Open AccessAll modern e-learning systems and standards support a module-based structure of the training materials. It means that independent and rather closed modules of training material form the courses of study. As compared to the unstructured arrangement of training material, the modulebased structure has a number of apparent advantages. In particular, it is highly flexible and allows a reuse of educational modules as a part of various courses and trainings.
The main cohort of theoretical researches in synthesis of e-learning course structure concerns a problem of designing a module-based structure. The important problem of rational ordering of the curriculum modules is investigated insufficiently. This is the second article of the cycle related to the rational ranking of the e-course modules. The work supposes that initial information is set as a fuzzy graph of preferences, which formalizes expert’s subjective information on precedence of module pairs. It is required to find a linear order, which is a good approximant of the initial structure of preferences.
The article offers a simple way for transforming values of membership function to lead an adjacency matrix of the fuzzy graph to a probabilistic calibration condition. It investigates the rational ordering methods capable to process matrixes of pair comparisons with probabilistic calibration and justifies an application of the ordering method, which uses a dominating function as a ranking factor. The proposed way to solve the task is based on decomposition of a fuzzy set into the levels and generations of a set of the minimum level that possesses acyclic properties. It is shown that this task is reduced to the search of such a shift of tops, which has the smallest possible potential among all the shifts of objects.