Páros összehasonlításon alapuló pontozási eljárások monotonitása: önkonzisztencia és önkonzisztens monotonitás. Adalékok a pontozási eljárások axiomatikus tárgyalásához = Monotonicity of paired comparison-based ranking methods: self-consistency and self-consistent monotonicity. Contributions to an axiomatic analysis of scoring methods

A cikk a páros összehasonlításokon alapuló pontozási eljárásokat tárgyalja axiomatikus megközelítésben. A szakirodalomban számos értékelő függvényt javasoltak erre a célra, néhány karakterizációs eredmény is ismert. Ennek ellenére a megfelelő módszer kiválasztása nem egy-szerű feladat, a különböző tulajdonságok bevezetése elsősorban ebben nyújthat segítséget. Itt az összehasonlított objektumok teljesítményén érvényesülő monotonitást tárgyaljuk az önkonzisztencia és önkonzisztens monotonitás axiómákból kiindulva. Bemutatásra kerülnek lehetséges gyengítéseik és kiterjesztéseik, illetve egy, az irreleváns összehasonlításoktól való függetlenséggel kapcsolatos lehetetlenségi tétel is. A tulajdonságok teljesülését három eljárásra, a klasszikus pontszám eljárásra, az ezt továbbfejlesztő általánosított sorösszegre és a legkisebb négyzetek módszerére vizsgáljuk meg, melyek mindegyike egy lineáris egyenletrendszer megoldásaként számítható. A kapott eredmények új szempontokkal gazdagítják a pontozási eljárás megválasztásának kérdését. _____ The paper provides an axiomatic analysis of some scoring procedures based on paired comparisons. Several methods have been proposed for these generalized tournaments, some of them have been also characterized by a set of properties. The choice of an appropriate method is supported by a discussion of their theoretical properties. In the paper we focus on the connections of self-consistency and self-consistent-monotonicity, two axioms based on the comparisons of object's performance. The contradiction of self-consistency and independence of irrel-evant matches is revealed, as well as some possible reductions and extensions of these properties. Their satisfiability is examined through three scoring procedures, the score, generalised row sum and least squares methods, each of them is calculated as a solution of a system of linear equations. Our results contribute to the problem of finding a proper paired comparison based scoring method.

Incomplete pairwise comparison matrices and weighting methods

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the property linear order preservation if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.

Comparison of different space indexing methods for ecological evaluation of urban openspaces

Nowadays we meet many different evaluation methods regarding the ecological performance of green surfaces and parks. All these methods are extremely valuable in determining how well a green surface performs from ecological aspect and to what extent the environment were damaged if these sites would be built or would be developed any other way causing reduction of green surfaces. The goal of the article is to clarify the differences between two evaluation methods (GSI – Green Space Intensity, BARC – Biological Activity Rate Calculation) suitable for urban green infrastructure analysis and to see if any significant difference can be observed evaluating the same site by these methods. Our research sites are in Budapest and their sizes vary between 2,5-8 acres. The most important aspects of site analysis are the following: size and boundaries of the park, existence or lack of water features, the characteristics of their surfaces and the complexity of vegetation. We summarize the data of the site analysis in tables, make a summarizing diagram for visual representation and draw conclusions from the results. As a final step, we evaluate how these two evaluation systems relate to urban open space developments.

Comparison of Explicit and Implicit Methods of Cross-Cultural Learning in an International Classroom

The paper addresses a gap in the literature concerning the difference between enhanced and not enhanced cross-cultural learning in an international classroom. The objective of the described research was to clarify if the environment of international classrooms could enhance cross-cultural competences significantly enough or if additional focus on cross-cultural learning as an explicit objective of learning activities would add substantially to the experience. The research question was defined as “how can a specific exercise focused on cross-cultural learning enhance the cross-cultural skills of university students in an international classroom?”. Surveys were conducted among interna- tional students in three leading Central-European Universities in Lithuania, Poland and Hungary to measure the increase of their cross-cultural competences. The Lithuanian and Polish classes were composed of international students and concentrated on International Management/Business topics (explicit method). The Hungarian survey was done in a general business class that just happened to be international in its composition (implicit method). Overall, our findings prove that the implicit method resulted in comparable, somewhat even stronger effectiveness than the explicit method. The study method included the analyses of students’ individual increases in each study dimension and construction of a compound measure to note the overall results. Our findings confirm the power of the international classroom as a stimulating environment for latent cross-cultural learning even without specific exercises focused on cross-cultural learning itself. However, the specific exercise did induce additional learning, especially related to cross-cultural awareness and communication with representatives of other cultures, even though the extent of that learning may be interpreted as underwhelming. The main conclusion from the study is that the diversity of the students engaged in a project provided an environment that supported cross-cultural learning, even without specific culture-focused reflections or exercises.