led to the birth of new branches of mathematics. One branch of mathematics that continues

to grow is fuzzy (Bělohlávek, Dauben, & Klir, 2017).

environment (Morice, Kennedy, Rayner, & Jones, 2012). In addition, the decisions made

by experts are subjective and depend on the competence of each one. Therefore, it is more

appropriate when the data is presented in fuzzy numbers rather than firm numbers. Fuzzy

has a vague or vague meaning. The fuzzy set was first discovered by Zadeh in 1965. The

priority of a model to predict fuzzy time series.

Alabama registrants was first investigated by Song and Chissom in 1993 (Song &

Chissom, 1993). That same year Song & Chissom, (1993), developed the FTS method into

a time-variant fuzzy time series model using a 3-layer back propagation neural network to

defuzzify and apply it to the University of Alabama enrollment dataset. Then Chen, (1996)

proposed a method that is more efficient than Song & Chissom, (1993) which is to use

simplified arithmetic operations also apply to the University of Alabama enrollment

dataset. The same application was also made Singh, (2007) by proposing a better and more

versatile forecasting method based on the FTS forecasting concept of developing a form of

1996, Chen first conducted FTS forecasting research using the Average-Based length

method to determine effective partitions (Chen, 1996). Then Huarng, (2001) found the

distribution-based length interval partitioning method, and the results of his research were

quite effective compared to the Average-Based length method discovered by (Chen, 1996).

Furthermore, research on determining interval pertiation based on frequency density (Chen

& Hsu, 2004; Jilani, Burney, & Ardil, 2007). Then in 2006, Kunhuang Huarng proposed a

new method of determining the length of intervals based on ratios (Huarng & Yu, 2006).

After that Chen et al., (2019), proposed a new fuzzy time series (FTS) forecasting method

based on interval proportions and particle swarm optimization (PSO) techniques.

equation matrices that use complex min-max composition operations and the time

consumed by various defuzzification processes. However, the weakness or rather the part

that can be explored to obtain better forecasting performance values from Singh's fuzzy

time series research is the interval partition section that uses the 7 interval partition rule.

Therefore, the author aims to propose Singh's fuzzy time series forecasting method based

on interval partitioning that is more effective, namely interval ratio. The method proposed

on the thesis was applied to the University of Alabama enrollment dataset. Next, measure

Chissom, 1993). This data is data on the number of applicants for the University of

Alabama. This study used data on the number of University of Alabama applicants from

1971 to 1992. By selecting data on the number of University of Alabama registrants, it is

expected to provide more accurate estimates than forecasting (Chen, 1996; Chen & Hsu,

references in the form of books, journals and writings published on the website. From this

method (Kumar & Gangwar, 2015), Singh's fuzzy time series forecasting algorithm can be

determined based on interval ratio partitions to solve forecasting problems.

AFER=t=1n|At-Ft|Atn×100%

AFER=0,009275+0,008253+0,000331+…+0,00945519×100%

AFER=0,0068937×100%

AFER=0,68937%.

and order 4 are presented in Table 4.11, Table 4.12, and Table 4.13. The following table

evaluates forecasting results using the average forecasting error rate (AFER) for order 2:

1991. Then for the red chart is better than the green chart because the pattern is closer to

relationships that affect forecasting results.

forecast data on the number of University of Alabama enrollees in 1993. Based on Table

4.6, obtained fuzzy logical relationship order 2 in 1993 is A21,A20. Because fuzzy logical

relationship (A21, A20→) is not the same as fuzzy logical relationship (AiAj) so that the

forecasting results in 1993 for order 2 do not follow Rule 2.1, but in the form of average

forecasting results corresponding to A21 and A20 namely 18941.27+18912.552=18926.91.

As for the 3rd order fuzzy logical relationship in 1993 it was A21,A21,A20. Because fuzzy

forecasting results in 1993 for order 4 did not follow Rule 2.3, but in the form of average

forecasting results corresponding to A21,A21,A21 and A20 namely

19127.57+19127.57+19127,57+18725,014=19026.93.

method based on interval ratios. Singh's fuzzy time series forecasting method based on

interval ratios applies fuzzy time series (Chen, 1996) in the section of determining the

speech universe you to fuzzification of historical data which includes fuzzy logical

raltionship (FLR) and fuzzy logical raltionship group (FLRG). Starting from the

determination of the universe of U-talk to the fuzzification of historical data which includes

FLR and FLRG, there is one step that plays an important role in forecasting fuzzy time

correct weaknesses, the determination of interval partitions using interval ratios (Huarng

&; Yu, 2006) with the aim of being able to reflect data variations and assist in forecasting

time series data and determining intervals based on ratios is considered better than the

same interval length.

suitable approach to determining interval length is how to determine the percentile sample

ratio. First, if the percentile sample ratio is set too large then there will be no fluctuations

in the fuzzy time series. Suppose the percentile sample ratio is determined 200% of the

first interval of the time series data 5000, 5100, ..., 10000, 10100. Causes the first interval

between 5000 and 15000 (5000+5000×200%). Indicates that the result is undesirable

data , which is also undesirable. Therefore, guidelines appear in determining the percentile

sample ratio , which must be large enough so that the length of the interval will not be

trivial. Intuitively the percentile sample ratio is set to 50%.

results in addition to determining interval partitions is the process of forming fuzzy logical

relationship groups (FLRG). In fuzzy time series forecasting (Chen, 1996), if the FLRG of

Ai is (Ai→A1,A2,...,Am) then Ft+1=A1,A2,...,Am and the crisp value is the average of

the fuzzy set corresponding to the middle value of the interval (Chen, 1996). However,

Singh 's fuzzy time series forecasting method based on interval ratios is different from

(Chen, 1996) because the forecasting concept is based on the upper and lower and midpoint

forecasting (Singh, 2007a) which uses computational algorithms that aim to minimize the

complexity of calculating min-max composition operations in the FLR equation and time

in the defuzzification process. In simple terms, heuristics are simple guidelines or rules that

are commonly used by humans in assessing something or used to make decisions. The

construction of three forecasting rules, namely Rule 2.1, Rule 2.2, and Rule 2.3 aims to

obtain better results and affect very small AFER values.

order fuzzy time series forecasting , and Rule 2.3 is used for 4th order fuzzy time series

forecasting . The three rules have almost the same steps, which differ only in the initial

step, namely the addition of a new difference parameter (Dt) (Yang & Shami, 2020). The

other parameters, namely Mt1=Nt1=Ot1=Xt+Dt, Mt2=Nt2=Ot2=Xt-Dt,

Mt3=Nt3=Ot3=Xt+Dt/2, and Mt4=Nt4=Ot4=Xt-Dt/2 where Mtp is for Rule 2.1, Ntp is for

Rule 2.2, and Otp is for Rule 2.3 with p∈1,2,3,4. The addition of more than one parameter

produces many forecasting results so that it is expected to be able to reflect data variations

through the average of the forecasting results obtained. In Singh's fuzzy time series

forecasting method based on interval ratios, forecasting based on upper and lower limits

is expected to have flexibility in approaching actual data (Pritpal Singh & Borah, 2013)v. .

Then if the forecasting result of the four parameters is not in the closed interval of the fuzzy

or unqualified set more than equal to the lower bound and less than equal to the upper limit,

ratios than previous fuzzy time series forecasting methods by (Song &; Chissom, 1993b),

(Chen, 1996), (Huarng, 2001), (Huarng &; Yu, 2006), (Singh, 2007a), (Singh, 2007b),

(Jilani et al., 2007), and (Zou et al., 2019). The effectiveness of the forecasting method

obtained can be determined based on the value of the average forecasting error rate

(AFER). Research (Song & Chissom, 1993b) obtained AFER 3.22%, (Chen, 1996)

obtained AFER 0.73%, (Singh, 2007a) obtained AFER 1.53%, (Singh, 2007b) obtained

AFER 1.46%, (Jilani et al., 2007) obtained AFER 1.02%, and (Zou et al., 2019) obtained

(AFER) 0.73%.

ratios can be known when the average forecasting error rate (AFER) value is very small.

Based on the calculation of AFER values for Singh's fuzzy time series forecasting method

based on interval ratios on order 2, order 3, and order 4 respectively are 1.06389%,

concluded that Singh's fuzzy time series forecasting method has the same algorithm as

fuzzy time series forecasting. Singh's fuzzy time series forecasting method based on

Chen, Shyi Ming. (1996). Forecasting enrollments based on fuzzy time series. Fuzzy Sets

Chen, Shyi Ming, & Hsu, Chia Ching. (2004). A new method to forecast enrollments using

Chen, Shyi Ming, Zou, Xin Yao, & Gunawan, Gracius Cagar. (2019). Fuzzy time series

Kumar, Sanjay, & Gangwar, Sukhdev Singh. (2015). Intuitionistic fuzzy time series: an

Morice, Colin P., Kennedy, John J., Rayner, Nick A., & Jones, Phil D. (2012). Quantifying