Nauka i Obrazovanie (Jan 2015)
Forming of Students’ Academic Achievement Integral Indicator Based on Aggregation Operators
Abstract
This work concerns the problem to form students’ academic achievement integral indicator using aggregation of ratings of individual disciplines based on expert knowledge.The goal is to improve the objectivity and accuracy of students’ academic achievement integral indicator. The current practice of above-mentioned integral indicator forming faces a number of challenges. And the need to make decisions based on fuzzy and subjective factors is the most important of them. Traditional approaches to forming the students’ academic achievement integral indicator include weighted arithmetic mean as aggregation operators.No additive aggregation operator including arithmetic mean allows us to formalize interdependence or mutual dependence of evaluations. Therefore, traditional approaches cannot be applied to formalize expert knowledge about the mutual dependence of evaluations. Apparatus of fuzzy measures and integrals is suitable for the formalization of such phenomena.An approach to formalization of expert knowledge based on application of fuzzy measures and Choquet integral as an aggregation operator was proposed.Method based on fuzzy measures’ entropy maximization was chosen to identify fuzzy measures under the proposed approach. This method allows us to obtain the least specific fuzzy measure which is limited by means of expert preferences.It is noted that during fuzzy measure identification there may be situations which suggest no solution.To prevent such situations it is necessary to work carefully on expert training of integral indicator formation using fuzzy measures and Choquet integral.Proposed approach to expert knowledge formalization is not so far mentioned in wellknown publications.Experimental formation of integrated academic achievement indicators using this method showed that resulting aggregation operator allows to formalize expert knowledge which is not possible to formalize using traditional approaches.The described approach to formation of integrated academic achievement indicators is perspective in terms of reducing the subjectivity in taking decision on enrolling students for certain vacancies on a competitive basis.
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