Papers by Lavoslav Čaklović
Kineziologija za 21. stoljeće, 1999
Abstract. A fundamental weakness of the Data Envelopment Analysis (DEA) is its weak discriminatio... more Abstract. A fundamental weakness of the Data Envelopment Analysis (DEA) is its weak discrimination in cases when a small number of decision making units are compared. There-fore, in such cases the basic DEA model (optimistic and pessimistic) is used in combination with other methods or additional constraints are added to the model. In this paper, the cross-efficiency method was combined with a self-ranking procedure which uses the Po-tential Method (PM). The results are similar to those of Wang and others [15] based on the Geometric Mean (GM). Another interesting result is that a preorder “domination by inputs ” and ordinal ranking derived from it produce results very close to those obtained by GM and PM.
Advances in Methodology and Statistics, 2005
In this article a notion of stochastic flow associated to stochastic preference is introduced. It... more In this article a notion of stochastic flow associated to stochastic preference is introduced. It is proved that stochastic flow is a consistent flow if and only if stochastic preference is consistent. If both of them are consistent, the flow and the stochastic preference, then, the normal integral of the flow is the logarithm of value function associated to stochastic preference flow. This means that normal integral of stochastic preference flow, which always exists, can be considered as a generalization of ordinal value function in that context. It is also proved that if flow preference is a weak preference order, then, normal integral of unimodular stochastic flow is a value function. This approach is applied to the data obtained from a web questionnaire when students were asked to give preference flows for certain criteria over the set of their lecturers. In that case the stochastic flow and the group flow generate equivalent ranking. Finally, we calculated the Condorcet's f...
U knjizi je obrađen algebarski pristup simpleks metodi, dualna i primarno-dualna simpleks metoda,... more U knjizi je obrađen algebarski pristup simpleks metodi, dualna i primarno-dualna simpleks metoda, teorem o separaciji sa konacno generirane konuse i njegove posljedice, teoremi dualnosti, metoda unutrasnje tocke (centralni put) te analiza osjetljivosti.
Knjiga se bavi samim pocecima odlucivanja kako u psihologiji tako i u matematici, s naglaskom na ... more Knjiga se bavi samim pocecima odlucivanja kako u psihologiji tako i u matematici, s naglaskom na matematiku, a redoslijed iznosenja materijala donekle slijedi povijesni razvoj misli. Sredisnje mjesto među aksiomima teorije ocekivane korisnosti zauzima aksiom nezavisnosti, koji na stanovit nacin definira racionalnost i racionalnog donositelja odluke. Od novijih neutilitaristickih pristupa spomenuta je Saatyjeva metoda svojstvenog vektora i detaljno je razrađena matematicka osnova za njeno razumijevanje (Perronov teorem). Teorija potencijala, razvijena od strane autora knjige, također spada u neformalne metode koje se ne zasnivaju na nekom aksiomatskom sustavu. U Dodatku su opisane neke prakticne procedure koje preciziraju pojedine faze odlucivanja. Dan je popis i opis i drugih metoda koje nisu spominjane u knjizi, a sve su ilustrirane na jednom primjeru.
Mathematical Communications, 2001
Here we propose a new ranking method for AHP, Potential method, based on Graph theory approach. T... more Here we propose a new ranking method for AHP, Potential method, based on Graph theory approach. This method works fine in the case when AHP-matrix is not complete. It makes easy to define an index of inconsistency of given data in a very natural way. The main purpose of this article is to examine the behaviour of rank order under successive neglecting of data in AHP-matrix preserving the graph connectedness. As we will show, the same ranking order is obtained for complete and incomplete AHP-matrix.
We are going to discuss methodological aspects of deriving clinical decision rules with the stres... more We are going to discuss methodological aspects of deriving clinical decision rules with the stress on the sensibility of the results. Evidence or sense is bringing focus on data analysis or judgment. Is it possible to use clinical decision rules to deliver patient-centered care is going to be discussed, as well as preference of course of action vs. probability of outcome as possible decision support format. Finally, assessing usefulness of medical information and sensibility of decision rules is going to be discussed.
Periodicum Biologorum, 2006
This paper identifies the values and value principles applied in evaluation of natural resources.... more This paper identifies the values and value principles applied in evaluation of natural resources... The results obtained using the potential method and the eigenvector method coincided considerably, suggesting that the use of the two methods results in similar values for an analyzed forest entity. .... The method supports modern evaluation trends in forestry, using available computer program for developing dynamic models.
Glasnik Matematicki
The first order Hamiltonian system is considered with T-periodic Hamiltonian that is sub-quadrati... more The first order Hamiltonian system is considered with T-periodic Hamiltonian that is sub-quadratic at infinity. Two kinds of sub-quadraticity are considered. The existence of T-periodic solution is proved using variational methods.
Mathematical model of a goal-oriented thinking with feedback is described. Basic notions: decisio... more Mathematical model of a goal-oriented thinking with feedback is described. Basic notions: decision graph, feed-back hierarchy and self-duality are introduced and explained. A source of the conflict in our approach is the ignorance about the importance of decision maker's goals. In contrast to Shar, Simonson & Tversky [4] and Deutsch [2] conflict resolution is modeled as a problem of finding a fixed point of a self-assessment operator, i.e. without adding or removing any decision element from decision hierarchy.
A common procedure in Multi-Criteria Decision Anal- ysis is pairwise comparison of alternatives w... more A common procedure in Multi-Criteria Decision Anal- ysis is pairwise comparison of alternatives with respect to some criteria. The result of this comparison, whether exact or subjec- tive, is a weight associated to the pair of alternatives measured on some scales. Some authors organize their results in pairwise com- parison matrix as a base for further calculation. Potential Method (PM), introduced here, uses a preference ow F, dened on a di- rected graph, which generated a 'value function' called potential on the set of alternatives. Each criterion, or decision maker, has his own preference ow and MCDM based on PM preferes these ows (graphs) rather then potentials in aggregation process. Preference ow can be complete (all pairs are evaluated) or in- complete (missing data). In both cases potential can be calculated as a solution of normal equation associated to the preference ow.
The fundamental weakness of a Data Envelopment Method (DEA) is its weak discrimination in cases w... more The fundamental weakness of a Data Envelopment Method (DEA) is its weak discrimination in cases when smaller numbers of Decision Making Units (DMU) have been compared. Therefore in such cases the basic DEA model is used in combination with other methods or additional constraints are added to the model. In this paper, the Cross-e-ciency method has been combined with the Potential Method (PM).
Glasnik matematicki, 2011
We consider sublinear Sturm-Liouville problem −u ′′ + ψ(t)|u| p−1 u = λu, p > 1, u(0) = u(1) = 0 ... more We consider sublinear Sturm-Liouville problem −u ′′ + ψ(t)|u| p−1 u = λu, p > 1, u(0) = u(1) = 0 where ψ is positive and continuous. Using the Nehari variational technique and critical point theory we prove that for each n ∈ N there is unique (up to the sign) n-nodal solution of the b.v.p. which is the critical point of a restricted functional associated to the problem.
Glasnik Matematicki, 2003
The first order dynamical systemż = F (t, z) is considered, where F is T-periodic in time and sub... more The first order dynamical systemż = F (t, z) is considered, where F is T-periodic in time and sub-linear at infinity. Existence of T-periodic solution is proved, using degree theory, and applications to non-convex Hamiltonian systems is given as well.
Although PM was basically created to treat subjective comparisons, given exact values it can be c... more Although PM was basically created to treat subjective comparisons, given exact values it can be converted to the Potential Method flow. A new feature of PM is a parameter called Flow Norm which helps to treat problems where each criterion has its own measurement scale. Complex hierarchical structures and problems modelled by decision tables can be handled. Incomplete data, such as incomplete belief is considered as well. To illustrate flexibility and universality of PM we compare it with PROMETHEE and Yang’s Evidential Reasoning method.
Mathematical Communications, Oct 15, 2014
This paper examines an alternative method for analyzing a collection of Likert items in the multi... more This paper examines an alternative method for analyzing a collection of Likert items in the multi-criteria decision framework. Likert items are compared in pairs and organized in a set of weighted digraphs aggregated according to the Potential Method rules. In combination with Factor Analysis this approach gives respondents preferences on the scale which approximates a measurable value function. As an application of the proposed methodology, we examine a potential set of incentives and explore a degree to which they would be accepted by the industry. We use the Potential Method to elicit firms preferences for given incentives and seek to explain the difference in these preferences by the firm/market factors. Data is collected through a survey of 190 Croatian enterprises performed in 2002.
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Papers by Lavoslav Čaklović