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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 Rs 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

textile table

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 R2 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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