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International Journal of Fiber and Textile Research
Universal Research Publications. All rights reserved
ISSN 2277-7156
Original Article
AN APPROACH FOR ACCEPTING/REJECTING CONSISTENCY OF
ANALYTIC HIERARCHY PROCESS AS A CRITERION DETERMINING
TECHNOLOGICAL VALUE OF EGYPTIAN COTTON
Khaled M. Hussein*1, Ibrahim A. M. Ebaido1, Rokaya.M.Hassan1 and Hayam S. A. Fateh2
1
Cotton Research Institute (CRI), Agricultural Research Center (ARC), Giza, Egypt
Cent. Lab. For Design and Stat. Anal. Res., Agricultural Research Center (ARC), Giza, Egypt
Email: [email protected]*
2
Received 10 January 2013; accepted 11 February 2013
Abstract
Two statistical approaches for accepting/rejecting consistency of analytic hierarchy process (AHP) were used in this paper.
First approach was the traditional and follows Consistency Ratio (CR); second approach was the new and follows Random
Index (RI).
By the two approaches we had acceptance consistency in pair-wise reciprocal comparison in the analytic hierarchy process
(AHP) as a quality criterion determining the technological value of cotton.
The highest technological value belongs cotton variety Giza 87 (16.97) and the lowest value belongs cotton variety Giza 90
(12.87). That is accepted due to the increase of weights of the main determinant for technological value criterias, i.e. fiber
length (UHML) and strength (FS).
The high values of spearman and partial correlations of fiber length and strength with yarn strength verify the accuracy of
these variables in modeling AHP. Values of partial correlation of micronaire value with yarn strength reveal the effect of
yarn count of yarn strength. The effect of short fiber content on yarn strength seemed to be inter-correlated with other
variables. Generally, partial correlation values verified the accuracy of weights fiber properties modeling AHP, except for
fiber elongation which showed insignificant either correlation or partial correlation with yarn strength. Therefore, it is
considerable to release fiber elongation of AHP equation in other run.
© 2013 Universal Research Publications. All rights reserved
Keywords: Consistency, Analytic Hierarchy Process, Random Index, Technological Value.
1. INTRODUCTION
Definition and fulfillment of the Analytic Hierarchy
Process (AHP) made by [1] and [2], as a Multi Criteria
Decision Making (MCDM) technique that represents a
complex decision problem as a hierarchy with different
levels. Each level of the Analytic Hierarchy Process (AHP)
contains different elements with a relevant common
characteristic, hence, to determine the degree of quality
requirements achieved in the Analytic Hierarchy Process
(AHP), [3], recommend using AHP a cardinal measure of
the importance or priority of each element in a level by
pair-wise comparisons of all elements in that level.
Each element in every level of the Analytic Hierarchy
Process (AHP) serves as the basis for effecting pair-wise
comparisons of the elements in the immediate lower level
of the hierarchy as noted both [4], [5] and [6]. They also
added the final priorities of the elements in the lowest level
(decision alternatives) obtained using the principle of
1
hierarchical composition, and consequently these lead to
the overall ranking of design alternatives.
The pair-wise reciprocal comparison matrices in the
analytic hierarchy process (AHP) has been used by [7] and
[8], in a trilogy reciprocal comparison matrix to determine
the technological value of upland cotton. Whilst, [9] and
[10], used the pair-wise in a trilogy reciprocal comparison
matrix and in a pentagonal matrix to determine each of
technological and marketing value of Egyptian cotton.
The approach for accepting/rejecting consistency of the
pair-wise reciprocal comparison matrices in the analytic
hierarchy process (AHP) by [1], [11], [4], and [2], was
depends on result of the consistency ratio (CR). The same
approach has been used by [7], [8], [9], and [10].
[12], have studied the consistency in random pair-wise
reciprocal comparison matrices which is the heart of the
Analytic Hierarchy Process (AHP) of different sizes and
they reached to different statistical approach for
International Journal of Fiber and Textile Research 2013; 3(1): 1-5
accepting/rejecting consistency of the pair-wise reciprocal
comparison matrices depends on Random Index (RI).
Therefore, this paper presents a comparison between two
approaches for accepting/rejecting consistency of the pairwise reciprocal comparison matrices used in Analytic
Hierarchy Process (AHP) as a quality criterion determining
technological value of the Egyptian cotton, as well as the
accuracy of weights criteria resulting from consistency.
2. MATERIAL AND METHODS
The material used in this study included the following
Egyptian cotton varieties, Giza70, Giza87, Giza88, and
Giza92 representatives of extra long Egyptian cotton
category, while the long staple Egypt class was represents
at Giza80, Giza86, and Giza90. Of each variety of Egyptian
cotton have been taking 3 levels of quality expressed in
Egyptian grading system in the following grades, G/FG (
Good to Fully Good), G (Good) and FGF/G ( Fully Good
Fair/ Good). The samples of those varieties and their grades
been taken from season 2011.
Fiber upper half mean length (UHML), uniformity index
(UI), micronaire value (MIC), fiber strength (FS) and fiber
elongation (FE %) were all determined on the High
Volume Instrument (HVI) according to [13]. Further the
Sutter Web Comb Sorter been used to determine short fiber
content by weight (SFC %) as directed in the [13].
The lint cotton samples were spun into the two-carded ring
counts number (Ne) 40 and 50 using the 3.6 twist
multiplier. Carded ring yarn skein strength (lea product)
was measured according to [13].
The measurements of the materials characterization used in
the present study were under controlled atmospheric
conditions (65 to 75 F° temperatures and 63 to 67% relative
humidity), due to conducted at the laboratories of the
Cotton Research Institute, Agricultural Research Center,
Giza - Egypt.
Collected data were subjected to the proper of statistical
analysis of spearman and spearman partial correlations
according to the procedure described by [14]. The data
were statistically analyzed by using the computer statistical
software package SAS statistical software [15].
Accepting/rejecting consistency
2.1. saatys approach
[8], and [9], introduced the pair-wise reciprocal comparison
matrices in trilogy matrix, and both of the pair-wise was as
a quality criterion determining the technological value of
cotton by using the analytic hierarchy process (AHP).
However [8], determined the technological value of the
upland cotton, while [9], determined the technological
value of the Egyptian cotton, so the weights of the criteria
used in the determination process was different between
both [8], and [9].
Table (1), presents review of the pair-wise reciprocal
comparisons in the form of trilogy matrix specific each of
[8], [9], moreover, Consistency Ratio (CR) and the criteria
weights obtained by both of them. Accepting/rejecting
consistency in the analytic hierarchy process (AHP)
according to saatys approach was depending on
apportionment Consistency Index (CI) and Random
Consistency Index (RCI) ≤ 0.1 consistency ratio (CR).
2
If the value of CR is 0.1 or less, then the pair-wise
reciprocal comparison matrix is considered to be consistent
and acceptable, otherwise the decision maker has to make
some changes in the entry of the pair-wise comparison
matrix, [1]. From results of consistency ratio (CR), we can
sum up that, saatys approach showed a consistent pair-wise
comparison by a 0.006 (CR) for Hussein and 0.003 (CR)
for Majumdar, these values of CR is less than 0.1,
consequently each of the MIAHP equation whether pertains
Hussein or Majumdar fits as a quality criterion determining
the technological value of cotton.
2.2. Alonso and Lamata approach
[12], derived the following approach and applied it through
a large number of generated matrices with different sizes.
They exploited the results to show the acceptance
maximum positive eigen-value (λ max) for various sizes of
matrices and under different levels of probability (α).
Finally, they found goodness of fit that regressed the λ max
values on their corresponding matrix order (matrix size)
(n). Where the linear relation between λ max values and the
matrix order (n) was more valid and accurate with a
correlation coefficient being r = 0.99**, consequently the
final product was depending on a consistency index (λ
max) and level of consistency needed (α) 0 < a ≤ 1.
In fact, this method is very simple criterion for
accepting/rejecting matrix; furthermore, this method is able
to test large sizes of matrices under different levels of
probability. In addition, this level provide adaptability to
different scopes, accordingly, we can decide if a specific
matrix is a sufficiently consistent matrix (or not) due to the
[12], approach in accepting/rejecting consistency by using
their equivalent:
RandomIndex(RI) = λMax N + α(1.7699N - 4.3513) ,
where ( α ) is the probability value, N is the matrix order
(size of the matrix), 1.7669 is the least- square and -4.3513
is the regression constant.
Table 2, clarifies that [12], approach consider to be a new
criterion for acceptance and a new index for representing
consistency in pair-wise reciprocal comparison matrices,
hence, this index and criterion allows the decision maker to
study the consistency of each matrix in an adaptable way.
The decision maker when using the Random Index (RI)
(maximum positive eigen-value - λ max) in different levels
of α can decide about the matrix consistency using not
only the matrix entries but also the level of consistency that
he needs in this particular case.
Generally, due to accepting / rejecting the pair- wise
reciprocal comparison matrices consistency in the analytic
International Journal of Fiber and Textile Research 2013; 3(1): 1-5
Table (1), Review each of pair-wise comparison matrix, Consistency Ratio (CR), as well as criteria weights obtained by
Majumdar and Hussein
Pair-wise comparison matrix of criteria according to
Majumdar
Criteria
Tensile
Length
Fineness
Tensile
1
1/2
3
Length
2
1
5
Fineness
1/3
1/5
1
Consistency Ratio (CR) = 0.003 (Accepted)
criteria weights obtained by Majumdar
Length
UHML
UI
SFC
0.291
0.145
0.145
Tensile
FS
FE
0.270
0.039
Fineness
FF
0.11
Pair-wise comparison matrix of criteria according to
Hussein
Criteria
Tensile
Length
Fineness
Tensile
1
1
7
Length
1
1
9
Fineness
1/7
1/9
1
Consistency Ratio (CR) = 0.006 (Accepted)
criteria weights obtained by Hussein
Length
UHML
UI
SFC
0.380
0.054
0.054
Tensile
FS
FE
0.394
0.056
Fineness
FF
0.059
Table (2). Accepting/rejecting consistency according to random index (maximum positive λ max), under different levels of α
Random Index (RI), according to Alonso and Lamata
Maximum positive eigen-value (λ max), Majumdar
Maximum positive eigen-value (λ max), Hussein
3.004
3.007
Random Index (RI) at α (0.10) = 3.095
Random Index (RI) at α (0.10) = 3.095
(Accepted)
(Accepted)
Random Index (RI) at α (0.08) = 3.076
Random Index (RI) at α (0.08) = 3.076
(Accepted)
(Accepted)
Random Index (RI) at α (0.05) = 3.047
Random Index (RI) at α (0.05) = 3.047
(Accepted)
(Accepted)
Random Index (RI) at α (0.01) = 3.009
Random Index (RI) at α (0.01) = 3.009
(Accepted)
(Accepted)
RandomIndex(RI) = λMax
N + α(1.7699N - 4.3513)
Table (3). Description of the technological characteristics Egyptian cotton varieties, as well as their Mi AHP quantitative
values
Variety
The technological characteristics
The technological value
UHML
UI
SFC
FS
FE
FF
Mi AHP, H
Min
33.8
80.1
9.8
42.4
7.0
3.5
15.56
Giza 70
Mean
34.1
82.8
12.4
44.0
7.2
3.8
15.57
Max
34.5
85.0
14.5
47.1
7.5
4.2
15.82
Min
30.0
78.2
13.7
34.2
7.3
3.5
13.37
Giza 80
Mean
30.7
82.8
15.9
36.6
7.8
4.0
13.63
Max
31.5
86.0
18.2
38.5
8.2
4.6
13.81
Min
32.0
79.2
12.0
39.8
7.0
3.6
14.67
Giza 86
Mean
32.9
83.5
13.4
40.9
7.3
3.9
14.83
Max
33.8
87.2
14.9
42.4
7.6
4.3
15.03
Min
33.7
82.1
6.0
46.7
7.2
3.4
16.60
Giza 87
Mean
34.8
84.7
8.3
48.6
7.4
3.6
16.72
Max
36.5
88.1
11.0
51.0
7.6
4.1
16.97
Min
34.0
80.8
9.0
46.2
7.0
3.5
16.21
Giza 88
Mean
35.4
84.8
10.4
47.4
7.1
3.9
16.43
Max
36.2
87.0
11.8
48.9
7.5
4.2
16.56
Min
28.8
75.2
16.2
32.6
7.0
3.2
12.87
Giza 90
Mean
29.5
80.3
17.8
34.6
7.6
3.7
13.10
Max
30.8
85.0
20.5
36.6
8.3
4.5
13.34
Min
34.0
82.0
5.5
47.1
7.0
3.5
16.54
Giza 92
Mean
34.7
85.2
8.2
48.1
7.3
3.6
16.67
Max
35.1
89.2
11.3
49.3
7.6
3.9
16.79
Mi AHP, H = Multiplicative Analytic Hierarchy Process, [9].
UHML = Upper Half Mean Length, UI = Uniformity Index, SFC = Short Fiber Content, FS = Fiber Strength, FE = Fiber
Elongation and FF is the Fiber Fineness expressed by Micronaire reading (MIC).
reciprocal comparison matrices consistency in the analytic
hierarchy process (AHP), by using the two approaches both
of [1], and [12]. We conclude that, acceptance consistency
in pair-wise reciprocal comparison by both [8] and [9], in
the analytic hierarchy process (AHP). Hence, this
acceptance qualifies the MiAHP (Multiplicative Analytic
Hierarchy Process) a quantification method the quality of
cotton in the form of technological value.
3
3. RESULTS AND DISCUSSION
3.1. Quantification the technological value of Egyptian
cotton
Results tabulated in Table 3 indicates that, the highest
technological value belongs Giza87 (16.97) and the lowest
technological value belongs Giza90 (12.87). That has
accepted due to increase the weights of criterias length
(UHML) and strength (FS) were 0.380 and 0.394,
International Journal of Fiber and Textile Research 2013; 3(1): 1-5
Table 4 . Spearman and spearman partial correlations between fiber properties and carded ring yarn strength.
Carded ring yarn strength
Fiber quality properties
Correlations
UHML
UI
SFC
FS
FE
Spearman (Rs)
0.97
0.36
- 0.57
0.98
- 0.29
40 Ne
Probability
< 0.0001 0.0993 0.0066 <0.0001 0.1946
Spearman partial (PRs)
0.51
0.43
- 0.09
0.43
- 0.01
Probability
0.0419
0.0959 0.7190
0.0941
0.9692
Spearman (Rs)
0.96
0.36
- 0.56
0.97
- 0.29
Probability
< 0.0001 0.0993 0.0075 <0.0001 0.1946
50 Ne
Spearman partial (PRs)
0.37
0.19
- 0.05
0.33
0.04
Probability
0.1512
0.4586 0.8415
0.2018
0.8766
respectively, according to [9], hence, these criterias are the
main determinant for technological value of Egyptian
cotton varieties. Generally, the extra long staple cotton
varieties (Giza70, Giza87, Giza88 and Giza92) were the
highest technological value than of long staple cotton
varieties (Giza80 and Giza90), however, the long staple
cotton variety Giza86 showed high technological value
because of the increase in length and strength of the lint on
those long staple cotton category to which it belongs.
3.2. Spearman (Rs) and spearman partial (PRs)
correlations between criteria and the end product
Spearman (Rs) and spearman partial (PRs) correlations
coefficient of fiber quality properties (criteria), i.e., UHML,
UI, SFC, FS, FE and FF used in modeling AHP with the
end product represented in carded ring yarn strength at 40
and 50 count number are shown in Table 4.
With yarn strength, the highest Spearman (Rs) correlations
were of UHML and FS followed by UI and SFC. These
variables showed spearman partial (PRs) correlation with
yarn strength in the same trend, except for SFC, which
exhibited quit low partial correlation. On the other hand,
micronaire value (FF) that gave low value of spearman
correlation, Unexpected showed partial correlation with
yarn strength at count 40(Ne) higher than its spearman
correlation. Whereas, partial correlation of micronaire
value with yarn strength at count 50 (Ne) was lower than
spearman correlation. This is due to the residual effect of
yarn count that did not use in modeling AHP and resulted
in shortcoming in micronaire value effect. Short fiber
content (SFC) showed high significant correlation with
yarn strength; whereas it is partial correlation with yarn
strength was insignificant. This result clarifies the
interrelation between SFC and the other variables with yarn
strength. It is apparent that neither spearman correlation nor
partial correlations of fiber elongation (FE) with yarn
strength were insignificant at the two count numbers (Ne)
40 and 50, this suggests that, there no imperative use of FE
in modeling AHP.
Generally, data in Table 4 managed to verify the accuracy
of weights of variables used to form AHP equation, except
for fiber elongation (FE) which maybe released in other
runs.
4. CONCLUSIONS
By the two approaches of Saaty and Alonso and Lamata,
we had acceptance consistency in pair-wise reciprocal
comparison in the analytic hierarchy process (AHP) as a
quality criterion determining the technological value of
cotton.
4
FF
0.14
0.5197
0.33
0.2022
0.15
0.4990
0.14
0.6008
The two main determinant criterias for technological value
were fiber length (UHML) and fiber strength (FS), which
had the highest weights in MIAHP. Comparison between
partial correlation and spearman correlation of fiber
properties with yarn strength managed to verify the
accuracy of weights of variables used to form MI AHP
equation, except for fiber elongation (FE) which maybe
released in other runs.
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Source of support: Nil; Conflict of interest: None declared
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