RETRACTED ARTICLE: Forecasting of the wind speed under uncertainty

In this paper, the semi-average method under neutrosophic statistics is introduced. The trend regression line for the semi-average method is given in the presence of Neutrosophy in the data. The application of the semi-average method under indeterminacy is given with the help of wind speed data. The efficiency of the semi-average method under the neutrosophic statistics is discussed over the semi-average method under classical statistics. From the analysis, it is concluded that the proposed method is effective, informative, and flexible for the forecasting of wind speed.


Semi-average method under indeterminacy
In the method of semi-average under indeterminacy, the time series data having neutrosophic numbers is divided into two equal or nearly equal halves. The neutrosophic average of each half is computed and placed them at the center of time spans. Suppose that be the neutrosophic averages of the first and the second half, respectively. Suppose also that X 1N and X 2N are the coded values corresponding to the first and second half, respectively. The neutrosophic trends values using this method can be obtained as follows Note here that Eq. (1) is used to estimate the following regression line under indeterminacy  Figure 1 is generated using R version 3.2.1 (https ://www.r-proje ct.org/).

R E T R
is the rate of change per unit in the presence of indeterminacy and computed as follows

Application using wind speed data
The application of the proposed semi-average method under indeterminacy is given using real wind speed data. The data of the year 2020 is collected from the Pakistan Meteorology department. The last available data of the first three months have been used to explain the proposed method. The wind speed (mph) data having the minimum value and the maximum value is taken. The energy expert is interested to forecast the wind speed on the basis of the given data. As the wind speed (mph) data is recorded in the interval, therefore, the use of the existing semi-average method under CS is not suitable. The proposed semi-average method under indeterminacy is suitable to apply for such wind speed data. The necessary calculations for the wind speed data of month January, February, and March 2020 using the proposed method are explained.   Fig. 1, we also note that for the month of January, several plotted points are close to the trend line. Therefore, the trend line for this month can be used to forecast the wind speed. From Fig. 1, it can be noted that the presence of Neutrosophy in the wind speed data can affect the forecasting analysis of the wind speed. The proposed method has some limitations that it can be

Competitive study based on wind speed data
As discussed earlier, the proposed semi-average method under indeterminacy is the generalization of the existing semi-average method under CS. The proposed method reduces to existing method when I L = 0 . We will compare both methods in terms of trended values for the three months of the year 2020. The neutrosophic form of trended values and measure of indeterminacy of January 2020 is given in Table 1. The neutrosophic form of trended values and measure of indeterminacy of February 2020 is given in Table 2. The neutrosophic form of trended values and measure of indeterminacy of March 2020 is given in Table 3. From Table 1, it is quite clear that the measure of indeterminacy is 1. Further, the determined part of the neutrosophic form is 0. It means that the presence of a high measure of indeterminacy will affect the forecasting of wind energy. From Table 2, it can be seen that the indeterminacy measure for the first three days is around 1. For the last four days, this measure is 0.96. For example, for day seven, the neutrosophic form of trended value is Y N = 0.1228 + 10.38I N ; I N ǫ[0, 0.99].
The trended value 0.1228 presents the value under CS. From this neutrosophic form, it can be seen that for seven days, the forecasting value of wind energy will be from 0.1228 to 10.38. We note a big gap between these values, the gap between these values is based on the difference between the lower and upper values of wind speed. The gap may be narrow if lower and upper values of wind speed are close. From this study, it can be noted that the www.nature.com/scientificreports/ existing method provided only the exact/determined forecasting value for wind speed. On the other hand, the proposed method provides the forecasting values in an interval. In addition, the proposed method gives information about the measure of indeterminacy. In an uncertain environment, the use of the existing method under CS will mislead the energy experts. The use of the proposed method to forecast the wind speed in the presence of indeterminacy is quite suitable and effective.

Conclusions
The semi-average method under neutrosophic was introduced in this paper. The proposed semi-average method is the extension of the semi-average method under classical statistics. The trend line under the indeterminacy was introduced. The proposed semi-average method can be applied effectively when the Neutrosophy is presented in the data. The application of the proposed method was given with the help of wind speed data. From the analysis, it can be concluded that the proposed method provides the forecasting wind speed values in intervals rather than the exact values. Therefore, the proposed method is quite reasonable to use when the data has imprecise and indeterminate observations. The other time series methods can be developed under neutrosophic statistics as future research. More statistical tests about the time series data under neutrosophic statistics can be studied as future research.