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October 2007 Volume 10 Number 4 - Educational Technology ...

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Q.2<br />

Q.n<br />

…<br />

~<br />

Q.13 F g<br />

13<br />

13<br />

~<br />

Q.14 F g<br />

14<br />

14<br />

~<br />

Q.21 F g<br />

21<br />

21<br />

~<br />

Q.22 F g<br />

22<br />

22<br />

~<br />

Q.23 F g<br />

23<br />

23<br />

~<br />

Q.24 F g<br />

24<br />

24<br />

…<br />

…<br />

~<br />

Q.n1 F g<br />

n1<br />

n1<br />

~<br />

Q.n2 F g<br />

n2<br />

n2<br />

~<br />

Q.n3 F g<br />

n3<br />

n3<br />

~<br />

Q.n4 F g<br />

n4<br />

n4<br />

…<br />

Total mark =<br />

In the generalized vague grade sheet shown in Table 9, each question Q.i consists of four sub-questions, i.e., Q.i1,<br />

Q.i2, Q.i3 and Q.i4. For all j = 1, 2, 3, 4 and for all i, gij is the derived letter grade by the proposed vague evaluation<br />

method VEM of the awarded vague mark F ij<br />

~ with respect to the sub-question Q.ij, and mi is the derived mark<br />

awarded to the question Q.i,<br />

1 4<br />

mi = × T (Q.i) × ~<br />

∑ [ K ( gij<br />

) × H ( w,<br />

Fij)],<br />

(13)<br />

400<br />

j=<br />

1<br />

and<br />

n<br />

∑<br />

i=<br />

1<br />

Total Mark = m .<br />

i<br />

where T(Q.i) denotes the mark allotted to Q.i in the question paper, gij denotes the derived letter grade awarded to<br />

Q.i, and K(gij) denotes the derived grade-point of the letter grade gij based on the index of optimism λ determined by<br />

the evaluator, whereλ ∈[0, 1], H(W ~ , ij F~ ) is the maximum value among the values of H( E ~ , ij F~ ), H(V ~ , ij F~ ),<br />

H(G ~ , ij F~ ), H( S ~ , ij F~ ) and H(U ~ , ij F~ ), W ~ ∈{ E ~ ,V ~ ,G ~ , S ~ ,U ~ }, such that the derived letter grade awarded to the<br />

question Q.ij is gij, 1 ≤ j ≤ 4, and 1 ≤ i ≤ n. If 0 ≤λ < 0.5, then the evaluator is a pessimistic evaluator. Ifλ = 0.5, then<br />

the evaluator is a normal evaluator. If 0.5

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