Estimating Levels of Learning Outcomes Acquirement Based on Fuzzy Sets, Relations, and Their Compositions

Estimating Levels of Learning Outcomes Acquirement Based on Fuzzy Sets, Relations, and Their Compositions

Aleksandra Mreła (Kazimierz Wielki University in Bydgoszcz, Poland) and Oleksandr Sokolov (Nicolaus Copernicus University in Torun, Poland)
DOI: 10.4018/978-1-7998-3476-2.ch006
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Abstract

New curriculum designers should prepare the set of learning outcomes that will be studied by students, and their acquirement will be verified by teachers. It is not easy to estimate whether students achieved the required learning outcomes even in the range of knowledge and skills, but when the competencies are considered, it becomes harder. Because of the convenience of using the linguistic terms (excellent, poor, good, and so on), it is better to apply fuzzy relations (type 1 if the numbers are chosen or type 2 if the sets are used), which can handle with the linguistic terms better than classical relations. The estimation of the learning outcome's acquirement can be conducted on the bases of a test or tests. For calculating the levels of learning outcome's acquirement, two fuzzy input relations are designed. Experts build one based on their knowledge, and the second one is based on the test results. The output relation, showing levels of learning outcome/outcomes' acquirement, is built with the application of the S-T composition of the first and second relations.
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Background

Presently in Poland, the concept of the European Qualification Framework (EQF) has been introduced in all curricula designed for all levels of education. According to the European Commission, ‘the European Qualifications Framework is a European-wide qualifications framework which joins the qualifications of different EU members together’ (European Qualifications Framework, 2012). One of the main aims of the EQF is to help institutions (among them higher educational institutions, HEIs), employers and individuals understand the qualifications of applicants, university candidates, and get to know their own, respectively. Understanding the applicant’s qualifications is especially important when they come from a different country. Qualification comprehension facilitates acceptance of students to universities and colleges, employment of graduates and reemployment of people already employed. The next aim is to help people get to know their set of qualifications and develop it some of them applying the process of lifelong learning (European Qualifications Framework (EQF), 2012).

Key Terms in this Chapter

T-norm: A function of two fuzzy sets which is equivalent to the intersection of sets in classical logic.

S-Conorm: A function of two fuzzy sets which is equivalent to the union of sets in classical logic.

Learning Outcome: A statement which describes the knowledge, skills, and competencies which students should acquire during the course and teachers should assess their acquirement.

Fuzzy Set: A set, which each element is accompanied by the degree of membership.

Fuzzy Relation: A fuzzy set contained into the Cartesian product of spaces.

S-T-Composition: A function, based on T-norm and S-conorm, for calculating the composition of two fuzzy relations.

Type 2 Fuzzy Relation: A type 2 fuzzy set contained into the Cartesian product of spaces.

Crisp Set: A set, which each element has got the degree of membership 1 and for a complement of this set, each element has got the membership equals 0.

Type 2 Fuzzy Set: A set in which each element is accompanied by type 1 fuzzy set.

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