Natalja Kosareva

Comparison of accuracy in ranking alternatives performing generalized fuzzy average functions

Abstract The paper defines the notions of point, interval and triangular intuitionistic fuzzy numbers expressing the degree of membership and non-membership in the fuzzy set. The generalized fuzzy weighted average function is introduced according to operation rules on intuitionistic fuzzy numbers. In special cases, the generalized weighted average coincides with an arithmetic average or a geometric average. The generalized fuzzy weighted average function could be applied for solving problems in multiple criteria decision making. Research on the stability of the generalized weighted averaging operator of ranking alternatives was performed applying the Monte Carlo method. The aim of the conducted research is to establish the types of intuitionistic fuzzy numbers and the exponent values of the generalized weighted averaging operator having the least error probabilities considering alternatives ranking. Computations were performed involving 3, 4 and 5 experts. In the case of 5 experts, initial decision matric...

Mathematical modelling of forecasting the results of knowledge testing

Abstract In this paper a mathematical model for obtaining probability distribution of the knowledge testing results is proposed. Differences and similarities of this model and Item Response Theory (IRT) logistic model are discussed. Probability distributions of 10 items test results for low, middle and high ability populations selecting characteristic functions of the various difficulty items combinations are obtained. Entropy function values for these items combinations are counted. These results enable to formulate recomendations for test items selection for various testing groups according to their attainment level. Method of selection of a suitable item characteristic function based on the Kolmogorov compatibility test, is proposed. This method is illustrated by applying it to a discreet mathematics test item.

Multiple criteria decision-making KEMIRA-M method for solution of location alternatives

Abstract Choice of location in many cases is a key factor setting up a new business object. In this article the KEMIRA-M method is proposed to establish priority of criteria and determine criteria weights. Weighted sum of criteria values was applied for ranking the alternatives. This technique is useful if the evaluation criteria naturally consist of several logically explained groups of criteria. Method requires much less initial information and is based upon searching the solution of optimisation problem. KEMIRA-M is applied for the case study of construction site for non-hazardous waste incineration plant in Vilnius City.

A Numerical Experiment on Mathematical Model of Forecasting the Results of Knowledge Testing

Abstract In this paper the new approach to the forecasting the results of knowledge testing, proposed earlier by authors, is extended with four classes of parametric functions, the best fitting one from which is selected to approximate item characteristic function. Mathematical model is visualized by two numerical experiments. The first experiment was performed with the purpose to show the procedure of selecting the most appropriate item characteristic function and adjusting the parameters of the model. Goodness-of-fit statistic for detecting misfit of the selected model is calculated. In the second experiment a test of 10 items is constructed for the population with latent ability having normal distribution. Probability distribution of total test result and test information function are calculated when item characteristic functions are selected from four classes of parametric functions. In the next step it is shown how test information function value could be increased by adjusting parameters of item cha...

Entropy–KEMIRA Approach for MCDM Problem Solution in Human Resources Selection Task

Entropy–KEMIRA approach is proposed for criteria ranking and weights determining when solving Multiple Criteria Decision-Making (MCDM) problem in human resources selection task. For the first time the method is applied in the case of three groups of criteria. Weights are calculated by solving optimization problem of maximizing the number of elements, which are “best” according to all three criteria, and minimizing the number of “doubtful” elements. The algorithm of problem solution is presented in the paper. The numerical experiment with three groups of evaluation criteria describing 11 life goals was accomplished.

Expert Estimates Averaging by Constructing Intuitionistic Fuzzy Triangles

AbstractThe problem of ranking (sorting) of m alternatives is considered when experts evaluate each alternative according to k criteria. Functions of arithmetic and geometric averages are constructed for decision making. We present a generalization of this scheme when there are evaluation matrices of several experts and this information is aggregated in the form of triangular intuitionistic fuzzy numbers. Fuzzy triangles were constructed with different uncertainty levels, experts decision matrices and the number of experts varied from 2 to 5. Moreover, method for construction of experts decision probability matrices is proposed in the paper. Ranking results obtained by performing Monte Carlo simulations. Probabilities of errors are compared for arithmetic, geometric, fuzzy arithmetic and fuzzy geometric averages.