CORRECTION OF PRIMARY POINTS VIA FUZZY SETS USING

Tudent level of preparedness, based on the use of fuzzy sets. For comparison two methods have been chosen, which are usually used in the exam: scaling method and the method of the Rasch’s logarithm. In particular, the article shows the decisive role of the choice of the scaling function, affecting the accuracy of estimates. The method of fuzzy sets is an adaptive algorithm. Thus, the test results in the form of primary points are used for construction of membership functions of fuzzy sets. We describe the steps of the algorithm, which makes it possible to «tweak» the primary points. 1) The relative frequencies pij appearance points B = j by the decision of the i -th task are calculating, where i =1, ..., M ( M is the number of test’s tasks), j=0,..., max. 2) The membership functions are forming so that the areas of their a curvilinear trapezoid equals to p_ij . 3) The numbers of E_k , k = 0, ..., max, are calculating for each membership function. These numbers are the result of diffusivities for fuzzy sets by the method of severity’s center. 4) Adjustment of the primary point B for the i-th task is made by the formula: . 5) The sum of all «adjusted» points calculates: . 6) Test points ТБ _кор is calculated by using of scaling. The main results of the article are as follows: 1) The method of fuzzy sets in testing enables to improve the accuracy of the classical scaling method, which is currently used in the exam, on average by 2.3 %. 2) However, the method of fuzzy sets in accuracy is worse than the method of Rasch’s logarithm, on average by 0.15 %. 3) Strong dependence of the accuracy of methods on the selection of scaling function is determined: a good choice of function improves the accuracy of the considered methods in 2.5-3 %. 4) Method of Rasch’s logarithm is the most successful method, which does not depend on the choice of the scaling function.

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