3 2 3
3 30 5
AHP
TOPSIS VIKOR

TOPSIS for Junior High School Math
Textbooks Selection Ranking
Chung Hua University
Hsing Wu University
Abstract
TOPSIS and VIKOR were used to make a multi-criteria decision
on selecting math textbooks in a junior high school. After reviewing
literature and interviewing experts, four dimensions and eleven
criteria were set. There were thirty senior math teachers in junior high
schools were asked expert questionnaires. In addition, five popular
math textbooks were selected be evaluated. The ranking results from
the TOPSIS and VIKOR were compared and analyzed.
Keywords: Math Textbook, AHP, TOPSIS, VIKOR.
3



MCDM
VIKOR TOPSIS
VIKOR (TOPSIS)
VIKOR
(AHP)

TOPSIS


2003


5






VIKOR TOPSIS








20002001
200220022003


Koopmans (Zeleny, 1982)


TOPSIS VIKOR
() TOPSIS
to Ideal Solution, TOPSIS) (Multi-Criteria Analysis Model,
MCAD) (Positive ideal solution)
(Negative ideal solution)
(Tzeng and Huang, 2011)

VIKOR VlseKriterijumska Optimizacija I Kompromisno
Resenje 1998 Opricovic TOPSIS (Technique for Order Preference by
Similarity to Ideal Solution) VIKOR
TOPSISMCDM (Compromise)
(Positive Ideal Solution) (Negative Ideal
Solution)
2005
TOPSIS
(Individual Regret)
2011)
TOPSIS VIKOR
11 2
A2.
EXCELSPSSSAS
R R
R pmr
11
3

(0.1805)

(1)
()
A x x x
A x x x
1C 2C
(2)
ijr 1,2, ,i m 1,2, ,j n
() A A
(3)
(4)
{ 1,2,....., |j j n j } ' { 1,2,....., |j j n j
}
A r r r
A r r r
1 1max | min | ' | 1,2,....., ( , ,..., ,..., )ij ij j n ii
A v j J v j J i m v v v v
1 1min | max | ' | 1,2,....., ( , ,..., ,..., )ij ij j n i i
A v j J v j J i m v v v v
2
1





VIKOR
2
1
ij
*
F c F
* F c
c Δ F
I1 I2
fi *fi
-
-
-
- - - -
(12)
Qj j
Qj (Qj )
1. 1

(3) J
S (S") Q R(R')
R (R")


11
4 [, A1] 3.833 30
A1
4
NO A1 A2 A3 B1 B2 C1 C2 C3 D1 D2 D3
3.833 4.100 4.133 3.933 3.667 4.000 3.933 3.833 4.033 3.900 4.067
3.800 3.967 3.800 3.933 3.600 3.767 3.800 3.833 3.900 3.667 4.233
3.833 3.767 3.967 3.967 3.767 3.900 3.633 3.900 3.667 4.000 4.033
4.167 3.833 3.967 4.467 3.333 4.067 3.733 4.200 4.133 4.067 4.300
4.267 4.133 3.467 4.067 3.333 3.733 4.267 3.833 4.067 3.867 4.133

()
5
No A1 A2 A3 B1 B2 C1 C2 C3 D1 D2 D3
0.430 0.463 0.477 0.431 0.463 0.459 0.453 0.437 0.455 0.447 0.438
0.426 0.448 0.439 0.431 0.454 0.432 0.438 0.437 0.440 0.420 0.456
0.430 0.425 0.458 0.435 0.475 0.448 0.419 0.445 0.414 0.458 0.434
0.468 0.433 0.458 0.490 0.421 0.467 0.430 0.479 0.466 0.466 0.463
0.479 0.466 0.400 0.446 0.421 0.429 0.492 0.437 0.459 0.443 0.445

6
VIKOR TOPSIS
Ci
19
1. 1Q" - Q' 1/(J-1) = 1/(5 -1) =0.25
Q – Q = 0.3776275> 0.25 1 2

2. Q – Q = 0.3777494 > 0.25 1 2

3. Q – Q = 0.1083805 < 0.25 1 2
4. Q – Q = 0.0331924 < 0.25 1 2
5.

TOPSIS

TOPSIS VIKOR

4 11
TOPSIS VIKOR
TOPSIS
TOPSIS

VIKOR Q R S
Q
Q 0.25
VIKOR TOPSIS

7-18
13135-168
(Agriculture and Economics)3469-90
4. 1994

2014
7. 2002

2(2)59-83
11. 1989

79-103
14. 1989()
27(6)5-27

313-11
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