is in the triangle range You might want to adjust how the centroid is calculated or reconsider the definition of your membership functions Adjust membership functions if the square waveform consistently results in a centroid indicative of a triangle It may be necessary to adjust the membership functions themselves so that the centroid calculation more accurately reflects the activation levels Testing and calibration test with various known waveforms and calibrate your system accordingly By doing so, you'll be able to refine the thresholds of the centroid values to ensure that the output classifications are accurate Refine fuzzy logic system, consider the possibility that your fuzzy logic system may need more fine tuning The membership functions, rules or even the method for aggregating the rules might need to be adjusted to better reflect the characteristics of the inward waveforms After making adjustments, test the system again with the same square waveform and check if the centroid value and the classification are now aligned with the expected outcome If the system still classifies the waveform incorrectly, continue to iterate on the fuzzy logic parameters and thresholds until the system performs as intended Re-evaluate thresholds, reconsider the centroid thresholds for classifying waveforms It might be that the boundary is a too strict or too lenient You might need to analyze a variety of waveforms and see where the centroid usually lie to adjust these thresholds better Waveform feature analysis, analyze the features of your waveforms, especially the symmetry and sharpness values that contribute to the centroid calculation The features that lead to the centroid being calculated as 0.53 for a square wave might need to be investigated to ensure they're being calculated correctly Instead of hard thresholds, consider using fuzzy thresholds This means instead of having a single cutoff value, you will have a range where the classification could be one type or another The centroid value being calculated as 0.53 suggests that, according to the fuzzy sets and rules defined, the inward waveform has a high membership in the category associated with a triangle waveform rather than a square waveform Here are some steps to analyze and potentially correct this issue Ensure that the calculations for symmetry and sharpness are correctly implemented For a square wave, you would expect high sharpness due to the sharp transitions and relatively high symmetry Verify that the functions calculate underscore symmetry underscore array and calculate underscore peak underscore sharpness underscore array in your python code accurately reflect the properties of a square wave Look at how the membership functions are defined in the SK fuzzy library within your python code The parameters that define low, mid and high membership for both symmetry and sharpness should correctly map to the expected values for square, triangle and trapezoid waves Check the fuzzy rules that determine the activation levels for the different waveform types It could be that the rules are not well tuned for the characteristics of a square wave or that the combination of rules is leading to an unexpected centroid value Ensure that the rules are capturing the essence of what it means for a waveform to be considered square or triangle in the context of your application Review membership functions Look at how the membership functions are defined in the SK fuzzy library within your python code The parameters that define low, mid and high membership for both symmetry and sharpness should correctly map to the expected values for square, triangle and trapezoid waves Analyze fuzzy rules Check the fuzzy rules that determine the activation levels for the different waveform types It could be that the rules are not well tuned for the characteristics of a square wave or that the combination of rules is leading to an unexpected centroid value Ensure that the rules are capturing the essence of what it means for a waveform to be considered square or triangle in the context of your application Adjust fuzzy logic parameters If the square wave is consistently producing a centroid value that indicates a triangle, you may need to adjust the parameters of your membership functions or the rules to better differentiate between these waveform types It could be helpful to perform sensitivity analysis on your fuzzy system to understand how different input values affect the centroid calculation Visualization and debugging Use visualizations to examine the activation of each fuzzy set given the input features This will help you understand why the system is leaning towards a triangle classification Plot the membership functions for symmetry and sharpness together with the values calculated from your square wave input to see where the system is attributing the highest membership Consider noise effects If noise is present in your input signal, consider how it affects the feature calculations Noise could potentially skew the symmetry and sharpness calculations leading to an incorrect centroid value Test with a variety of inputs Test the system with a variety of square waves, different amplitudes, frequencies and noise levels, and see if the issue persists across different instances Use these tests to refine the membership functions and rules By analyzing these aspects, you can begin to understand why the system is not classifying the square wave correctly and make informed adjustments to improve accuracy Based on the screenshots and the code snippets you've provided, here's a list of what is currently being plotted as the output of the fuzzy logic system Input waveform, a graph showing the input waveform over time, which includes any noise that had been added to a signal Detection error and unknown percentage over time, a graph showing the percentage of detection error and the percentage of unknown classification over multiple iterations or time Aggregated output fuzzy set was centroid, a graph displaying the aggregated membership function values for all the rules and the calculated centroid, which is used for defuzzification and determining the final output Rule activation, a graph that illustrates the activation levels for each rule, square, triangle, and trapezoid, based on the input signal's features Symmetry and sharpness membership functions, plots that show the individual membership functions for the symmetry and sharpness of the input signal This will help to understand how each input is being fuzzified Symmetry and sharpness activation levels, graphs displaying the calculated symmetry and sharpness values for the input signal and all these values activate below, mid, and high membership functions This is crucial for diagnosing why certain rules are being activated more than others Fuzzy inference graph, a step-by-step visualization of the fuzzy inference process, showing how the input values map through the membership functions and rules to produce the aggregated output Temporal rule activation, if the system is running over time or through iterations, a graph showing how rule activations changed over these periods could be insightful, especially if the input signal changes or evolves Noise analysis, if noise significantly affects the system's performance, a plot showing the noise profile or the signal to noise ratio could be beneficial Defuzzification detail, a more detailed plot showing the defuzzification process, possibly including other defuzzification candidates, e.g., bisector, mean of maximum, for comparison Comparison of input and classified waveform, a side-by-side comparison or overlay of the input waveform and what the system believes the classified waveform should look like based on the fuzzy logic decision This can help identify mismatches or classification errors Rule weights, if there are weights or other parameters that adjust the influence of certain rules, visualizing these could help understand their impact on the decision-making process Fuzzy sets overlap, a plot showing the overlap between different fuzzy sets can be useful to see if there is too much or too little overlap between categories, which might affect classification Certainly, let's correct the based on the information from the code snippets you've shared Your fuzzy logic system currently visualizes the following six charts Symmetry membership functions, shows the membership functions for symmetry, low, mid, high, and their activation levels Sharpness membership functions, shows the membership functions for sharpness, low, mid, high, and their activation levels To enhance the diagnostic capabilities of the system and get a full picture of the fuzzy logic decision-making process, consider adding the following visualizations Symmetry and sharpness actual values, even though you have the membership function activations, plotting the actual calculated symmetry and sharpness values over the duration of the waveform can help you see where the signal lies in relation to the fuzzy sets Temporal activation of rules, if your data is temporal or sequential, showing how the rule activations chained over time could provide insights into the system's performance across different segments of the signal Detailed defuzzification process visualization, a close look at the defuzzification process, showing how the final output value is derived from the centroid of the aggregated fuzzy set Comparison of input and classified waveform, overlaying the input waveform with the expected output waveform based on the classification can highlight discrepancies Interrule relationships, if your rules are not independent, visualizing the interaction or the combined effect of multiple rules can be informative Fuzzy set overlap analysis, a visual analysis of how much the fuzzy sets overlap may provide insights into whether the sets are too broad or too narrow, which could affect classification accuracy To incorporate the additional visualizations into your existing system, you will need to adjust your Python back end code and JavaScript front end code Here's a guide on how to proceed with each of the suggested visualizations Overlay symmetry and sharpness actual values Back end, ensure the actual symmetry and sharpness values are being sent to the front end in the JSON response Front end, modify the existing plotly graphs for symmetry and sharpness to include a new trace representing the actual values calculated from the input waveform Back end, include detailed data for the defuzzification process in the JSON response, such as the values of the aggregated fuzzy set at the points where the centroid is calculated Front end, create a new plotly graph or add to the existing aggregated output fuzzy set graph to show these details Back end, along with the input waveform data, send the expected waveform shape based on the final classification For example, if the input is classified as a square wave, generate a square wave based on the input's properties, like period and amplitude Front end, add a new trace to the input waveform graph that plots this expected classified waveform shape This will allow for a direct visual comparison between the input waveform and the system's final classification Adjustments require a thorough understanding of your existing code and how the data flows between the back end and front end For any new data points you wish to send to the front end, like the actual symmetry and sharpness values or the expected waveform shape You need to ensure that the back end is calculating these values correctly and including them in the response object returned by your flask roots For the comparison visualization, your back end should calculate the expected waveform based on the classification Then, in the front end, you'd plot it alongside the input waveform Here's an example of how you might adjust the back end to send the actual symmetry values Then, you would adjust the front end code to plot these values, as shown in the JavaScript example above For the comparison of the input and classified waveform, you'd need symmetry and sharpness actual values Even though you have the membership function activations, plotting the actual calculated symmetry and sharpness values over the duration of the waveform can help you see where the signal lies in relation to the fuzzy sets Temporal activation of rules, if your data is temporal or sequential, showing how the rule activations chained over time could provide insights into the system's performance across different segments of the signal Detailed defuzzification process visualization, a close look at the defuzzification process, showing how the final output value is derived from the centroid of the aggregated fuzzy set Comparison of input and classified waveform, overlaying the input waveform with the expected output waveform based on the classification can highlight discrepancies Interrule relationships, if your rules are not independent, visualizing the interaction or the combined effect of multiple rules can be informative Fuzzy set overlap analysis, a visual analysis of how much the fuzzy sets overlap may provide insights into whether the sets are too broad or too narrow, which could affect classification accuracy Centroid trace, show how the centroid value changes with different inputs to understand its sensitivity and robustness These additional visualizations can help to diagnose specific issues in the fuzzy logic process, such as why certain waveforms may be misclassified By understanding these aspects, you can adjust your fuzzy logic system for better accuracy Certainly, to overlay the actual symmetry and sharpness values for the current wave on top of their respective membership function graphs, you will need to modify both the back end to send these values in the front end to plot them First, ensure that your back end is sending the actual symmetry and sharpness values for the current wave These values should be calculated at the same points as the membership functions On the front end, you will use the received actual values to plot them on the existing graphs The following example is for symmetry, and you will do something similar for sharpness Please note that the functions calculate underscore symmetry underscore value and calculate underscore sharpness underscore value would need to be implemented in your Python code to calculate the actual single value representations of symmetry and sharpness These would not be arrays, but single values representing the overall symmetry and sharpness of the entire waveform Hash a simplified example to calculate a single symmetry value for the entire waveform Yes, you can modify the calculate underscore symmetry underscore array function to calculate a single symmetry value that represents the overall symmetry of the entire waveform One approach could be to average the symmetry across all points of the signal to get a single value Here's how you might adapt the existing function This function will return a single symmetry value that is the average of the symmetry at each point in the signal This value can then be used as a representative measure of the waveform's overall symmetry Front end, receive this single value and plot it as a vertical line on your symmetry membership function graph, as previously described The centroid of a fuzzy set resulting from the aggregation of multiple fuzzy rules should naturally fall within the range of the universe of discourse used for those rules The universe of discourse is the range over which your membership functions are defined, which typically would be between 0 and 1 for normalized fuzzy logic systems Properly define membership functions, ensure that all membership functions are defined over the range, 0, 1 This includes setting the correct parameters for the membership functions such that they start at 0 and end at 1 Correctly aggregate rule outputs, when combining the outputs of various rules to get the aggregated fuzzy set, make sure the aggregation process does not produce values outside the, 0, 1, range Using standard fuzzy operators like fmax for OR and fmin for and should ensure that the aggregated output remains within this range Use the correct universe of discourse for defuzzification, when performing the defuzzification, ensure that the universe of discourse who passed the defuzzification function matches the range over which the aggregated fuzzy set is defined For example, if you are using the fuzz, defuzz function, the x parameter should be an array representing the universe of discourse, typically nb, linspace, 0, 1, num underscore points Normalization, if there is any risk that the operations could lead to a centroid calculation outside the, 0, 1, range, you can normalize the centroid value However, this should not be necessary if the above steps are correctly implemented If you follow these guidelines, your centroid should always fall within the, 0, 1, range If you find that it does not, it's a sign that there is a mistake somewhere in the process that needs to be identified and corrected To ensure that the centroid resulting from your fuzzy logic system dynamically covers the full range from 0 to 1 and is not just centered around 0.5, you may need to adjust your fuzzy logic rules, membership functions, or even the inputs themselves Here are some steps to consider Revisit membership functions Ensure that your membership functions are spread out across the entire range of, 0, 1 If they are too concentrated in the middle, the centroid will likely be around 0.5 Adjust the parameters of the membership functions to either broaden them or shift them towards the extremes The issue of the system not outputting, trapezoid, as the classification, even though, trapezoid, is selected as the input wave, could be due to several factors related to the fuzzy logic processing Rule activation visualization The rule activation chart seems to show significant activation for both the triangle and trapezoid rules, but the triangle rule appears to have a slightly higher peak If the fuzzy system uses the maximum activation rule to determine the output, this could be why triangle is being selected over trapezoid Rule activation visualization The rule activation chart seems to show significant activation for both the triangle and trapezoid rules, but the triangle rule appears to have a slightly higher peak If the fuzzy system uses the maximum activation rule to determine the output, this could be why triangle is being selected over trapezoid From your description, if the rule activation graph shows mainly trapezoid rule activation with minimal triangle rule activation, but the system still outputs triangle, it suggests there may be an issue with how the defuzzification process is being carried out or interpreted Confirm that the centroid is being calculated correctly The centroid should be a weighted average of the aggregated fuzzy set, and it should reflect the predominant activation If the trapezoid rule is the one primarily activated, the centroid should be closer to the area with the highest trapezoid activation Double check the defuzzification code to ensure it's not incorrectly interpreting the centroid location, or there isn't an error in the centroid calculation Aggregated output Ensure that the aggregated fuzzy set is correctly combining the individual rule activations The aggregation should accurately reflect the predominance of the trapezoid rule Review the logic that maps the centroid to the final output classification Ensure that the centroid thresholds or decision boundaries are set correctly according to the intended design of the system Assess if the membership functions and the rules are set up correctly The system should output trapezoid if that rule is the most activated There might be a need to adjust the shapes or the ranges of the membership functions to ensure they represent the intended logic Verify that the rule activation graph is accurately representing the activation levels Sometimes visualization scales or axis limits can be misleading Ensure that the scales and the presentation accurately reflect the rule activations Confirm that there is no mismatch between the back end processing and the front end display Ensure that the data sent from the back end is correctly received and interpreted by the front end To ensure the output classification correctly reflects the rule activation for a fuzzy logic system You must set appropriate thresholds based on the centroid value If the centroid value is expected to be between 0 and 1 and the activation for the trapezoid rule is predominant The code should correctly reflect that However, without changing the thresholds, if the activations are mainly for trapezoid, that the centroid calculation results in triangle It might suggest that the centroid is not being calculated correctly or the activation functions are not correctly defined If you're confident that the centroid calculation is correct and you want to adjust the thresholds to reflect a different distribution of the output, you might consider something like this If you find that trapezoid should have a wider range and triangle should be less likely, you can adjust the threshold underscore square and threshold underscore triangle values accordingly For example, if you want trapezoid to be the output more often, you can move the threshold underscore triangle down These changes should only be made after careful consideration and analysis of how the centroid relates to the rule activations It's also important to validate these changes with various test cases to ensure that they correctly classify the different waveform types under different conditions Deciding on the proper threshold values for classifying the output based on the centroid in a fuzzy logic system involves understanding the characteristics of the data, the behavior of the system, and potentially some trial and error Here are some steps to guide you in setting these thresholds Consult with domain experts to understand the typical characteristics of each classification category, square, triangle, trapezoid Experts might provide insights into what a typical centroid value should be for each type of waveform Statistical analysis Analyze a dataset of labeled waveforms where the correct classification is known Calculate the centroid for each waveform and observe the distribution of centroid values for each category Statistical measures like mean, median, and standard deviation can inform threshold setting Visual inspection Plot the centroid values against the known classifications and visually inspect where the natural divisions occur This can often reveal clear cut-off points Sensitivity analysis Perform a sensitivity analysis by varying the threshold values and observing the effect on the classification accuracy Look for values that maximize the correct classification rate Machine learning techniques Use machine learning algorithms to find the optimal threshold values For example, you can treat it as an optimization problem where the goal is to maximize classification performance Cross-validation Implement cross-validation by dividing your dataset into training and testing sets Use the training set to determine the thresholds and validate them on the testing set to ensure they generalize well Error metrics Use error metrics such as confusion matrices, precision, recall, F1 score to evaluate the performance of different thresholds Choose thresholds that lead to the best balance of these metrics according to your systems requirements Rule refinement Adjust your fuzzy rules if needed If the centroids for certain classifications are consistently off, it might indicate that the rules or membership functions need tweaking Iterative process Use an iterative approach where you start with initial threshold values based on your best understanding, then refine them based on the results of your analysis and system performance User feedback If possible, incorporate user feedback into the threshold setting process Users familiar with the system's domain can often provide valuable input on whether the classifications make sense Setting these thresholds is not always a straightforward process, and it might require several iterations to get it right Be prepared to adjust your approach based on the system's performance and any new insights you gain as you collect more data and feedback Using machine learning algorithms to optimize threshold values for classification in a fuzzy logic system can be an effective approach Here's a simplified workflow for using machine learning to find the optimal threshold values Data preparation Collect a dataset where each instance has the calculated centroid and the correct classification, square, triangle, trapezoid Ensure the dataset is large and diverse enough to represent the range of scenarios the fuzzy logic system will encounter Feature selection Use the centroid as the primary feature for classification If you have other relevant features that influence the classification, include them as well Label encoding Encode the classifications, square, triangle, trapezoid, trapezoid, trapezoid, trapezoid Encode the classifications, square, triangle, trapezoid, as numerical labels if they're not already in numerical form Choose a machine learning model