Data estimator determination method and device based on fuzzy self-adaption

Abstract

The invention provides a data estimator determination method and device based on fuzzy self-adaption, and relates to the technical field of data processing, and the method comprises the steps: obtaining an uncertain data set comprising a plurality of data observation values; calculating a mutual distance value between every two data observation values, and superposing the mutual distance values to obtain a mutual distance sum value; in combination with the mutual distance value and the mutual distance sum value, introducing an index coefficient greater than 1 to calculate the fuzzy membership degree of each data observation value relative to the uncertain data set estimator representing the trend of the data observation value; and determining an uncertain data set estimator, namely a data estimator, through a weighted median algorithm and an HL estimator algorithm according to the fuzzy membership degree. According to the method, the influence of abnormal values and data pollution on the estimator can be effectively reduced, the robustness of the estimator is improved, the real trend of the data can be accurately reflected, and particularly, the robustness and the accuracy are relatively high when the method faces uncertain or noise data.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and apparatus for determining data estimates based on fuzzy adaptive methods. Background Technology

[0002] Data estimators are used to estimate the value of a statistic (such as a location parameter). They are inferred from sample data, and common examples include the mean, variance, and median. For data with uncertainty or noise, traditional estimators (such as the mean) may be affected by outliers or isolated points, thus requiring more robust estimation methods.

[0003] Data estimators are central to statistical inference, helping us deduce population characteristics from sample data. However, in practice, data often contains noise or outliers, and these uncertainties can affect the accuracy of estimators. Without robust estimators, conclusions drawn from such disturbed data may deviate from reality. Therefore, determining an appropriate estimator is crucial; it provides more accurate results, especially when dealing with data containing outliers or noise, thereby enhancing the reliability of the analysis and the effectiveness of decision-making.

[0004] However, existing technologies mainly rely on traditional estimation methods such as the mean or median in determining data estimates. These methods are highly sensitive to outliers and data contamination, resulting in significant biases in data estimates when faced with uncertain or noisy data. They lack sufficient robustness and cannot accurately reflect the true trend of the data. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this invention is to provide a data estimation method based on fuzzy adaptive estimation, which can solve the technical problem that the existing technology mainly relies on traditional estimation methods such as mean or median in the process of determining data estimation. These methods are highly sensitive to outliers and data contamination, resulting in large deviations in data estimation when facing uncertain or noisy data, lacking sufficient robustness, and failing to accurately reflect the true trend of the data.

[0006] A first aspect of this invention provides a method for determining data estimates based on fuzzy adaptive methods, comprising: S1: Obtain an uncertain dataset that includes multiple data observations; S2: Calculate the mutual distance between every two data observations, wherein the mutual distance values ​​are summed to obtain a sum of mutual distances; S3: Combining the mutual distance value and the sum of mutual distances, an exponential coefficient greater than 1 is introduced to calculate the fuzzy membership degree of each of the data observations relative to the uncertain dataset estimator representing the trend of the data observations; S4: Based on the fuzzy membership degree, determine the estimator of the uncertain dataset, i.e., the data estimator, through the weighted median algorithm and the HL estimator algorithm.

[0007] A second aspect of the present invention provides a data estimation device based on fuzzy adaptive estimation: The acquisition module is used to acquire uncertain datasets that include multiple data observations; The first calculation module is used to calculate the mutual distance value between every two data observations, wherein the mutual distance values ​​are superimposed to obtain a mutual distance sum value; The second calculation module is used to combine the mutual distance value and the sum of mutual distance values, and introduce an exponential coefficient greater than 1 to calculate the fuzzy membership degree of each of the data observations relative to the uncertain dataset estimator representing the trend of the data observations. The determination module is used to determine the estimate of the uncertain dataset, i.e., the data estimate, based on the fuzzy membership degree, using the weighted median algorithm and the HL estimator algorithm.

[0008] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: In this embodiment of the invention, the mutual distances between data observations are calculated and summed to obtain a sum of mutual distances. An exponential coefficient is then used to introduce fuzzy membership, thereby quantifying the contribution of each data observation to the final data estimate. Outliers, being far from other observations, have lower fuzzy membership and thus contribute less to the final estimate, effectively suppressing the influence of outliers. Then, the final data estimate is determined using a weighted median algorithm and a Hodges-Lehmann (HL) estimator algorithm. In the weighted median, observations with higher fuzzy membership have a greater weight, while outliers or noisy observations have a smaller weight, thus avoiding their influence on the final estimate. The Hodges-Lehmann (HL) estimator further enhances the robustness of the estimate by calculating the median between data pairs, ensuring that the central trend of the data can be estimated stably even with noise or outliers. This method effectively reduces the impact of outliers and data contamination on the estimate, improves the robustness of the estimate, and accurately reflects the true trend of the data, especially exhibiting strong robustness and accuracy when facing uncertain or noisy data. Attached Figure Description

[0009] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0010] Figure 1 This is a flowchart illustrating a data estimation method based on fuzzy adaptive estimation provided in an embodiment of the present invention. Figure 2 This is a comparison chart of the proportion of collapse points of data estimates obtained by different methods under different sample sizes, provided by an embodiment of the present invention. Figure 3 This is a graph showing the variation of data estimates obtained by different methods with outliers when the sample size is 100, provided by an embodiment of the present invention. Figure 4 This is a graph showing the variation of estimators obtained by different methods with outliers when the sample size is 110, provided by an embodiment of the present invention. Figure 5 This is a graph showing the variation of data estimates obtained by different methods with outliers when the sample size is 120, provided by an embodiment of the present invention. Figure 6 This is a graph showing the variation of data estimates obtained by different methods with outliers when the sample size is 130, provided by an embodiment of the present invention. Figure 7 This is a graph showing the variation of data estimates obtained by different methods with outliers when the sample size is 140, provided by an embodiment of the present invention. Figure 8 This is a graph showing the variation of data estimates obtained by different methods with outliers when the sample size is 150, provided by an embodiment of the present invention. Figure 9 This is a schematic diagram of a data estimation device based on fuzzy adaptive estimation provided in an embodiment of the present invention. Detailed Implementation

[0011] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. It should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0012] The data estimation method based on fuzzy adaptive estimation provided by the present invention will be described in detail below with reference to the accompanying drawings, through specific embodiments and application scenarios.

[0013] Reference manual attached Figure 1 The diagram shows a flowchart of a data estimation method based on fuzzy adaptive estimation provided by an embodiment of the present invention.

[0014] This invention provides a method for determining data estimates based on fuzzy adaptive methods, which may include the following steps: S1: Obtain an uncertain dataset that includes multiple data observations.

[0015] In this context, data observations are specific numerical values ​​collected from actual or experimental data, with each observation representing a sample or data point. An uncertain dataset refers to a dataset containing data observations, which may include inaccurate, missing, noisy, or outlier data. The acquired uncertain dataset contains multiple data observations that may be affected by measurement errors, noise, or outliers, and are therefore not entirely reliable. The purpose of this step is to collect and prepare this data so that subsequent steps can process and estimate it using appropriate methods, ensuring that the final estimate remains accurate and robust even with data uncertainty.

[0016] S2: Calculate the distance between any two data observations.

[0017] The sum of the mutual distances is obtained by summing the individual distance values.

[0018] The mutual distance value refers to the degree of difference between two data observations in the dataset. The sum of mutual distances is the sum of the mutual distance values ​​between all data observations. The sum of mutual distances is obtained by calculating the mutual distance between each pair of data observations and summing these distances.

[0019] In one possible implementation, the mutual distance value is calculated as follows: .

[0020] in, Indicates the mutual distance value. and They represent the first i The and the first j One data observation, , .

[0021] The specific method for calculating the sum of mutual distances is as follows: .

[0022] in, Represents the distance and value between each other. n This represents the total number of data observations.

[0023] It should be noted that calculating and summing the distances between every two data observations provides a foundation for subsequent fuzzy membership calculations. This method quantifies the differences between data observations, allowing the weight of each observation to be adjusted based on these differences, effectively reducing the impact of outliers on the final result and enhancing the robustness of the estimator. This calculation method can better handle data containing noise or outliers, improving the accuracy of the estimator.

[0024] S3: Combining the mutual distance values ​​and the sum of mutual distances, an exponential coefficient greater than 1 is introduced to calculate the fuzzy membership degree of each data observation relative to the uncertain dataset estimator representing the trend of the data observation values.

[0025] Fuzzy membership is a measure of the contribution of each data observation to the final estimator. It is derived by calculating the distances between observations and combining the sum of these distances with an exponential coefficient greater than 1. A higher fuzzy membership indicates a greater contribution of that observation to the estimator. This process quantifies the similarity of a data observation to other observations and adjusts the influence of each data point based on its relative position. Outliers or points far from other observations have lower fuzzy memberships, thus reducing their impact on the estimator. Introducing an exponential coefficient greater than 1 enhances the suppression effect of observations far from other data points on the estimator, significantly reducing the influence of distant observations on the final result. This effectively reduces the interference of outliers on the estimator, ensuring its robustness and accuracy.

[0026] In one possible implementation, the fuzzy membership degree is calculated as follows: .

[0027] in, Indicates the first i The fuzzy membership degree of a data observation relative to a data statistic This represents an exponential coefficient greater than 1. This indicates the avoidance of local minima where the denominator is zero.

[0028] It should be noted that by calculating fuzzy membership degrees, the contribution of each observation to the estimator is quantified, which can effectively identify and reduce the interference of outliers or abnormal data. Since fuzzy membership degrees are adjusted based on the relative distance between data observations, the influence of outliers on the estimation results can be effectively suppressed, while observations that truly reflect the data trend receive greater weight. This improves the robustness and accuracy of the estimator, especially when the data contains noise or uncertainty, ensuring a more robust estimation.

[0029] S4: Based on the fuzzy membership degree, determine the estimator of the uncertain dataset, i.e., the data estimator, through the weighted median algorithm and the HL estimator algorithm.

[0030] The weighted median algorithm is an extension of median calculation, considering the weight of each observation when calculating the median. In this algorithm, observations with higher weights have a greater impact on the final median calculation, while observations with lower weights have a smaller impact. The weights are set based on fuzzy membership, so the contribution of each observation to the final estimator is dynamic. The Hodges-Lehmann (HL) estimator is a robust estimation method for estimating location parameters. It estimates the median or central location of a dataset by calculating the median of all pairs of observations. Because it is based on the median among data pairs, it is insensitive to extreme values ​​(outliers) and has strong robustness against interference. The data estimator refers to the final result calculated by combining the weighted median and the HL estimator, aiming to reflect the true central location or trend of the dataset.

[0031] In one possible implementation, the statistics for the uncertain dataset are calculated as follows: .

[0032] in, This represents statistics for an uncertain dataset. This indicates the weighted median operation. Indicates the first j The fuzzy membership degree of a data observation relative to a data statistic.

[0033] Specifically, suppose there is an observation set For all possible pairs of observations Calculate the midpoint Therefore, two subscripts are needed. i and j To enumerate combinations, for example ,for i and j For different size relationships, the calculation method for statistics in uncertain datasets is consistent and stable. These different size relationships specifically include... , and . When the diagonal and duplicates are removed, only unique unordered pairs are counted, such as... wait; At that time, it includes self-pairing, including Add the original observation points; When, including all combinations, that is, including There is redundancy, but it is symmetrical. i , j It only represents the index of the observed samples, used to enumerate all possible pairwise combinations. It does not express the order. The case-based approach is to control whether the combinations contain duplicates, self-pairing, or self-symmetry. The purpose of the three cases is to express the robustness of the method to the estimator results under various conditions.

[0034] It's important to note that combining the weighted median algorithm and the HL estimator algorithm allows the final data estimate to adjust for the influence of each observation based on fuzzy membership, enhancing the robustness of the estimate. The weighted median ensures suppression of outliers, while the HL estimator further reduces the impact of noise by calculating the median of data pairs. This combination enables the method to provide more accurate and robust results when dealing with uncertain data, ensuring that the final estimate reflects the true trend of the data.

[0035] Reference manual attached Figure 2 This diagram illustrates a comparison of the proportion of collapse points in data estimates obtained through various methods under different sample sizes, as provided in an embodiment of the present invention. It should be noted that the Mean value is a commonly used anti-contamination estimator, primarily reflecting the central tendency of the data by calculating the arithmetic mean. However, from... Figure 2 It can be seen that the collapse rate of the Mean estimator is relatively low, stabilizing at only around 0.17, exhibiting weak anti-contamination performance. This is because the Mean estimator is highly sensitive to outliers and easily affected by extreme data, causing the results to deviate from the true center. When the data distribution is asymmetrical or contains significant noise, the stability and robustness of the Mean estimator are poor, making it difficult to provide reliable estimation results. Experiments show that the data estimator determination method in this scheme... Figure 2The (AF-GCKP) collapse rate consistently remained above 0.35 and showed almost no fluctuation with increasing sample size. This indicates that this data estimator method maintains stable robustness in the face of outliers or data contamination, effectively solving the problem of traditional Mean estimators being susceptible to outlier interference. Furthermore, this data estimator method accurately reflects the central tendency of the data even without weights, improving the stability and reliability of the estimation results. In summary, the Mean estimator and this data estimator method show significant differences in collapse rate performance. The Mean estimator has the lowest collapse rate and poor stability, failing to provide robust results under severe data contamination. In contrast, this data estimator method has a significantly higher collapse rate, remaining stable across the entire sample size range, demonstrating superior anti-contamination performance. This indicates that this method better handles outliers and noise in the data, providing more robust and reliable estimation results, and is suitable for practical applications with high requirements for data stability and anti-interference performance.

[0036] Reference manual attached Figure 3 The figure shows the variation of data estimates obtained by various methods with outliers when the sample size is 100, according to an embodiment of the present invention.

[0037] Reference manual attached Figure 4 The figure shows the variation of the estimator obtained by various methods with outlier values ​​when the sample size is 110, according to an embodiment of the present invention.

[0038] Reference manual attached Figure 5 The figure shows the variation of data estimates obtained by various methods with outliers when the sample size is 120, according to an embodiment of the present invention.

[0039] Reference manual attached Figure 6 The figure shows the variation of data estimates obtained by various methods with outliers when the sample size is 130, according to an embodiment of the present invention.

[0040] Reference manual attached Figure 7 The figure shows the variation of data estimates obtained by various methods with outliers when the sample size is 140, according to an embodiment of the present invention.

[0041] Reference manual attached Figure 8 The figure shows the variation of data estimates obtained by various methods with outliers when the sample size is 150, according to an embodiment of the present invention.

[0042] Depend on Figures 2 to 8It can be seen that, with the sample size changing from 100 to 150, the shift ratio of each estimator increases with the number of outliers. The results show that the Mean estimator exhibits a rapid increase in the shift ratio as the number of collapse points increases, especially showing a significant shift even with only a small number of outliers, with a shift ratio approaching 0.2. This indicates that it is extremely sensitive to outliers, has poor robustness, and is difficult to provide stable and reliable results in contaminated data. The data estimator determination method in this scheme includes (…). , and In all three scenarios, this method demonstrates a clear advantage. The offset ratio increases slowly with the number of outliers, and the overall offset ratio is significantly lower than that of the Mean estimator, exhibiting strong stability and robustness. Furthermore, the offset ratio curve of this data estimator determination method remains almost consistent with increasing sample size, further proving its anti-contamination performance under different sample sizes. In conclusion, this data estimator determination method significantly outperforms the Mean estimator in dealing with outliers and data contamination.

[0043] Furthermore, the proposed method for determining the data estimator demonstrates superior performance when handling data containing outliers. First, by introducing a fuzzy weighting mechanism, it accurately captures the central tendency of the data even without weights, avoiding the vulnerability of the Mean estimator to outliers. Second, it exhibits strong robustness to outliers, with a stable and slow-growing offset ratio, effectively suppressing the impact of abnormal data on the estimation results. Moreover, the scheme demonstrates highly consistent stability regardless of sample size variations, indicating that its performance is not significantly affected by sample size and is suitable for various data scenarios. In summary, this method excels in robustness, stability, and accuracy, making it an ideal estimator for handling data contamination issues.

[0044] In practical applications, the uncertain dataset is first acquired, and the distances between data observations are calculated to obtain the distance sums, laying the foundation for the calculation of fuzzy membership degrees. Fuzzy membership degrees quantify the contribution of each observation to the final estimator by introducing an exponential coefficient, reducing the impact of outliers and abnormal data. Then, the weighted median algorithm and the Hodges-Lehmann (HL) estimator algorithm are combined to finally determine the data estimator. This method effectively enhances the robustness of the estimator by dynamically adjusting the weights of the observations, providing more accurate and robust results when facing noise and outliers, accurately reflecting the true trend of the data.

[0045] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: In this embodiment of the invention, the mutual distances between data observations are calculated and summed to obtain a sum of mutual distances. An exponential coefficient is then used to introduce fuzzy membership, thereby quantifying the contribution of each data observation to the final data estimate. Outliers, being far from other observations, have lower fuzzy membership and thus contribute less to the final estimate, effectively suppressing the influence of outliers. Then, the final data estimate is determined using a weighted median algorithm and a Hodges-Lehmann (HL) estimator algorithm. In the weighted median, observations with higher fuzzy membership have a greater weight, while outliers or noisy observations have a smaller weight, thus avoiding their influence on the final estimate. The Hodges-Lehmann (HL) estimator further enhances the robustness of the estimate by calculating the median between data pairs, ensuring that the central trend of the data can be estimated stably even with noise or outliers. This method effectively reduces the impact of outliers and data contamination on the estimate, improves the robustness of the estimate, and accurately reflects the true trend of the data, especially exhibiting strong robustness and accuracy when facing uncertain or noisy data.

[0046] The data estimation method based on fuzzy adaptive estimation provided in this application can be executed by a data estimation device based on fuzzy adaptive estimation. This application uses the execution of the data estimation method based on fuzzy adaptive estimation by a data estimation device based on fuzzy adaptive estimation as an example to illustrate the data estimation device based on fuzzy adaptive estimation provided in this application.

[0047] Reference manual attached Figure 9 The diagram shows a schematic of a data estimation device based on fuzzy adaptive estimation provided in an embodiment of the present invention.

[0048] This invention provides a data estimation device 20 based on fuzzy adaptive estimation, comprising: The acquisition module 201 is used to acquire an uncertain dataset that includes multiple data observations.

[0049] The first calculation module 202 is used to calculate the mutual distance between every two data observations, wherein the mutual distance values ​​are superimposed to obtain the mutual distance sum value.

[0050] The second calculation module 203 is used to combine the mutual distance value and the sum of mutual distance values, and introduce an exponential coefficient greater than 1 to calculate the fuzzy membership degree of each data observation relative to the uncertain dataset estimator representing the trend of the data observation value.

[0051] The determination module 204 is used to determine the estimator of the uncertain dataset, i.e. the data estimator, based on the fuzzy membership degree, through the weighted median algorithm and the HL estimator algorithm.

[0052] In one possible implementation, the mutual distance value is calculated as follows: .

[0053] in, Indicates the mutual distance value. and They represent the first i The and the first j One data observation, , .

[0054] The specific method for calculating the sum of mutual distances is as follows: .

[0055] in, Represents the distance and value between each other. n This represents the total number of data observations.

[0056] In one possible implementation, the fuzzy membership degree is calculated as follows: .

[0057] in, Indicates the first i The fuzzy membership degree of a data observation relative to a data statistic This represents an exponential coefficient greater than 1. This indicates the avoidance of local minima where the denominator is zero.

[0058] In one possible implementation, the minimum value is specifically: .

[0059] In one possible implementation, the statistics for the uncertain dataset are calculated as follows: .

[0060] in, This represents statistics for an uncertain dataset. This indicates the weighted median operation. Indicates the first j The fuzzy membership degree of a data observation relative to a data statistic.

[0061] The fuzzy adaptive data estimation device 20 provided by the present invention can implement the steps of the above-mentioned fuzzy adaptive data estimation method and achieve the same technical effect. To avoid repetition, the present invention will not elaborate further.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining data estimators based on fuzzy adaptive estimation, characterized in that, include: S1: Obtain an uncertain dataset that includes multiple data observations; S2: Calculate the mutual distance between every two data observations, wherein the mutual distance values ​​are summed to obtain a sum of mutual distances; S3: Combining the mutual distance value and the sum of mutual distances, an exponential coefficient greater than 1 is introduced to calculate the fuzzy membership degree of each of the data observations relative to the uncertain dataset estimator representing the trend of the data observations; S4: Based on the fuzzy membership degree, determine the estimator of the uncertain dataset, i.e., the data estimator, through the weighted median algorithm and the HL estimator algorithm.

2. The data estimator determination method based on fuzzy adaptive estimation according to claim 1, characterized in that, The calculation method for the mutual distance value is as follows: ； in, Indicates the mutual distance value. and They represent the first i The and the first j One data observation, , ; The specific method for calculating the sum of the mutual distances is as follows: ； in, Represents the distance and value between each other. n This represents the total number of data observations.

3. The data estimator determination method based on fuzzy adaptive estimation according to claim 2, characterized in that, The specific method for calculating the fuzzy membership degree is as follows: ； in, Indicates the first i The fuzzy membership degree of a data observation relative to a data statistic This represents an exponential coefficient greater than 1. This indicates the avoidance of local minima where the denominator is zero.

4. The data estimator determination method based on fuzzy adaptive method according to claim 3, characterized in that, The minimum value is specifically... .

5. The data estimator determination method based on fuzzy adaptive method according to claim 3, characterized in that, The specific method for calculating the statistics of the uncertain dataset is as follows: ； in, To represent statistics for an uncertain dataset, This indicates the weighted median operation. Indicates the first j The fuzzy membership degree of a data observation relative to a data statistic.

6. A data estimator determination device based on fuzzy adaptive estimation, characterized in that, include: The acquisition module is used to acquire uncertain datasets that include multiple data observations; The first calculation module is used to calculate the mutual distance value between every two data observations, wherein the mutual distance values ​​are superimposed to obtain a mutual distance sum value; The second calculation module is used to combine the mutual distance value and the sum of mutual distance values, and introduce an exponential coefficient greater than 1 to calculate the fuzzy membership degree of each of the data observations relative to the uncertain dataset estimator representing the trend of the data observations. The determination module is used to determine the estimate of the uncertain dataset, i.e., the data estimate, based on the fuzzy membership degree, using the weighted median algorithm and the HL estimator algorithm.

7. The data estimation device based on fuzzy adaptive estimation according to claim 6, characterized in that, The calculation method for the mutual distance value is as follows: ； in, Indicates the mutual distance value. and They represent the first i The and the first j One data observation, , ; The specific method for calculating the sum of the mutual distances is as follows: ； in, Represents the distance and value between each other. n This represents the total number of data observations.

8. The data estimator determination device based on fuzzy adaptive method according to claim 7, characterized in that, The specific method for calculating the fuzzy membership degree is as follows: ； in, Indicates the first i The fuzzy membership degree of a data observation relative to a data statistic This represents an exponential coefficient greater than 1. This indicates the avoidance of local minima where the denominator is zero.

9. The data estimator determination device based on fuzzy adaptive method according to claim 8, characterized in that, The minimum value is specifically... .

10. The data estimation device based on fuzzy adaptive estimation according to claim 8, characterized in that, The specific method for calculating the statistics of the uncertain dataset is as follows: ； in, To represent statistics for an uncertain dataset, This indicates the weighted median operation. Indicates the first j The fuzzy membership degree of a data observation relative to a data statistic.

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