The intangible sub-criteria are measured

5.5 The evaluation

5.5.3 The intangible sub-criteria are measured

According to DUT evaluation guidelines, 18 of the sub-criteria are intangibles as discussed in section 5.3 (Sattar, 2012). Since the intangible sub-criteria lend themselves more to a qualitative evaluation, they cannot be quantified as was done for tangible sub-criteria in section 5.5.2.

Intangible (qualitative) sub-criteria are reliant on human judgment with subjective viewpoints and the decision-makers will have diverse opinions regarding the alternatives. Therefore, in order to attain a more consistent outcome, a group decision method is used. The Centre for Quality Promotion and Assurance has a panel of four evaluators (D₁, D_2, D₃ and D₄)that will be responsible for grading each academic in a department.

The panel decided to use a linguistic assessment scale from Table 5-3 for the alternatives and the sub-criteria. These scales are attained from a triangular fuzzy ratio scale indicated in Figure 5- 2.

Linguistic term Membership function Very weak (VW) (1,1,3) or 1̃

Weak (W) (1,3,5) or 3̃

Average (A) (3,5,7) or 5̃

Good (G) (5,7,9) or 7̃

Very Good (VG) (7,9,9) or 9̃

¹

0 X

1 3 5 7 9

Figure 5-2: Triangular fuzzy ratio scales

Table 5-3: Linguistic terms for alternatives

90

The following Java method was used to convert the linguistic terms from Figure 5-3 into fuzzy numbers.

/**

* Converts a linguistic code to its corresponding fuzzy.FuzzyNumber * @param code Linguistic term code

* @return The fuzzy.FuzzyNumber corresponding to the linguistic code */

public FuzzyNumber linguisticToFuzzy(String code) {

switch(code) {

case "VW":

return new FuzzyNumber(1,1,3);

case "W":

return new FuzzyNumber(1,3,5);

case "A":

return new FuzzyNumber(3,5,7);

case "G":

return new FuzzyNumber(5,7,9);

case "VG":

return new FuzzyNumber(7,9,9);

}

throw new IllegalArgumentException("Invalid linguistic code used");

}

The decisions of the panel regarding the intangible sub-criteria for criteria C1 are indicated in Table 5-4.

A_i C₁₁ C₁₂

D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄

A₁ G VG G G G VG VG G

A₂ A G G A G VG G G

A₃ G VG G VG G VG VG VG

By using equations 3.2 to 3.5, the four decision-makers sub-scores for C11 and C12 are integrated.

A detailed method for attaining the sub-score for C11 with regard to alternative A1 is presented.

The same method will apply when calculating all the other sub-scores. The four decision-makers choices for C11 with regard to A1 is G, VG, G and G respectively are shown in Table 5-4. These linguistic values are equivalent to the fuzzy numbers indicated in Figure 5.2 as follows: G1111 = (5, 7, 9), G₁₁₁₂ = (7, 9, 9), G₁₁₁₃ = (5, 7, 9) and G₁₁₁₄ = (5, 7, 9) respectively. By applying equation 3.3, that is, 𝐿_𝑖𝑗𝑘 = min(𝐿_{𝑖𝑗𝑘𝑝}), the following is attained: 𝐿₁₁₁ = min(5, 7, 5, 5) = 5. By

Table 5-4: Grades of each academic with regard to C₁₁ and C₁₂

91 applying equation 3.4, that is, 𝑀_𝑖𝑗𝑘 = ^{(∑ 𝑀𝑖𝑗𝑘𝑝}

𝑡

𝑝=1 )

𝑝 the following is atained: 𝑀₁₁₁ =

(∑^𝑡 𝑀_{𝑖𝑗𝑘𝑝}

𝑝=1 )

𝑝 =

7+9+7+7

4 = ³⁰₄ = 7.5. By applying equation 3.5, that is, 𝑈_𝑖𝑗𝑘 = max(𝑈_{𝑖𝑗𝑘𝑝}), the following is attained: 𝑈₁₁₁ = max(𝑈_{𝑖𝑗𝑘𝑝}) = max(9, 9, 9 ,9) = 9. The fuzzy number attained is therefore 𝐺₁₁₁

= (5, 7.5, 9). All other sub-scores can be attained in the same way and the results for C11 and C12

are depicted in Table 5-5.

A_i C₁₁ C₁₂

A₁ (5, 7.5, 9) (5, 8, 9)

A₂ (3, 6, 9) (5, 7.5, 9)

A₃ (5, 8, 9) (5, 8.5, 9)

The following Java methods were used to convert the linguistic values into fuzzy numbers:

/**

* Convert an array of qualitative values into a fuzzy.FuzzyNumber * @param decisions Array of decisions which are linguistic terms * @return fuzzy.FuzzyNumber

*/

public FuzzyNumber qualitativeToFuzzy(String [] decisions) {

double minArray[] = new double[decisions.length];

double geoMeanArray[] = new double[decisions.length];

double maxArray[] = new double[decisions.length];

for(int i=0;i<decisions.length;i++) {

// Converting the linguistic term to a Fuzzy number, then extract each component

minArray[i] = linguisticToFuzzy(decisions[i]).getMin();

geoMeanArray[i] = linguisticToFuzzy(decisions[i]).getMean();

maxArray[i] = linguisticToFuzzy(decisions[i]).getMax();

}

return new FuzzyNumber(getMinValue(minArray),

getAverage(geoMeanArray), getMaxValue(maxArray));

} /**

* Determines the maximum value from the given array of values * @param values Array of values

* @return Maximum value in the values array */

public double getMaxValue(double [] values) {

Arrays.sort(values);

Table 5-5: Sub-scores of each academic with regard to C11 and C12

92 return values[values.length-1];

} /**

* Determines the minimum value from the given array of values * @param values Array of values

* @return Minimum value in the values array */

public double getMinValue(double [] values) {

Arrays.sort(values);

return values[0];

} /**

* Calculates the geometric mean of a given array * @param data Array of values

* @return Geometric mean */

public double geometricMean(double[] data) { if (data.length == 0)

return 0;

// calculates the product double geoMean = 1.0;

for (int i = 0; i < data.length; i++) { geoMean *= data[i];

}

// raise the product to 1/(the number of elements in data) geoMean = Math.pow(geoMean, 1.0 / (double) data.length);

// rounding off to one decimal place

geoMean = (double) Math.round(geoMean * 10) / 10;

return geoMean;

}

The decisions of the panel regarding the intangible sub-criteria for criteria C2 are indicated in Table 5-6.

A_i C₂₂ C₂₃ C₂₄ C₂₅ C₂₆

D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ A₁ A G G W VG G G VG W A G G A VG G G VG W G G A₂ G G VG VG W A VG G G G A G A G VG A G G W A A₃ VG A G A G VG A A W G G VG G G A G G VG W G

By using equations 3.2 to 3.5, the four decision-makers sub-scores for C22,C23,C24, C25 and C26

are integrated. The method is identical to the method used to attain the sub-scores for C11 and Table 5-6: Grades of each academic with regard to C22,C23, C24, C25 and C26

93

C₁₂ (see computations above). The sub-scores for criteria C₂ are therefore presented without showing the calculations. These sub-scores are indicated in Table 5-7.

The decisions of the panel regarding the intangible sub-criteria for criteria C3 are indicated in Table 5-8.

A_i C₃₁ C₃₄ C₃₅

D1 D2 D3 D4 D1 D2 D3 D4 D1 D2 D3 D4

A₁ A VG A G W A G G A G G A A₂ VG G G G G A G G VG A G G A₃ G VG G A A G A A G VG G A

By using equations 3.2 to 3.5, the four decision-makers sub-scores for C₃₁, C₃₄, and C₃₅ are integrated. The sub-scores are presented in Table 5-9.

The decisions of the panel regarding the intangible sub-criteria for criteria C4 are indicated in Table 5-10.

A_i C₂₂ C₂₃ C₂₄ C₂₅ C₂₆

A₁ (1, 5.5, 9) (5, 8, 9) (1, 5.5, 9) (3, 7, 9) (1, 6.5, 9) A₂ (5, 8, 9) (1, 6, 9) (3, 6.5,9) (3, 6.5, 9) (1, 5.5, 9) A₃ (3, 6.5, 9) (3, 6.5, 9) (1, 6.5, 9) (3, 6.5, 9) (1, 6.5, 9)

A_i C₃₁ C₃₄ C₃₅

A₁ (3, 6.5, 9) (1, 5.5, 9) (3, 6, 9) A₂ (5, 7.5, 9) (3, 6.5, 9) (3, 7, 9) A₃ (3, 7, 9) (3, 5.5, 9) (3, 7, 9)

Table 5-7: Sub-scores of each academic with regard to C22,C23, C24, C25 and C26

Table 5-8: Grades of each academic with regard to C₃₁,C₃₄ and C₃₅

Table 5-9: Sub-scores of each academic with regard to C₃₁,C₃₄ and C₃₅

94

A_i C₄₂ C₄₃

D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ A₁ A G G A G G A A A₂ G VG G G G VG G A A₃ A W G A W A A A

By using equations 3.2 to 3.5, the four decision-makers sub-scores for C42 and C43 are integrated.

These sub-scores are presented in Table 5-11.

The decisions of the panel regarding the intangible sub-criteria for criteria C₅ are indicated in Table 5-12.

A_i C₅₁ D₁ D₂ D₃ D₄ A₁ A A G A A2 W A W W A₃ G A G G

By using equations 3.2 to 3.5, the four decision-makers sub-scores for C51 are integrated. These sub-scores are presented in Table 5-13.

A_i C₄₂ C₄₃

A₁ (3, 6, 9) (3, 6, 9) A₂ (5, 7.5, 9) (3, 7, 9) A₃ (1, 5, 9) (1, 4.5, 7)

A_i C₅₁

A₁ (3, 5.5, 9) A₂ (1, 3.5, 7) A₃ (3, 6.5, 9)

Table 5-10: Grades of each academic with regard to C42 and C43

Table 5-11: Sub-scores of each academic with regard to C42 and C43

Table 5-12:Grades of each academic with regard to C₅₁

Table 5-13: Sub-scores of each academic with regard to C51

95

The decisions of the panel regarding the intangible sub-criteria for criteria C₆ are indicated in Table 5-14.

A_i C₆₁ C₆₂ C₆₃ C₆₄ C₆₅

D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ D₁ D₂ D₃ D₄ A₁ G A G G A VG G G G A VG G G G G A G VG G G A₂ W A A W A G G A A G G W W G G A G A W A A₃ VG G VG G G A G G A G VG G VG G G G VG G G G

By using equations 3.2 to 3.5, the decision makers sub-scores for C₆₁, C₆₂, C₆₃, C₆₄ and C₆₅ are integrated. The sub-scores for criteria C₆ are presented in Table 5-15.