**DETERMINATION OF THE
TECHNOLOGICAL VALUE OF COTTON FIBRE: 2**

**Material and Methods**

__Data collection and
analysis __

Each year the International Textile Centre (USA) conducts a crop study for different varieties of cotton. The results of the crop study of 1997 and 1998, which includes 33 sets of fibre and yarn data for two different yarn counts (22 Ne and 30 Ne), were used in our investigation. We ranked the 33 cotton fibres according to their FQI, SCI, PDI and multiplicative AHP (MIAHP) values. We also ranked the 33 cottons according to the final yarn tenacity. Separate rankings were obtained for 22 Ne and 30 Ne. The difference between the two rankings (fibre quality ranking and yarn tenacity ranking) was calculated to measure the rank correlation coefficient between them by using the following equation.

where *R _{s}*
is the rank correlation,

*d*is the absolute difference between the two rankings, and

*M*is the total number of alternatives (33). The summary statistics of fibre properties are given in Table 3.

**Table 3.**
Summary statistics of cotton fibre properties

__Hierarchy formulation for
multiplicative AHP __

The goal or objective of the
present investigation is to determine the technological
value of cotton, which should reflect the achievable level
of yarn quality (yarn strength). In general, the cotton
fibre criteria of this problem can be classified under three
headings, namely tensile properties, length properties and
fineness properties. Tensile properties can be divided into
two sub-criteria, fibre bundle tenacity (*FS*)
and elongation (*FE*).
Similarly, UHML, UI and SFC are the relevant sub-criteria of
length properties to be considered here. Fineness is solely
represented by the micronaire (*FF*)
value of cotton. At the lowest level of the hierarchy, there
are 33 cotton fibre alternatives, which should be ranked
according to their technological value. The schematic
representation of the problem is depicted in Figure 1.

__Determination
of criteria weights __

With respect to the overall objective problem, the pair-wise comparison matrix of three criteria is given in Table 4. Here the comparisons are made according to Saaty’s scale given in Table 1.

**Table 4.**
Pair-wise comparison matrix of criteria with respect to
objective

It can be inferred from Table 4
that tensile properties moderately predominate over the
fineness properties. However, the length properties
demonstrate a strong preponderance over the fineness
properties. The dominance of length properties over the
tensile properties is between equal to moderate. The
normalised *GM* column of
Table 4 indicates that the length properties of cotton
fibres have the most dominant influence with a relative
weight of 0.581. The relative weights of tensile and
fineness properties are 0.309 and 0.110 respectively. For
the measurement of consistency of judgment, the original
matrix is multiplied by the weight vector to obtain the
product as shown below:

The next step is concerned with
finding the relative weights of various sub-criteria (Level
3) with respect to the corresponding criteria (Level 2). The
pair-wise comparison between the sub-criteria of tensile and
length properties and the derived weight vectors are shown
in Tables 5 and 6 respectively. Then the global weights of
sub-criteria are calculated by multiplying the relative
weight of a sub-criterion with respect to the corresponding
criterion and the relative weight of that criterion with
respect to the objective. For example, the global weight of
tenacity is 0.875 x 0.309 = 0.270. For tenacity, elongation, *UHML*, *UI*,
*SFC* and *FF*,
the values of global weights are 0.270, 0.039, 0.291, 0.145,
0.145 and 0.110 respectively.

**Table 5.**
Pair-wise comparison of sub-criteria with respect to tensile
properties

Therefore, according to the multiplicative AHP model, the equation to calculate the technological value of cotton (MIAHP) is as follows:

__Determination of
premium-discount index formula __

The % contribution of various
cotton properties on the ring yarn tenacity was determined
separately for 22 Ne and 30 Ne, using the method described
earlier. The results are shown in Table 7. The negative sign
associated with *UHML* is
unexpected, and may be ascribed to the prevailing
autocorrelation among the fibre properties. The *
R ^{2}* values of
the multiple regression equation were 0.745 and 0.676 for 22
Ne and 30 Ne respectively. The resultant formula to
calculate the premium-discount index of cotton fibre is as
follows:

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