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Eugenijus Kurilovas et al.
Then hierarchical synthesis is used to weight the eigenvectors by the weights of the criteria and the
sum is taken over all weighted eigenvector entries corresponding to those in the next lower level of
the hierarchy:
In order to check the correctness of calculation, having made all the pair-wise comparisons the
eigenvalue λ max is calculated:
The method of consecutive triple application of AHP consists of application of aforementioned AHP in
three consistent stages:
Establishment of comparative weights of three different groups of LS quality criteria and weights a
i of all quality criteria;
Establishment of comparative weights of ‘internal quality’ and ‘quality in use’ criteria groups from
activist learner point of view; and
Establishment of final weights of quality criteria from activist learners point of view by application
of AHP once again only for ‘quality in use’ criteria.
3.2.2 Use of triangular and trapezoidal fuzzy numbers to establish values of quality criteria
The widely used measurement criteria of the decision attributes’ quality are mainly qualitative and
subjective. Decisions in this context are often expressed in natural language, and evaluators are
unable to assign exact numerical values to the 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 (Kurilovas and Serikoviene 2010ab).
Therefore, the authors have proposed to use fuzzy group decision making theory (Ounaies et. al.
2009) to obtain final assessment measures. The fuzzy numbers are: (1) triangular fuzzy numbers, (2)
trapezoidal fuzzy numbers, and (3) bell-shaped fuzzy numbers (Zhang Li Li and Cheng De Yong
1992, Kurilovas et. al., 2011). In the presented paper, the authors use triangular (Fig. 3) and
trapezoidal (Fig. 4) fuzzy numbers for evaluating quality of LS and their suitability to activist learner
profile:
Figure 3: Triangular fuzzy numbers Figure 4: Trapezoidal fuzzy numbers
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