Modern Economy, 2011, 2, 421-426
doi:10.4236/me.2011.23047 Published Online July 2011 (http://www.SciRP.org/journal/me)
Copyright © 2011 SciRes. ME
An Applications of Information Systems on
Macro-Economic Climate Index of China#
Mei He1, Xun Ge2*
1School Mathematical Science, Huaiyin Normal University, Huaian, China
2College of Zhangjiagang, Jiangsu University of Science and Technology, Zhangjiagang, China
E-mail: hemei94@126.com, *zhugexun@163.com
Received January 11, 2011; revised March 2, 2011; accepted March 21, 2011
Abstract
Recently, National Bureau of Statistics of China has released macro-economic climate index of China from
2009-02 to 2010-05.Based on these indices, we establish an information system. In this information system,
monitoring signal is taken as a decision attribute and coincident index, leading index, lagging index are taken
as condition attributes. We use rough-set theory to investigate the importance of each condition attribute with
respective to decision attribute and the strength of each condition attribute supporting decision attribute. Re-
sults of this investigation will be helpful for Chinese government to make active macro-economic policy and
to maintain the steady and relatively fast development of Chinese economy.
Keywords: Information System, Condition Attribute, Decision Attribute, Macro-Economic Climate Index,
Monitoring Signal, Coincident Index, Leading Index, Lagging Index
1. Introduction
The global financial crisis that started two years ago has
taken its toll on the world economy on an unprecedented
scale. Ow to make world economy recovery as soon as
possible? Art of the recent optimism in world markets
rests on the belief that China’s iscal-stimulus package is
boosting its economy and that GDP growth ould come
close to the government’s target of 8% this year. China
has not only accomplished considerable fiscal and mone-
tary easing, but also Beijing is passing on some of that
boost to the rest of the world. Recently, National Bureau
of Statistics of China has released the following table of
macro-economic climate index of China from 2009-02 to
2010-05 (Table 1) [1]. For this table, the compilation
methods and summary analysis can be found at www.
cemac.org, and following remark is given at first.
Remark 1. 1) The monitoring signal shows state of the
economic operation.
2) The coincident index is the index reflecting the cur-
rent basic trend of the economy, and it is calculated with
the following data:
(a) industrial production;
Table 1.
Macro-economic climate index of China from 2009-02 to
2010-05,
(year 1996 = 100).
Date Monitoring
Signal
Coincident
Index
Leading
Index
Lagging
Index
2009.0276.0 94.0 99.0 92.7
2009.0382.0 94.5 100.0 91.2
2009.0478.0 94.9 101.0 90.7
2009.0584.0 95.4 101.9 90.0
2009.0686.7 96.0 102.6 89.5
2009.0794.0 96.6 103.4 89.6
2009.0896.7 97.3 104.1 90.0
2009.09103.3 98.2 105.0 90.8
2009.10110.7 99.5 105.7 92.0
2009.11117.3 100.4 105.4 93.2
2009.12116.7 102.1 105.4 93.8
2010.01114.0 103.1 104.7 95.0
2010.02104.7 103.9 104.7 95.8
2010.03106.0 104.1 105.0 96.3
2010.04107.3 104.0 104.4 96.3
2010.05114.0 103.7 103.4 97.3
#Project supported by the National Nature Science Foundation of China
(No. 10971185 and 11061004). And Natural Science Research Project
of Ordinary Universities in Jiangsu (08KJB110002). *Corresponding
author
M. HE ET AL.
422
b) employment;
c) social demands (including investment, consump-
tion and foreign trade);
d) social incomes (including the government taxes,
profits of enterprises and income of residents).
3) The leading index is calculated with a group of
leading indicators, which take a lead before the coinci-
dent index, and is used for forecasting the future eco-
nomic trend.
4) The lagging index is calculated with the lagging in-
dicators, which lag behind the coincident index, and is
mainly used for confirming the peak and valley of the
economic cycle.
Naturally, we are interested in some relations between
monitoring signal and its impacting factors (coincident
index, leading index, lagging index) in the above table.
In macro-economic climate index of China, monitoring
signal of each month, as well as the associated its im-
pacting factors are uncertain decisions, so it is unlikely to
be appropriate to use traditional analytic methods (e.g.
synthesis, appraisal, stratification and estimate of prob-
ability). However rough-set theory, which is a logic-
mathematical method proposed by Z. Pawlak, has shown
to be an effective tool in analyzing this type of issues
[2-5]. In recent years, this theory has been widely imple-
mented in the many fields of natural science and societal
science [6-9,10,11-13]. In this paper, we establish an in-
formation system based on the above table. In this infor-
mation system, monitoring signal is taken as a decision
attribute and coincident index, leading index, lagging
index are taken as condition attributes. We use rough-set
theory to investigate the importance of each condition
attribute with respective to decision attribute and the
strength of each condition attribute supporting decision
attribute. Results of this investigation will be helpful for
Chinese government to make active macro-economic
policy and to maintain the steady and relatively fast de-
velopment of Chinese economy.
2. Propaedeutics
Propaedeutics in this section belongs to Z. Pawlak [2-5,
13].
Remark 2. 1) For a set B, B denotes the cardinal of
B.
2) For a family of sets


12
,,,,: 1,2,,
F:1, 2,,: F,1,2,,
ki
iii
FFFF ik
ikFi

 

 k
.
3) Let R be an equivalence relation on a set U. U/R
denotes the family consisting of all equivalence classes
with respect to R and [u] denotes the equivalence class
with respect to R containing uU
.
4) Let R be a family of equivalence relations on U.
Then
R:RUR is a partition of U and is de-
noted by RU. The equivalence relation induced by
RU is also denoted by R.
Definition 1.
,,,SUAVfis called an information
system.
1) U, a nonempty finite set, is called the universe of
discourse.
2)
A
CD
is a finite set of attributes, where C
and D are disjoint nonempty sets of condition attributes
and decision attributes respectively.
3) :
f
UA V
is an information function.
4)
:VV A
, where .


,:VfuuU

Remark 3. An information system
can be expressed a date table, which is called decision
table, whose columns are labeled by elements of A, rows
are labeled by elements of U, and f(u,a) lies in the cross
of the row labeled by u and the column labeled by a.

,,,SUAVf
Definition 2. Let
,,,SUCDVf be an infor-
mation system.
1) For aCD
, we define an equivalence relation
~ on U as follows:

~,
ij ij
uufuafua,
.
U/a denotes the family consisting of all equivalence
classes with respect to ~.
2) For ,
BCD
:UbbB is a partition of
U, which is denoted U/B. The equivalence relation in-
duced by U/B is also denoted by B.
Definition 3 Let R be an equivalence relation on an
universe U of discourse, and
U. Put
RX
 
,uu URuX.

RX is called lower ap-
proximation of X.
3. Decision Table
In this section, we establish an information system
,,,SUCDVf for our investigation, which is
obtained by transforming the table of macro-economic
climate index of China from 2009-02 to 2010-05 and
includes all information we need in this investigation.
Remark 4. Put
123456789
10 1112 13 14 15 16
,,,,,,,,,
,,,,,,
U uuuuuuuuu
uuuuuuu
where
12345678910111213141516
,,,,,,,,, ,, , , ,,uuuuuuuuuu uu u u uu
denote sixteen months from 2009-02 to 2010-05 in turn.
U is the universe of discourse in
,,,SUCDVf.
Remark 5. Put D = {d}, where d denotes monitoring
signal. D is the set of a decision attribute in
Copyright © 2011 SciRes. ME
M. HE ET AL.423

,,,SUCDVf.
Remark 6. Put , where 123
de-
note coincident index, leading index, lagging index re-
spectively. C is the set of three condition attributes in
.
123
,,Cccc

,f
,,ccc
,,SU
CDV
Remark 7. f and V in
,f,,CDVSU are given
as Definition 1 and Remark 3.
This information system is
expressed by the following decision table. (Table 2)
,,,SUCDVf
Remark 8. Monitoring signals are divided three levels:
cooling, stable and heating.
1) indicates monitoring signal less than 95.0.
1
d
d
2) indicates monitoring signal between 95.0 and
110.0.
2
3) indicates monitoring signal more than 110.0.
3
Remark 9. Coincident Indices are divided three levels:
cooling, stable and heating.
d
1) indicates coincident index less than 97.0.
11
c
c
2) indicates coincident index between 97.0 and
101.0.
21
3) indicates coincident index more than 101.0.
31
Remark 10. Leading Indices are divided three levels:
cooling, stable and heating.
c
1) indicates leading index less than 103.0.
12
c
c
2) indicates leading index between 103.0 and
104.9.
22
3) indicates leading index more than 104.9.
32
c
Table 2. Decision table.
U d 1
c 2
c
1
u 1
d 11
c 12
c 23
c
2
u 1
d 11
c 12
c 23
c
3
u 1
d 11
c 12
c 13
c
4
u 1
d 11
c 12
c 13
c
5
u 1
d 11
c 12
c 13
c
6
u 1
d 11
c 22
c 13
c
7
u 2
d 21
c 22
c 13
c
8
u 2
d 21
c 32
c 13
c
9
u 3
d 21
c 32
c 23
c
10
u 3
d 21
c 32
c 23
c
11
u 3
d 31
c 32
c 23
c
12
u 3
d 31
c 22
c 33
c
13
u 2
d 31
c 22
c 33
c
14
u 2
d 31
c 32
c 33
c
15
u 2
d 31
c 22
c 33
c
16
u 3
d 31
c 22
c 33
c
Remark 11. Lagging Indices are divided three levels:
cooling, stable and heating.
1) indicates lagging index less than 91.0.
13
c
c
2) indicates lagging index between 91.0 and
94.0.
23
3) indicates lagging index more than 94.0.
33
By some simple operations, we obtain the following
related partitions of .
c
U
Proposition 1. The following are some related parti-
tions of .
U
1)
 
123456 78131415
,,,,,,,, , ,,Uduuu uu uuu uuu
910111216
,,,,uu uu u.
2)
 
1123456 78910
,,,,,, ,,,,Ucuuuuuuu u u u
1112 1314 15 16
,,,,,uuuuuu .
3) 2123456712131516
/{{,,,,},{,,,,,}Ucuuuuuuuu u u u,
89 10 1114
,,, ,uuuu u.
4)
 
3345678 1291011
,,,,,,,,, ,,Ucuu uu u uuu u uu
12 13 14 15 16
,,,,uuuuu .
5)
 
12 3456 78
,,,,,, ,
,
UCuuuuuu u u

910 111213151614
,,, ,,,,uuuu u uuu.
6)
 
2312345 67 8
,,,,,,,,Uccuuuuu uuu,
 
910111213151614
,,, ,,,,uu uu u uuu.
7)
 
1312 3456 78
,,,,,,,,,
Uccuuuuuu uu
910 111213141516
,,,,,,uuuu uu uu .
8)
  
1212345 6 7
,,,,,,,Uccuuuuu u u,


89 10111412 13 15 16
,,,,,,, ,uuuuuuuuu.
4. Importance
Definition 4. Let be a family of equivalence rela-
tions on URR
and
R
Let Q be an equivalence
relan
.
tioon U.
1) Put
:posQRXXU Q
R.
R
posQ is called positive region of Q with respect
to R.
2) Put

R
R
pos Q
QU
.
RQ
is called dependable degree of Q with respect
to R.
3) Put
RQRR R
RQ


Q
.
RQ R
is called importance of R’ with respect to
Q .
Remark 12. For information system
,,,SUCDVf, let cC
.Put
Copyright © 2011 SciRes. ME
M. HE ET AL.
424
D
According to Z. Pawlak rough-set theo


 
CD C
cD

.

Cc

ry,
CD c
is
2)
4)
Lemma 1 and Definition 4(2), we have the follow-
in
the importance of condition attribute c with respect to
decision attribute d [13] .
By Proposition 1 and Definition 4(1), we have the fol-
lowing proposition by some simple operations.
Lemma 1. The following hold.
1)

C
posD

456789101114
,,,,,, , ,uuuuuuu u.
12
,,uu3
,uu
11



23 12 3 4 5891014
,,,,,,,, , ,
cc
posDuuuuuuuu u u.
3)


13
,cc
pos D
1234
,,uuuu

567891011
,,,,,,,,uuuu u. uu



12 1234567
,,,,,,,
cc
posD uuuuuuu.
By
g proposition by some simple operations.
Lemma 2. The following hold.
1)
 
12 0.750
C
pos D
D

16
CU.
2)




23
23
,
,
10 0.625
16
cc
cc
pos D
DU
.
3)




13
13
,
,
11 0.688
16
cc
cc
pos D
DU
.
4)




12
12
,
,
70.438
16
cc
cc
pos D
DU

.
Bye follo Lemma 2 and Remark 12, we have thwing
pr
2) D
3)
oposition by some simple operations, which gives the
importance of condition attribute cCwith respect to
decision attribute d.
Proposition 2. The following hold.
1)





23
1,
CDC cc
cD D


0.750 0.6250.125 .





13
2,
CDC cc
cD


0.750 0.6880.062 .




12
3,
CDCcc
cD


0.750 0.4380.3
D
Remark 13. By Remark 12 and Proposition 2, we have
th
port
in all condition attributes (the im-
po
or information system
12 .
e following conclusions.
1) Coincident index (with respect to monitoring signal)
is the less important than lagging index and more im-
portant than leading index (the importance is 0.125).
2) Leading index (with respect to monitoring signal) is
the least important in all condition attributes (the im-
ance is 0.062).
3) Lagging index (with respect to monitoring signal) is
the most important
rtance is 0.312).
5. Support
Definition 5. F
,,,SUCDVf, let and WUcC.
1) Put
W. : an
C
SWuuUcd u
C
SW
conditio
is called pport su W wh respect
ton attribute c.
a subset ofit
2) Put

c
c
SW
spt WU
.
c
s
pt Wppo
ect to cond
is called the surt degree of W with re-
spition attribute c.
3) Put
:
cc
d SWWUd. S
Sd is called a support s
c
with res
ubset of decision attribute
d pect to condition attribute c.
Remark 14. For information system
,,,UCDVf, let cC.Put. S

c
c
Sd
spt dU
According to Z. Pawugh-ry, lak roset theo
c
s
pt d
c support
re-
flects the strength of condition attribute ing
decision attribute d [13].
Remark 15. Put
1 123456
,,,,,W uuuuuu,
,, , ,Wuuuuu,
2 781314215 39 10 111
,,W uuu

16
,,uu .Then
123
. ,,Ud WWW
The following lemma known [9].
Lemma 3. For inrmation system
is
fo
,,,UCDVf, let cC. ThS
ho
en the following
1)
ld.
12cc
Sd SWWSW

3c c
S.
2)
cic j
SWSW
for all 3 and ,1,2,ij
ij
.
3)

12cc cc

3
s
ptdsptWspt WsptW.
By Prork 15,
ve t
position 1, Definition 5(1) and Remawe
hahe following lemma by some simple operations.
Lemma 4. The following hold.
1)

1
6 2
,,,,, ,
c
S WuuuuuuS W
1
1 12345c
13c
SW
.

22
1 123452
,,,,,
cc
SWuuuuuSW
23c
SW
.
2)

33 3
123cc c
SW SWSW
. 3)
ition 5(2) and Lemma 4, we have the follow-
inma.
By Defin
g lem
Copyright © 2011 SciRes. ME
M. HE ET AL.425
Lemma 5. The following hold.
1)
 
1
1
1
1
6;
16
c
c
SW
spt WU


1
1
ci
ci
SW
spt WU
00;
16

for
2)
2,3i.
 

2
22
2
1;
16
c
ci
cci
SW
SW
spt Wspt W
UU

15
00;
16

for .
3)
2,3i
 
3
3
0i
01
,2,3.
16
ci
ci
SW
spt Wfor
U
 
ma 3(3), Lemma 5 and Remark 14, weave
the following proposition, which gives the strength of
co
follow
) 3
By Lem h
ndition attribute cCsupporting decision attribute
d.
Proposition 3. The ing hold.
1
 

1
c
11 1
12cc c
s
ptdsptWspt Wspt W
60.375
16
 .
2) 3
 

22 22
12cc cc
s
ptdspt WWspt W spt
50.313
16
 .
3)
ark 16. By Remark 14 and Proposition 3, we have
thllowing conclusions.
is maximal in strength
co
hich is less than the strength of
co
al) is 0, which is minimum in strengths of c
tio
per, we give some explanations
1) The investigation in this paper is conducted with a
ndex
of
nite universe $U$ of discourse, but by using
th
u of Statistics of China, “Macro-Economic
of China from 2009-02 to 2010-05,” May
lysis,” European
 

33 33
123
0
cc cc
sptdspt WsptWsptW
Rem
e fo
1) The strength of coincident index (supporting moni-
toring signal) is 0.375, whichs of
ndition attributes.
2) The strength of leading index (supporting monitor-
ing signal) is 0.313, w
incident index and more than the strength of lagging
index.
3) The strength of lagging index (supporting monitor-
ing signondi-
n attributes.
6. Postscript
In the end of this pa
sample of 13 months for macro-economic climate i
China. The validity of the research conclusion and
associated discussions is limited by the relatively small
sample size. However, as stated earlier, results of this
investigation will be helpful for Chinese government to
make active macro-economic policy and to maintain the
steady and relatively fast development of Chinese eco-
nomic.
2) The investigation in this paper is based on partitions
of the fi
ese partitions we are not able to solve neighboring
question in numerical representations for some condition
attributes. For example, leading index 98.86 is cooling
and leading index 99.09 is stable in this paper. In recent
years, the rough-set theory has been developed from par-
titions of the universe of discourse to covers of the uni-
verse of discourse [14,15], which may provide a satis-
factory solution for this neighboring question. Further
exploratory might be performed towards this direction.
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