Technological Evaluation and Optimization of E-Learning Systems Components - E-Infrastructures and Technologies for Lifelong Learning - page 169

Table 7. Conversion of linguistic variables into
triangular fuzzy numbers (TFNs)

as to ensure the comprehensiveness of the tool
avoiding the overlap of the criteria.

Linguistic variables TFN

3.2. Multiple Criteria Evaluation
and Optimization of E-Learning
Systems Components

Excellent (0.700, 0.850, 1.000)

Good (0.525, 0.675, 0.825)

Fair (0.350, 0.500, 0.650)

Poor (0.175, 0.325, 0.475)

3.2.1. Ratings of the Quality
Evaluation Criteria

Bad (0.000, 0.150, 0.300)

There is a number of methods to explore the level
of customization offered in learning software.
The authors suggest using the multiple criteria
evaluation method of the learning software qual-
ity that employs an experts' utility function (see
Equation 3 below) and includes evaluation criteria
of alternatives, their ratings (values) and weights.
The evaluation criteria used in this method
should conform to the software engineering
principle based on the evaluation criteria division
to 'internal quality' and 'quality in use' criteria.
The scientists who have explored the quality of
software consider that there exists no simple way to
evaluate the functionality characteristics of the in-
ternal quality of software. According to Gasperovic
and Caplinskas (2006), it is a hard and complicated
task that requires relatively high overhead in terms
of both time and labour. According to Zavadskas
and Turskis (2008), each alternative in the multi-
criteria decision making problem can be described
by a set of criteria. Criteria can be qualitative and
quantitative. Usually they have different units of
measurement and a different optimization direction.
Also, following the multiple criteria evaluation
method , we also need LORs and VLEs evaluation
criteria ratings (values).
The wide-used measurement criteria of the
decision attributes quality are mainly qualitative
and subjective. In this context, decisions are often
expressed in natural language and evaluators are
unable to assign exact numerical values to different
criteria. Assessment can be often performed by
linguistic variables: 'bad', 'poor', 'fair', 'good'
and 'excellent'. These values are imprecise and

uncertain; they are commonly called fuzzy values.
Integrating these different judgments to obtain a
final evaluation is not evident. Therefore, Ounaies,
Jamoussi & Ben Ghezala (2009) suggest using
the fuzzy group decision making theory to obtain
final assessment measures.
First, linguistic variable values are mapped into
triangular fuzzy numbers (l, m, u) as in Table 7.
After the defuzzification procedure which
converts the global fuzzy evaluation results, ex-
pressed by a TFN (l, m, u) to a non-fuzzy value
E, the following equation has been adopted:

E = [ (u - 1) + (m - 1) ] / 3 + 1 (1)

The non-fuzzy values E for all the aforemen-
tioned linguistic variables calculated according to
the Equation (1) are presented in Table 8.

3.2.2 Experts' Additive Utility Function

If we want to evaluate (or optimize) the technologi-
cal quality of learning software (e.g. VLEs) for
particular learner needs (i.e. to personalize his/her
learning process in the best way in conformance
with the prerequisites, preferred learning speed
and methods, etc.), we should use the experts'
additive utility function together with the weights
of evaluation criteria.
The weight of the evaluation criterion reflects
the experts' opinion on its importance level in
comparison with the other criteria for an individual
learner/user.