An LP-based inconsistency monitoring of pairwise comparison matrices

A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied in the process of filling in the matrix as the decision maker gets automatic feedback. As soon as a serious error occurs among the matrix elements, even due to a misprint, a significant increase in the inconsistency index is reported. The high inconsistency may be alarmed not only at the end of the process of filling in the matrix but also during the completion process. Numerical examples are also provided.

An inconsistency control system based on incomplete pairwise comparison matrices

Incomplete pairwise comparison matrix was introduced by Harker in 1987 for the case in which the decision maker does not fill in the whole matrix completely due to, e.g., time limitations. However, incomplete matrices occur in a natural way even if the decision maker provides a completely filled in matrix in the end. In each step of the total n(n–1)/2, an incomplete pairwise comparison is given, except for the last one where the matrix turns into complete. Recent results on incomplete matrices make it possible to estimate inconsistency indices CR and CM by the computation of tight lower bounds in each step of the filling in process. Additional information on ordinal inconsistency is also provided. Results can be applied in any decision support system based on pairwise comparison matrices. The decision maker gets an immediate feedback in case of mistypes, possibly causing a high level of inconsistency.

Knowledge representation and evaluation an ontology-based knowledge management approach

Competition between Higher Education Institutions is increasing at an alarming rate, while changes of the surrounding environment and demands of labour market are frequent and substantial. Universities must meet the requirements of both the national and European legislation environment. The Bologna Declaration aims at providing guidelines and solutions for these problems and challenges of European Higher Education. One of its main goals is the introduction of a common framework of transparent and comparable degrees that ensures the recognition of knowledge and qualifications of citizens all across the European Union. This paper will discuss a knowledge management approach that highlights the importance of such knowledge representation tools as ontologies. The discussed ontology-based model supports the creation of transparent curricula content (Educational Ontology) and the promotion of reliable knowledge testing (Adaptive Knowledge Testing System).