Frontiers in Computer Education

Frontiers in Computer Education – Wang (ed.)

© 2015 Taylor & Francis Group, London, ISBN 978-1-138-02797-8

A fuzzy time series forecasting model based on percentages

HongXu Wang & JianChun Guo

Tourism Management College, Qiongzhou University, Sanya, China

Hao Feng

Science and Technology College, Qiongzhou University, Sanya, China

HaiLong Jin

Tourism Management College, Qiongzhou University, Sanya, China

ABSTRACT: Song & Chissom founded a fuzzy time series forecasting theory in 1993. But the existing fuzzy

time series forecasting model can only study the simulation and forecast of historical data. In this paper we have

presented a forecasting model of fuzzy time series based on percentages. It can predict the data about unknown

years.

1 INTRODUCTION

Classical time series forecasting theory was founded

in the middle of the last century, and is widely applied.

‘But the classical time series methods cannot deal

with the forecasting problems in wich the values of

time series are linguistic terms represented by fuzzy

sets [1, 2]’. Song & Chissom had founded a fuzzy

time series forecasting theory in 1993, and first stud-

ies the forecasting problem of the enrolments in the

University ofAlabama. It is called ‘the enrolment fore-

casting problem’ in that the values of time series are

the problem of linguistic terms represented by fuzzy

sets. Many scholars have put forward many fuzzy time

series forecasting models, and have study ‘the enrol-

ment forecasting problem’. But the existing fuzzy time

series forecasting model can only study the simulation

and forecasting of historical data. Stevenson & Porter

[4] and Saxena, Sharma & Easo [2] used the percentage

changes of year to year enrolments. Jilani, Burney &

Ardil [1] and Stevenson & Porter [4] and Saxena,

Sharma & Easo [2] established and applied the concept

of the inverse fuzzy numbers. This paper has presented

a Fuzzy Time Series Forecasting Model Based on Per-

centage (FTSFMBP). Because FTSFMBP can predict

the data of the unknown years, so the range of possible

applications of the FTSFMBP is much wider.

2 BUILDING THE FORECASTING FORMULA

OF THE FTSFMBP

The enrolments ei in the University of Alabama in

1971–1992 are found in the Table 1, as given by Song

and Chissom [3] in 1993. From table 1 we may get the

enrolment universe E ={e

1971

= 13055, ..., e

1992

=

18876}. Using the formula

to compute the percentage changes in year to year

enrolments, and obtained the percentage universe P =

{P

1972

= 3.89, P

1973

= 2.24, ..., D

1992

=−2.38}, and

write in the Table 1. In the percentage universe P,

P

min

=−5.83, P

max

= 7.66. we take

as the unit segment, and obtained the segmented

universe of percentage as:

On the universes e, P, T , to set up the forecasting

formula of the FTSFMBP as

3 A SIMULATION AND FORECASTING OF

HISTORICAL DATA

We use the enrolments of the University of Alabama in

1971–1992 as a historical data as a forecasting function

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