Fuzzy Forecast Based on Fuzzy Time Series DOI: http://dx.doi.org/10.5772/intechopen.82843

The following steps in the procedure are performed when using fuzzy time

Step 1. First, we take the logarithm of the STI data to reduce variation and

Step 2. Maintaining stationary data while forecasting helps to improve the forecast quality; therefore, we conduct a stationary test on the STI data. For fuzzy time series, a fuzzy trend test can measure whether the STI's fuzzy trend moves upward or downward. Using this fuzzy trend test, the STI data can be converted into a stationary series. If the original STI data exhibited a fuzzy trend, it can be eliminated by taking the difference. We then repeat the test after taking the first difference to measure if the STI data exhibits a fuzzy trend. If a fuzzy trend is again

Letting STIð Þt be the historical data under consideration and fuzzy time series, a difference test is used (following Definition 11) to understand whether the stability of the information. Recursion is performed until the information is determined to

Step 3. According to the interval setting of the STI data, we define the upper and lower bounds, which facilitate dividing the linguistic value intervals later. From

Step 4. After defining the upper and lower bounds of the STI data in Step 3, we can define the SCFI range by determining the membership function as well as the linguistic values. We can also define the range of the subinterval for each linguistic value, assuming that the following linguistic values are under consideration: extremely few, very few, few, some, many, very many, and extremely many. According to Definition 11, the supports of fuzzy numbers that represent these

1 for x∈ ½ Þ 3:627 þ ð Þ i � 1 ð Þ 0:129 ; 3:627 þ ið Þ 0:198

1 for x∈ ½ � 3:627 þ ð Þ i � 1 ð Þ 0:129 ; 3:627 þ ið Þ 0:198

where A<sup>1</sup> = "extremely few," A<sup>2</sup> = "very few," A<sup>3</sup> = "few," A<sup>4</sup> = "some," A<sup>5</sup> = "many," A<sup>6</sup> = "very many," and A<sup>7</sup> = "extremely many." Thus, the supports are suppð Þ¼ A<sup>1</sup> ½ Þ 3:627; 3:825 , suppð Þ¼ A<sup>2</sup> ½ Þ 3:825; 4:023 , suppð Þ¼ A<sup>3</sup> ½ Þ 4:023; 4:221 , suppð Þ¼ A<sup>4</sup> ½ Þ 4:221; 4:419 , suppð Þ¼ A<sup>5</sup> ½ Þ 4:419; 4:617 , suppð Þ¼ A<sup>6</sup> ½ Þ 4:617; 4:815 ,

Step 5. According to the subinterval setting of each linguistic value, we classified

Step 6. We apply fuzzy theory to define the corresponding value for the inter-

vals of the STI data, arrange the corresponding method for the STI data, and

each historical dataset of the STI into its corresponding interval to measure the value corresponding to the linguistic value for each interval. The fuzzy time series F tð Þ was given by F tðÞ¼ Ai when d tð Þ∈ suppð Þ Ai . Therefore, Fð Þ¼ 201501 A5, Fð Þ¼ 201502 A6, Fð Þ¼ 201503 A5, Fð Þ¼ 201504 A6, …, and Fð Þ¼ 201806 A3. Table 1 shows the comparison between the actual SCFI data and the fuzzy enroll-

<sup>2</sup> <sup>þ</sup> <sup>C</sup><sup>42</sup>�<sup>22</sup> 2

� � <sup>¼</sup> <sup>432</sup> , C C<sup>42</sup>

� � � �

<sup>n</sup> <sup>p</sup> <sup>≈</sup> <sup>5</sup>:011. That is, <sup>U</sup> <sup>¼</sup> ½ � <sup>3</sup>:627; <sup>5</sup>:<sup>011</sup> .

<sup>2</sup> � ð Þ <sup>1</sup> � <sup>0</sup>:<sup>2</sup> �

<sup>¼</sup> C C <sup>¼</sup> <sup>C</sup><sup>22</sup>

¼ 688:8, the STI data are considered in a stable state and are not rejected.

Definition 10, the discourse U ¼ ½ � DL; DU . From Table 1, Dmin ¼ 4:067 , Dmax ¼ 4:571, s ¼ 0:172, and n ¼ 42 can be obtained. Lettingα ¼ 0:05, since n is large than 30, a standard normal Z was used. Thus, Z0:<sup>05</sup> ¼ 1:645, DL ¼ Dmin�

where 1≤ i ≤ m � 1;

where i ¼ m; 0 otherwise:

�

improve the forecast accuracy, letting <sup>S</sup>TIðÞ¼ <sup>~</sup><sup>t</sup> ln <sup>S</sup>TIð Þ<sup>t</sup> .

Time Series Analysis - Data, Methods, and Applications

observed, then we take the second difference, and so on.

series to analyze STI.

be stable. Once the region C<sup>00</sup>

<sup>n</sup> <sup>p</sup> <sup>≈</sup> <sup>3</sup>:627, and DU <sup>¼</sup> <sup>D</sup>max <sup>þ</sup> stα<sup>=</sup> ffiffiffi

linguistic values are given as follows:

8 >>>>>>><

>>>>>>>:

uAi ð Þ¼ x

and suppð Þ¼ A<sup>7</sup> ½ � 4:815; 5:011 .

ment data.

30

stα= ffiffiffi



group. We used Table 1 data in our analysis according to the root mean square percentage error (R.M.S.P.E.) method, with an average prediction error of 1.708%. Figure 3 shows the forecast visitor arrivals determined through fuzzy time series analysis and the actual STI values. Based on the fuzzy time series results, the

In this article, a long-term predictive value interval model is developed for forecasting the STI. This model facilitates minimizing the uncertainties associated with fuzzy numbers. The method is examined by forecasting the STI by using data

rate of return is negative and its volatility is increasing. The long-term predictive significance level of the STI is at the ΔS level; the STI should thus exhibit extreme

The current model for the STI 201806 forecast level deviates insignificantly from the actual values for an average of 68.090 and is within the group; the

prediction error does not exceed 1.708% of the significance level. By constructing a fuzzy time series forecasting model for the STI with an error of less than 1.708%, with the traditional fuzzy time excluded from the single-point forecast comparison,

Furthermore, the proposed method can be computerized. Thus, by improving fuzzy linguistic assessments as well as the evaluation of fuzzy time series, decision makers can automatically obtain the final long-term predictive significance level. The STI used in this chapter is used as a forecasting example. If you predict that

The four functions of management are mainly four functions: planning, organization, leadership and control. The fuzzy time series mode used in this chapter can be applied to controlled projects to compare and correct whether the re-executed work meets expectations. If you meet expectations, re-plan the original settings.

This chapter is extended and revised the article "An improved fuzzy time series

theory with applications in the Shanghai containerized freight index".

the future will rise, you can use the buying strategy. For example, if the index

d tð Þ is obtained. For index returns, the current

average STI is estimated to be 68.090 in 201806 (Figure 3).

this model provides a long-term predictive significance level.

returns in the future, you can use the selling strategy.

5. Conclusions and future work

Fuzzy Forecast Based on Fuzzy Time Series DOI: http://dx.doi.org/10.5772/intechopen.82843

from which ΔS = 74.981 and ΔS > ^

volatility.

Acknowledgements

33

## Table 1.

Fuzzy historical STI data and the forecasted results.


#### Table 2.

Fuzzy transitions derived from Table 1.

#### Figure 3.

Forecast STI and actual STI.

integrate the changes from all the rules to determine the rules for the STI. The transition rules are derived from Table 1. For example, Fð Þ! 201501 Fð Þ 201502 is A<sup>5</sup> ! A5. Table 2 shows all transition rules obtained from Table 1.

Step 7. We calculate each rule by determining all the rules of the STI, and the calculation results can be used to forecast future values. Table 1 shows the forecasting results from 201001 to 201806.

Step 8. The calculated STI rules can define the intervals of the STI data; using these intervals, we can determine the variation in future long-term intervals. The long-term predictive value interval for the STI is given as (3.726, 4.913). Thus, the long-term predictive interval for the STI is given as (41.506, 136.022). Therefore, the current long-term S STI is bounded by this interval. According to Step 8, the fuzzy STI of 201501 shown in Table 1 is A5, and from Table 2, we can see that the rules are the fuzzy logical relationships in Rule 8 of Table 2, in which the current state of fuzzy logical relationships is A3. Thus, the 201806 STI predictive value is 41.506.

Step 9. Letting defuzzified S be ΔS, the STI 201806 forecast value based on our investigation is 68.090, and its trading range is between 41.506 and 136.002. Thus, the new triangular fuzzy numbers by S = (41.506, 68.090, 136.002). Thus, the defuzzified S is ΔS = 74.981, and ΔS = 74.981 > ^ d tð Þ = 68.090. ΔS is called a longterm significance level up.

The result shows that based on the long-term significance level, the STI is currently oversold. This result and the risk–reward ratio are both related within the group. We used Table 1 data in our analysis according to the root mean square percentage error (R.M.S.P.E.) method, with an average prediction error of 1.708%. Figure 3 shows the forecast visitor arrivals determined through fuzzy time series analysis and the actual STI values. Based on the fuzzy time series results, the average STI is estimated to be 68.090 in 201806 (Figure 3).
