Abstract: There are many approaches to obtain the numerical solution of the curvature driven level set equation [7]. They are based on the finite differences method [7], or the finite element method [3] or the finite volume method [5]. The proposed numerical scheme uses the so called discrete duality finite volumes as in [1].

Keywords: curvature driven level set equation; discrete duality finite volume method

Abstract: In the paper a three dimensional dynamic model of a small open economy, describing the development of net real national income, real physical capital stock and the expected exchange rate of the near future, which was introduced by T. Asada in [1], is analysed under flexible exchange rates. We study the question of the existence of business cycles. Sufficient conditions for the existence of a pair of purely imaginary eigenvalues with the third one negative in the linear approximation matrix of the model are found. For the existence of business cycles and their properties the structure of the bifurcation equation of the model is very important. Formulae for the calculation of the bifurcation coefficients in the bifurcation equation of the model are derived. Theorem on the existence of business cycles in a small neighbourhood of the equilibrium point is presented.

Keywords: dynamical model; matrix of linear approximation; eigenvalues; bifurcation equation; business cycle

Abstract: An alternative approach to testing linearity against Markov-switching type nonlinearity is proposed. The main problem of the classical testing via the likelihood ratio test is that the test statistic does not have a standard distribution. Therefore, time-consuming simulations must be carried out. Instead of the classical test we suggest using Hamilton’s dynamic specification test for the validity of Markov assumptions. We show that this new approach provides much faster calculations. With the same idea we calculate the test for remaining non-linearity to compare 2-regime with 3-regime models. We compare these two approaches with 100 selected real time series from economy and finance.

Keywords: Markov-switching model; Markov assumptions; testing linearity, dynamic specification test

Abstract: The autocorrelation function describing linear dependence is not suitable for the description of the residual dependence of regime-switching models. Therefore, we would like to investigate the description of this dependence with a ‘k-lag auto-copula’, which is a 2-dimensional joint distribution function of the bivariate random vector (Yt , Yt−k ) of time lagged values of random variables that generate time series (in the analogy of the autocorrelation function of stationary time series). In this contribution, we will describe the dependence of time lagged residuals of SETAR models by means of copulas, and we will test the independence of these residuals.

Keywords: time series; regime-switching models; residuals; autocopula; product copula; goodness-of-fit tests for autocopulas

Keywords: Cayley graph; group; degree; diameter

Abstract: The Choquet integral plays an important role in models of multiple criteria evaluation. Compared to the weighted average, the Choquet integral can be used to aggregate partial evaluations of an object even if the criteria are redundant or synergic. In the paper, we employ the Choquet integral for the generalization of the Partial Goals Method. We also discuss the application of the fuzzified Choquet integral to multiple criteria evaluation and propose a new technique for fuzzy measure construction. The theory is demonstrated on an example implemented in a new software capable of dealing with multiple criteria evaluation via the fuzzified Choquet integral.

Keywords: Choquet integral; multiple criteria evaluation; fuzzification; software

Abstract: In order to solve decision making problem we have to compare and rank a finite set of alternatives. In this paper we want to show some approaches to creating the preference structure (ranking) of alternatives. These approaches lead us to use chosen multicriteria decision methods and aggregation operators. ARRA (Academic ranking and rating agency) uses one fixed way to create a ranking of public universities and their faculties. In this paper many more approaches to creating such rankings (or preference structures) of alternatives are discussed and the results are compared.

Keywords: Alternative; preference structure; multicriteria method; aggregation operator

Abstract: In the paper we describe the development process of the academic staff performance evaluation model for Palacky University in Olomouc (Czech Republic). Various alternatives of the mathematical solution are discussed. All the models share the same basic idea – we evaluate the staff member’s performance in the area of Pedagogical Activities and in the area of Research and Development. The input data for the models is obtained from structured forms containing information about all the activities performed by a current staff member in the respective year. We require an aggregated piece of information concerning the yearly performance of a particular staff member at a current work position (achievement of standard performance, achievement of excellence, etc.). In the first part of the paper we analyse a group of models that share the algorithm for normalized partial evaluations in both areas of interest (Pedagogical Activities, Research and Development); the partial evaluation normalization function is determined by the scores for standard and excellent performance (defined by the evaluator for different work positions and for both areas of interest separately). Models within this group differ by the aggregation operator used to calculate the overall performance evaluation – weighted arithmetic average (WA), OWA, and WOWA. The second part of the paper presents a model where partial evaluations are determined simply as multiples of standard score for the current work position and area of interest, but the aggregation of these partial evaluations is performed by a fuzzy-rule-based system. This fuzzy model is currently being implemented at Palacky University.

Keywords: evaluation; academic staff; aggregation; fuzzy model

Abstract: The aim of this paper is to demonstrate the different possible applications of fuzzy sets in HR management. This project is currently being carried out by the AXIOM SW company, which specializes in the implementation of the Microsoft Dynamics NAV information system. The evaluation of employees is based on multiple criteria evaluations. The criteria are derived from typical competencies of the employees. A competency model has been created for any given role with different normalized weights assigned to various competencies. The evaluation proceeds in the following manner: Firstly, the appointed evaluators fill in a questionnaire indicating to what extent, in their view, the tested employee meets his/her competencies. These evaluations are expressed using fuzzy scales. Normalized weights assigned to the evaluators of any given employee are set based on the intensity of cooperation between the employee and his/her evaluators. The level of fulfilment of each competency by the given employee is calculated as a weighted average of the fuzzy evaluations, conducted by each of his/her evaluators. Then, the overall fulfilment level of the employee’s working role, again as a weighted average of fuzzy numbers, is calculated according to a specified model. This produces an overall evaluation of the employee. The evaluation process is followed by an interview where the employee is informed of his/her evaluation results, the employees gaps are discussed, and possibilities for improvement are proposed.

Keywords: evaluation; fuzzy sets; human resources