| 5.2.2 Team rank (Test Match)
With ICC ranking Australia is on first position England on second and South Africa on third but with our output Australia stand first, England stands second and South Africa stands third position because of increase in their link weightage. When we are calculating team rank of test matches we require innings runs and wickets.
Table 9: Team Rank of All Teams
TEAMS
|
INDIA
|
PAK
|
SRI
|
S.AFR
|
N.LAND
|
ENG
|
W.IES
|
BANG
|
ZIMB
|
AUS
|
INDIA
|
0
|
3
|
5
|
8
|
2
|
6
|
2
|
0
|
1
|
11
|
PAK
|
4
|
0
|
6
|
5
|
2
|
7
|
3
|
0
|
0
|
10
|
SRI
|
8
|
6
|
0
|
7
|
1
|
7
|
2
|
0
|
0
|
7
|
S. AFR
|
4
|
2
|
5
|
0
|
1
|
7
|
2
|
0
|
0
|
14
|
N.LAND
|
2
|
5
|
3
|
7
|
0
|
8
|
0
|
0
|
4
|
5
|
ENG
|
5
|
7
|
3
|
7
|
2
|
0
|
2
|
0
|
0
|
16
|
W.IES
|
7
|
6
|
6
|
11
|
3
|
15
|
0
|
2
|
0
|
15
|
BANG
|
6
|
8
|
12
|
8
|
8
|
8
|
4
|
0
|
5
|
4
|
ZIMB
|
5
|
3
|
5
|
3
|
1
|
3
|
4
|
1
|
0
|
2
|
AUS
|
9
|
1
|
0
|
5
|
8
|
9
|
1
|
0
|
0
|
0
|
TABLE 10: Team Rank W.R.T Test Match
TEAM RANKING WITH RESPECT TO TEST MATCH
|
India
|
0.11662
|
Pakistan
|
0.0959763
|
Sri Lanka
|
0.0968203
|
South Africa
|
0.122923
|
New Zealand
|
0.08725
|
England
|
0.136533
|
West Indies
|
0.0746774
|
Bangladesh
|
0.0522367
|
Zimbabwe
|
0.0587397
|
Australia
|
0.158223
|
5.2.3 Team index (ODI’s)
As in team index of ODIS we have to calculate no. of wickets and no. of runs so by calculating their averages we have the following result. Australia in first position, Sri Lanka and South Africa in second position and Pakistan on third position and so on.
Table 11: ODI Runs
ONE DAY INTERNATINAL RUNS
|
TEAMS
|
INDIA
|
PAK
|
SRI
|
S.AFR
|
N.LAND
|
ENG
|
W.IES
|
BANG
|
ZIMB
|
AUS
|
INDIA
|
0
|
797
|
1133
|
705
|
437
|
303
|
319
|
15
|
0
|
1240
|
PAK
|
504
|
0
|
849
|
820
|
431
|
343
|
396
|
0
|
0
|
890
|
SRI
|
886
|
811
|
0
|
720
|
171
|
422
|
82
|
0
|
0
|
966
|
S.AFR
|
454
|
509
|
502
|
0
|
143
|
200
|
0
|
67
|
0
|
844
|
N.LAND
|
380
|
800
|
884
|
320
|
0
|
204
|
0
|
21
|
91
|
1412
|
ENG
|
648
|
184
|
485
|
266
|
410
|
0
|
178
|
5
|
104
|
699
|
W.IES
|
641
|
274
|
386
|
714
|
358
|
182
|
0
|
52
|
170
|
1521
|
BANG
|
435
|
1409
|
1058
|
739
|
790
|
357
|
470
|
0
|
393
|
558
|
ZIMB
|
480
|
843
|
944
|
1488
|
626
|
702
|
793
|
561
|
0
|
577
|
AUS
|
370
|
172
|
194
|
402
|
174
|
147
|
49
|
0
|
0
|
0
|
Table 12: ODI Wickets
ONE DAY INTERNATINAL WICKETS
|
TEAMS
|
INDIA
|
PAK
|
SRI
|
S.AFR
|
N.LAND
|
ENG
|
W.IES
|
BANG
|
ZIMB
|
AUS
|
INDIA
|
0
|
41
|
58
|
66
|
43
|
38
|
54
|
5
|
21
|
65
|
PAK
|
68
|
0
|
45
|
66
|
58
|
44
|
24
|
0
|
0
|
80
|
SRI
|
123
|
78
|
0
|
48
|
24
|
26
|
7
|
9
|
12
|
73
|
S.AFR
|
38
|
8
|
42
|
0
|
41
|
57
|
27
|
0
|
2
|
35
|
N.LAND
|
59
|
50
|
50
|
70
|
0
|
9
|
25
|
14
|
8
|
79
|
ENG
|
74
|
32
|
57
|
32
|
49
|
0
|
33
|
2
|
9
|
123
|
W.IES
|
71
|
67
|
29
|
99
|
44
|
43
|
0
|
14
|
22
|
43
|
BANG
|
57
|
38
|
76
|
59
|
43
|
62
|
35
|
0
|
59
|
82
|
ZIMB
|
48
|
66
|
80
|
65
|
44
|
71
|
75
|
108
|
0
|
36
|
AUS
|
33
|
20
|
23
|
47
|
39
|
35
|
15
|
5
|
0
|
0
|
Table 13: Team Index W.R.T ODIS
TEAM INDEX WITH RESPECT TO ODIS
|
India
|
3.3541
|
Pakistan
|
3.4641
|
Sri Lanka
|
3.53553
|
South Africa
|
3.53553
|
New Zealand
|
3.08221
|
England
|
2.95804
|
West Indies
|
2.78388
|
Bangladesh
|
2.17945
|
Zimbabwe
|
2.12132
|
Australia
|
3.80789
|
5.2.4 Team index (Test Match)
When we are calculating team index for test match we have to consider no. of inns runs and no. of wickets. By their average we concluded the result in which Australia comes on first position, England on second and Sri Lanka on third. It is different from ICC ranking because they are rating teams on basis of matches won and loss but we have considered other two important concepts (inns runs, wickets) other than this
Table 14: Test Match Inns&Runs
TEST MATCH INN& RUNS
|
TEAMS
|
INDIA
|
PAK
|
SRI
|
S.AFR
|
N.LAND
|
ENG
|
W.IES
|
BANG
|
ZIMB
|
AUS
|
INDIA
|
0
|
509
|
316
|
366
|
0
|
1147
|
155
|
0
|
0
|
1684
|
PAK
|
378
|
0
|
308
|
302
|
217
|
875
|
316
|
0
|
0
|
1337
|
SRI
|
785
|
385
|
0
|
388
|
38
|
125
|
0
|
0
|
0
|
755
|
S.AFR
|
267
|
0
|
689
|
0
|
545
|
245
|
0
|
0
|
0
|
1342
|
N.LAND
|
198
|
764
|
515
|
0
|
0
|
354
|
0
|
0
|
0
|
818
|
ENG
|
52
|
373
|
465
|
590
|
267
|
0
|
116
|
0
|
0
|
1794
|
W.IES
|
276
|
945
|
492
|
1012
|
231
|
1089
|
0
|
95
|
0
|
1284
|
BANG
|
575
|
795
|
1875
|
727
|
584
|
878
|
638
|
0
|
345
|
310
|
ZIMB
|
191
|
119
|
1069
|
83
|
675
|
370
|
339
|
226
|
0
|
175
|
AUS
|
748
|
0
|
0
|
20
|
7
|
850
|
0
|
0
|
0
|
0
|
Table 15: Test Match Wickets
TEST MATCH WICKETS
|
TEAMS
|
INDIA
|
PAK
|
SRI
|
S.AFR
|
N.LAND
|
ENG
|
W.IES
|
BANG
|
ZIMB
|
AUS
|
INDIA
|
0
|
9
|
10
|
18
|
14
|
0
|
10
|
0
|
4
|
19
|
PAK
|
6
|
0
|
17
|
22
|
0
|
15
|
1
|
0
|
0
|
18
|
SRI
|
7
|
20
|
0
|
13
|
5
|
23
|
13
|
0
|
0
|
0
|
S.AFR
|
20
|
13
|
1
|
0
|
9
|
24
|
0
|
0
|
0
|
42
|
N.LAND
|
10
|
17
|
0
|
22
|
0
|
26
|
0
|
0
|
0
|
49
|
ENG
|
26
|
14
|
0
|
15
|
0
|
0
|
0
|
0
|
0
|
36
|
W.IES
|
13
|
9
|
26
|
32
|
10
|
61
|
0
|
4
|
0
|
45
|
BANG
|
19
|
24
|
18
|
5
|
12
|
24
|
7
|
0
|
16
|
3
|
ZIMB
|
29
|
17
|
0
|
9
|
15
|
0
|
10
|
0
|
0
|
9
|
AUS
|
14
|
3
|
0
|
30
|
0
|
9
|
3
|
0
|
0
|
0
|
Table 16: Team Index W.R.T Test Match
TEAM INDEX WITH RESPECT TO TEST MATCH
|
India
|
2.95804
|
Pakistan
|
3
|
Sri Lanka
|
3.20156
|
South Africa
|
2.95804
|
New Zealand
|
2.69258
|
England
|
3.31662
|
West Indies
|
2.34521
|
Bangladesh
|
1.5
|
Zimbabwe
|
1.65831
|
Australia
|
3.7081
|
5.2.5 Weighted Team rank (ODI’s)
According to our ODI team ranking South Africa is in first position, Sri Lanka on second and Australia on third position. But we have calculated outlinks weightage by using our weighted team rank formula. By calculating weightage we have following result South Africa, Sri Lanka and Australia on first three positions respectively.
Table 17: Weighted Outlinks W.R.T ODIS
WEIGHTED OUTLINKS WITH RESPECT TO ODIS
|
TEAM
|
INDIA
|
PAK
|
SRI
|
S.AFR
|
N.LAND
|
ENG
|
W.IES
|
BANG
|
ZIMB
|
AUS
|
INDIA
|
0
|
0.0475
|
0.0479
|
0.0475
|
0.0474
|
0.0463
|
0.0459
|
0.0423
|
0.0361
|
0.0480
|
PAK
|
0.0466
|
0
|
0.0477
|
0.0475
|
0.0468
|
0.0467
|
0.0477
|
0
|
0
|
0.0476
|
SRI
|
0.0469
|
0.0474
|
0
|
0.0480
|
0.0451
|
0.0475
|
0.0460
|
0.0367
|
0.0389
|
0.0479
|
S.AFR
|
0.0472
|
0.048
|
0.0469
|
0
|
0.0449
|
0.0456
|
0.0380
|
0.0485
|
0.03
|
0.0476
|
N.LAND
|
0.0469
|
0.0475
|
0.0478
|
0.0467
|
0
|
0.0474
|
0.0397
|
0.04
|
0.0456
|
0.0488
|
ENG
|
0.0467
|
0.0456
|
0.0473
|
0.0467
|
0.0471
|
0
|
0.0458
|
0.0346
|
0.0475
|
0.0465
|
W.IES
|
0.0468
|
0.0446
|
0.0477
|
0.0047
|
0.0464
|
0.0445
|
0
|
0.0448
|
0.04589
|
0.04847
|
BANG
|
0.0474
|
0.0486
|
0.0481
|
0.0484
|
0.0484
|
0.0471
|
0.0479
|
0
|
0.0457
|
0.0476
|
ZIMB
|
0.0469
|
0.0475
|
0.0478
|
0.0486
|
0.0484
|
0.0477
|
0.0474
|
0.0460
|
0
|
0.0481
|
AUS
|
0.0466
|
0.0412
|
0.0456
|
0.0471
|
0.0448
|
0.0448
|
0.0437
|
0.0375
|
0
|
0
|
Table 18: Weighted Team Rank W.R.T ODIS
WEIGHTED TEAM RANKING WITH RESPECT TO ODIS
|
India
|
0.0512553
|
Pakistan
|
0.051204
|
Sri Lanka
|
0.0512691
|
South Africa
|
0.0512701
|
New Zealand
|
0.0512466
|
England
|
0.0512424
|
West Indies
|
0.0511923
|
Bangladesh
|
0.0509535
|
Zimbabwe
|
0.0508243
|
Australia
|
0.0512602
|
5.2.6 Weighted Team Rank (Test Match)
According to our ODI team ranking England is in first position, South Africa on second and Australia on third position. But as we have calculated outlink weightage of test matches by considering inns runs and wickets of all teams so by our weightage Australia South Africa and India got first three positions.
Table 19: Weighted Outlinks W.R.T Test Match
WEIGHTED OUTLINKS WITH RESPECT TO TEST MATCH
|
TEAM
|
INDIA
|
PAK
|
SRI
|
S.AFR
|
N.LAND
|
ENG
|
W.IES
|
BANG
|
ZIMB
|
AUS
|
INDIA
|
0
|
0.0494
|
0.0485
|
0.0480
|
0.04
|
0.0494
|
0.0488
|
0
|
0.0357
|
0.0493
|
PAK
|
0.0489
|
0
|
0.0482
|
0.0485
|
0.0491
|
0.0492
|
0.0490
|
0
|
0
|
0.0492
|
SRI
|
0.0490
|
0.0485
|
0
|
0.0483
|
0.0478
|
0.0458
|
0.0394
|
0
|
0
|
0.0490
|
S.AFR
|
0.0486
|
0.0394
|
0.0492
|
0
|
0.0498
|
0.0475
|
0.0166
|
0
|
0
|
0.0490
|
N.LAND
|
0.0490
|
0.0493
|
0.0494
|
0.0337
|
0
|
0.0480
|
0
|
0
|
0.0166
|
0.0494
|
ENG
|
0.0446
|
0.0482
|
0.0493
|
0.0488
|
0.0492
|
0
|
0.0483
|
0
|
0
|
0.0491
|
W.IES
|
0.0477
|
0.0493
|
0.0488
|
0.0489
|
0.0488
|
0.0487
|
0
|
0.0480
|
0
|
0.0489
|
BANG
|
0.0490
|
0.0490
|
0.0493
|
0.0489
|
0.0487
|
0.0491
|
0.0493
|
0
|
0.0486
|
0.0487
|
ZIMB
|
0.0478
|
0.0479
|
0.0495
|
0.0470
|
0.0498
|
0.0492
|
0.0488
|
0.0495
|
0
|
0.0489
|
AUS
|
0.0488
|
0.0333
|
0
|
0.0423
|
0.0241
|
0.0489
|
0.0333
|
0
|
0
|
0
|
Table 20: Weighted Team Rank W.R.T Test Match
WEIGHTED TEAM RANKING WITH RESPECT TO TEST MATCH
|
India
|
0.0515155
|
Pakistan
|
0.0514129
|
Sri Lanka
|
0.0513102
|
South Africa
|
0.0514199
|
New Zealand
|
0.0513838
|
England
|
0.0515
|
West Indies
|
0.0511389
|
Bangladesh
|
0.0502923
|
Zimbabwe
|
0.0503121
|
Australia
|
0.0514915
|
5.2.7 Unified weighted team rank (ODI’s)
As unified team rank is the combination of two techniques which are team index and weighted team rank so that’s mean we are mixing the result of these. With our ranking for ODI matches Australia hold first position, South Africa and Sri Lanka on second and third.
Table 21: Unified Team Ranking W.R.T Odis
UNIFIED TEAM RANKING WITH RESPECT TO ODIS
|
India
|
0.00556624
|
Pakistan
|
0.00573821
|
Sri Lanka
|
0.00586098
|
South Africa
|
0.00586111
|
New Zealand
|
0.00512497
|
England
|
0.00492394
|
West Indies
|
0.00463663
|
Bangladesh
|
0.00363257
|
Zimbabwe
|
0.00352188
|
Australia
|
0.00630054
|
5.2.8 Unified Weighted Team Rank (Test Match)
With the results of test matches applying unified weighted team rank formula Australia, England and Sri Lanka comes on first three positions
Table 22: Unified Team Rank W.R.T Test Matches
UNIFIED TEAM RANKING WITH RESPECT TO TEST MATCH
|
India
|
0.00556456
|
Pakistan
|
0.0056282
|
Sri Lanka
|
0.00598051
|
South Africa
|
0.00555422
|
New Zealand
|
0.00506361
|
England
|
0.0062163
|
West Indies
|
0.00440602
|
Bangladesh
|
0.00276505
|
Zimbabwe
|
0.00305885
|
Australia
|
0.00692822
|
5.3 Effect of weighted parameters setting on team ranking
To calculate outbound links of weighted team rank we see effect of three different weighted parameters:
-
60(matches)+20(wickets)+20(runs)/matches+wickets+runs=>ans=>1/ans
-
50(matches)+25(wickets)+25(runs)/matches+wickets+runs=>ans=>1/ans
-
40(matches)+30(wickets)+30(runs)/matches+wickets+runs=>ans=>1/ans
We use arithmetic mean formula to calculate three different things
-
Weightage of matches
-
Weightage of wickets
-
Weightage of runs
Arithmetic mean formula is used to normalize values. As we are decreasing the weighted parameters of arithmetic mean formula very minor changes have been seen.
Table 23: calculation of weighted parameter No 1
Table 24: Final Output of Weighted Parameter No. 1
Table 25: Calculation of Weighted Parameter No 2
Table 26: Final Output of Weighted Parameter No. 2
Table 27: Calculation of Weighted Parameter No 3
Table 28: Final output of weighted parameter No. 3
5.4 EFFECT OF PARAMETER D ON RANKINGS
Parameter d is used in our three proposed methods. As d is the dampening actor which is used to normalize values usually ranges from 0 .1 to 0.9. We have discussed its effect on our methods in the following section:
5.4.1 Team Rank (ODIS)
Table 29: Effect of d on TR
TEAMS
|
0.1
|
0.2
|
0.3
|
0.4
|
0.5
|
0.6
|
0.7
|
0.8
|
0.9
|
INDIA
|
0.104174
|
0.108426
|
0.112761
|
0.117181
|
0.121694
|
0.126308
|
0.131012
|
0.135833
|
0.144152
|
PAK
|
0.103736
|
0.107546
|
0.11143
|
0.115389
|
0.119422
|
0.123533
|
0.127723
|
0.131998
|
0.139516
|
SRI
|
0.102832
|
0.105669
|
0.108513
|
0.111369
|
0.11424
|
0.117129
|
0.12004
|
0.12298
|
0.128763
|
S.AFR
|
0.101953
|
0.104003
|
0.106149
|
0.108392
|
0.110733
|
0.113171
|
0.115709
|
0.11835
|
0.123723
|
N.LAND
|
0.0993819
|
0.0988813
|
0.0984996
|
0.0982385
|
0.0981
|
0.0980861
|
0.0981995
|
0.0984451
|
0.100893
|
ENG
|
0.0987806
|
0.0976335
|
0.0965564
|
0.0955476
|
0.0946053
|
0.0937277
|
0.0929136
|
0.0921635
|
0.09333
|
WEST INDIES
|
0.096462
|
0.0928696
|
0.0892187
|
0.0855048
|
0.081723
|
0.0778685
|
0.0739361
|
0.0699214
|
0.067062
|
BANG
|
0.0928436
|
0.0854698
|
0.0778688
|
0.0700306
|
0.0619443
|
0.0535986
|
0.0449817
|
0.0360811
|
0.0272266
|
ZIMB
|
0.0932214
|
0.0862088
|
0.0789539
|
0.0714479
|
0.0636812
|
0.0556436
|
0.047324
|
0.0387109
|
0.030184
|
AUS
|
0.106616
|
0.113293
|
0.120049
|
0.126899
|
0.133857
|
0.14094
|
0.148162
|
0.155542
|
0.166412
|
5.4.2 Weighted Team Rank (ODIS)
Table 30: Effect of d on WTR
TEAMS
|
0.1
|
0.2
|
0.3
|
0.4
|
0.5
|
0.6
|
0.7
|
0.8
|
0.9
|
INDIA
|
0.0904436
|
0.0807923
|
0.0710447
|
0.0611995
|
0.0512553
|
0.0412107
|
0.0310643
|
0.0208148
|
0.0104605
|
PAK
|
0.0904255
|
0.0807599
|
0.071002
|
0.0611505
|
0.051204
|
0.0411613
|
0.0310209
|
0.0207815
|
0.0104417
|
SRI
|
0.0904485
|
0.080801
|
0.0710562
|
0.0612127
|
0.0512691
|
0.041224
|
0.031076
|
0.0208237
|
0.0104655
|
S.AFR
|
0.0904489
|
0.0808017
|
0.0710571
|
0.0612137
|
0.0512701
|
0.041225
|
0.0310769
|
0.0208244
|
0.0104659
|
N.LAND
|
0.0904406
|
0.0807869
|
0.0710375
|
0.0611912
|
0.0512466
|
0.0412024
|
0.031057
|
0.0208091
|
0.0104573
|
ENG
|
0.0904391
|
0.0807842
|
0.071034
|
0.0611872
|
0.0512424
|
0.0411983
|
0.0310535
|
0.0208064
|
0.0104558
|
W.INDIES
|
0.0904214
|
0.0807525
|
0.0709922
|
0.0611393
|
0.0511923
|
0.0411499
|
0.0310109
|
0.0207739
|
0.0104374
|
BANG
|
0.0903368
|
0.0806016
|
0.0707934
|
0.060911
|
0.0509535
|
0.0409197
|
0.0308086
|
0.020619
|
0.0103499
|
ZIMB
|
0.0902912
|
0.0805201
|
0.0706858
|
0.0607875
|
0.0508243
|
0.0407951
|
0.0306991
|
0.0205352
|
0.0103025
|
AUS
|
0.0904454
|
0.0807954
|
0.0710488
|
0.0612042
|
0.0512602
|
0.0412154
|
0.0310685
|
0.0208179
|
0.0104623
|
Unified weighted team rank (ODIS)
Table 31: Effect of d on UWTR
TEAMS
|
0.1
|
0.2
|
0.3
|
0.4
|
0.5
|
0.6
|
0.7
|
0.8
|
0.9
|
INDIA
|
0.00983817
|
0.00878472
|
0.00772167
|
0.00664889
|
0.00556624
|
0.00447358
|
0.00337077
|
0.00225767
|
0.00113413
|
PAK
|
0.0101571
|
0.00906613
|
0.00796609
|
0.00685683
|
0.00573821
|
0.0046101
|
0.00347236
|
0.00232486
|
0.00116745
|
SRI
|
0.0103681
|
0.00925589
|
0.00813406
|
0.00700247
|
0.00586098
|
0.00470944
|
0.00354773
|
0.00237568
|
0.00119315
|
S.AFR
|
0.0103681
|
0.00925597
|
0.00813417
|
0.0070026
|
0.00586111
|
0.00470957
|
0.00354784
|
0.00237576
|
0.0011932
|
N.LAND
|
0.00904418
|
0.00807889
|
0.00710402
|
0.00611942
|
0.00512497
|
0.00412052
|
0.00310595
|
0.0020811
|
0.00104583
|
ENG
|
0.00868176
|
0.00775687
|
0.00682236
|
0.00587809
|
0.00492394
|
0.00395977
|
0.00298543
|
0.00200078
|
0.00100569
|
W.INDIES
|
0.00817152
|
0.00730181
|
0.00642284
|
0.00553449
|
0.00463663
|
0.00372913
|
0.00281185
|
0.00188467
|
0.000947429
|
BANG
|
0.00639826
|
0.0057181
|
0.00503051
|
0.00433536
|
0.00363257
|
0.00292201
|
0.00220359
|
0.00147719
|
0.0007427
|
ZIMB
|
0.0062227
|
0.00555684
|
0.00488482
|
0.00420653
|
0.00352188
|
0.00283079
|
0.00213315
|
0.00142888
|
0.00071786
|
AUS
|
0.0111626
|
0.00996136
|
0.00875072
|
0.00753049
|
0.00630054
|
0.00506073
|
0.00381091
|
0.00255095
|
0.0012807
|
REFERENCES
References
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[2]. Page Rank for Ranking Authors in Co-citation Networks, Ying Ding and Erjia Yan School of Library and Information Science, Indiana University, 1320 East 10th Street, Bloomington
[3]. An index to quantify an individual’s scientific research output J. E. Hirsch, Department of Physics, University of California at San Diego, La Jolla
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Computer science department, Stanford University Stanford. CA 94305, USA
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[11]. PageRank for Bibliographic Networks , Dalibor Fiala, François Rousselot, Karel Ježek, University of West Bohemia in Pilsen, Czech Republic, INSA Strasbourg, France.
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[13]. LogRank: A Clickstream-Based Web Page Importance Metric for Web Crawlers, Fatemeh Ahmadi-Abkenari, Ali Selamat, Intelligent Software Engineering Laboratory, Faculty of Computer Science & Information Systems, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia.
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