DOI: 10.7763/IPEDR. 2014. V70. 2

Quality Evaluation of Erasmus Student Mobility Using Fuzzy -

TOPSIS Framework

Bruno Trstenjak 1 and Dzenana Donko 2 1 Dept. of Computer Engineering, Medimurje University of Applied Sciences Cakovec, Croatia

2 Dept. of Computer Science, Faculty of Electrical Engineering, Sarajevo, Bosnia and Herzegovina

Abstract. Fuzzy TOPSIS is one of the sensitive methods for multi-criteria decision making (MCDM). This paper presents the possibility of using fuzzy TOPSIS method and fuzzy evaluation framework for the quality of student mobility in the Erasmus programme. The framework estimates the mobility quality by analysing the answers from the final report study of the implemented mobility. The quality analysis is carried out at the level of individual responses, the entire report and the faculties participating in the programme. The numerical example demonstrates the use of frameworks and determination of quality.

Keywords: Student Mobility, Erasmus, Fuzzy-TOPSIS, HEI, Quality Evaluation.

1. Introduction

Modern education is the foundation of every society and linking educational institutions has become a daily need. The idea of connecting educational institutions, exchange of students and teachers and sharing knowledge has been present for a long time. Currently worldwide there are several programmes whose basic objective is implementation of such an idea, either at the primary level of education or at the HEI level [1]. One of them is the Erasmus programme, currently named Erasmus for All. Since it started in 1987, the programme has so far included almost 3 million students, as well as over 300 000 higher education teachers and other staff since 1997.

To successfully achieve the goals of the programme, it is necessary to ensure the quality of the implementation of mobility, especially at the level of host institutions where it is implemented. Each participant in the programme at the end of mobility has an obligation to fulfil the final report study about the conducted mobility. One of the goals is getting feedback on the quality of the implemented mobility, obtain students' opinions about what could be improved and what the conditions of study at a particular institution are. It is a way of getting clear answers and guidance on how to improve the programme. Very frequently descriptive, unclearly defined answers could be found in the reports, and it is very difficult to assess the quality of mobility.

How can the answer to a question have an impact on the overall evaluation of the mobility quality? To answer this question it is necessary to use a measuring mechanism, the mechanism that will give a numerical value as its result. The value allows ranking and comparison with other reports. For the purpose of such an exact measurement Fuzzy-TOPSIS Framework was designed. The framework uses scientific methods to evaluate the quality of student and teaching staff mobility, based on fuzzy logic and TOPSIS method for multi-criteria decision [3].

2. Final report study

Each student who has participated in a mobility programme needs to fill in the final report prescribed by the EU Agency. Questions in the report are organized in the following categories, with several questions in each [2]:

1) Identification of the student 2) Study period and motivation 3) Academic quality

Corresponding author. Tel.: +385 40 328246. E-mail address: btrstenjak@mev.hr.

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4) Information and support 5) Accommodation and infrastructure 6) Linguistic preparation 7) Academic recognition 8) Costs 9) Your personal experience The first category contains mostly demographic data that have no impact on the evaluation of the

mobility quality. In such reports it is necessary to determine the importance of questions, which categories are of particular interest for the programme. Therefore it is necessary to clearly define the indicators in the report, which have the most impact on the student motivation and involvement in the mobility programme. For example the question: “To what extent did the Erasmus grant cover your needs?”. the question of great importance for the implementation of mobility. This means that the answer to this question has a significant impact on the final assessment of the mobility quality. The question is, how large the impact is. Selecting the importance of questions and answers evaluation becomes more sensitive.

Solving a request must involve a method of multi-criteria decision making, which has been integrated in the new designed Fuzzy-TOPSIS Framework, the conception of which will be the subject of this article.

3. Fuzzy-TOPSIS Framework

3.1 General information

The Framework is designed to support the fulfilment of the final report and automate data processing with the aim of measuring the quality of mobility. It is conceived as a set of modules that guide the user through the data entry process, measurement, recording results, analysis of the evaluation results on the student level or institution level. The framework is designed to be modular, flexible and adaptable to specific requirements of measurement.

3.2 Framework structure

As previously noted, the framework consists of several separate modules. Fig. 1 shows the structure of the new Framework concept.

Fig. 1: Framework structure

The framework has four basic modules: GUI module, Fuzzy module, Weight module, TOPSIS module.

GUI module is designed for selection of the report type and data entry. The module performs validation of input data, control of fulfilling report and data transfer to a temporary and permanent memory. The Fuzzy module uses fuzzy logic to convert linguistic variables into crisp values in a given interval defined by the fuzzy membership function. Each question in the report is assigned with a fuzzy membership function. Results of fuzzification are passed to the next TOPSIS module. The weight module defines the importance of individual answers in the report. The simplest option is when all questions and answers in the final report

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have the same importance, weight. However, it is known that not all the facts are equally important for students and their mobility. The module defines the indicators and their impact on the final evaluation result. Defined weighting factors together with fuzzy value are the input data in the TOPSIS module as the last step in evaluating the mobility quality. TOPSIS module with multi-criteria analysis calculates the final value of the quality of mobility. The analytical model is designed to display the statistical results of measurements of quality according to various criteria.

3.3 Fuzzy TOPSIS model

The word fuzzy means something unclear, slightly cloudy and foggy. In fuzzy logic membership of an element in a given set is not precisely defined, its membership is expressed in percentages.

Linguistic variables - fuzzy logic uses linguistic variables for describing the input variables and results obtained by fuzzy model. Linguistic variable is presented with a triangular fuzzy number. Membership function – the function which determines the degree of membership linguistic variables in a fuzzy set. The function must be scaled between the values 0 and 1[4], [5], [6].

Fuzzy TOPSIS method tries to estimate how close a particular alternative is to the ideal solution. Distance of alternatives can be in positive or negative direction. The method calculates two values: the Fuzzy Positive Ideal Solution (FPIS A+), which represents a project benefit and the Fuzzy Negative Ideal Solution (FNIS A-), a cost of project. The method selects the alternative which has the smallest distance from the positive-ideal solution and the greatest distance from the negative-ideal solution [4,5,6]. Calculate the distance of each alternative from FPIS A+ and FNIS A-. The closeness coefficient CCi is defined to determine the ranking order of all alternatives. The index CCi indicates that the alternative is close to the FPIS(di

+) and far from the FNIS(di-) [4], [5], [6].

4. Framework evaluation

4.1 Determination of question

Table 1: List of Questions from Final Report Study

N

o.

Criter

ia

Question N

o.

Crite

ria

Question

1. C1 Your type of accommodation at host institution

6. C6 A language module/course

2. C2 How useful was this information?

7. C7 Were any other special events organised for Erasmus students in the host institution during your stay?

On your arrival at the

host institution, were you

offered:

Did you receive adequate support

from your host and home

institution before and during your

Erasmus study period?

3. C3 An information session 8. C8 Home institution 4. C4 A welcome event 9. C9 Host institution 5. C5 An orientation

programme 1

0. C10 How do you consider your degree

of integration with local students in the host institution?

For the purposes of this paper, this section presents the results of measuring the quality in the category

“Information and support". Table 1 presents the questions from the final report, evaluation criteria about how a student was informed and supported before and during mobility. The marks from the original document are

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to a lesser extent adapted to framework for the purpose of quality evaluation [2]. All the answers were evaluated on a scale of 1-5 (1 = poor / negative, 5 = excellent). The final results of the measurement will show the quality of mobility implemented in three selected faculties. For evaluation purposes the data of the students who participated 5 months during a few years in the mobility scheme were used.

4.2 Selection of criteria and Fuzzy linguistic variables

In the previous section criteria were determined. Ten of them (C1–C10) determine the information and support quality. For the fuzzy TOPSIS method we need to define linguistic variables and importance weight for each criterion, as shown in Table 2. Also, it is necessary to determine the linguistic variables for rating the answers to questions instead of numerical values and for faculty rating, as shown in Table 3 and 4.

Table 2: Linguistic terms for criteria and the importance weight of each question

Linguistic term Fuzzy number (weight)

Unimportant (U) (0.0, 2.0, 3.5)

Not very important (L) (3.0, 4.5, 6.0)

Important (I) (5.5, 7.0, 8.5)

Very Important (V) (7.5, 9.0, 10.0)

Table 3: Linguistic variables for the weight of each report question

Linguistic variables Fuzzy number (weight)

Poor (P) (0.0, 1.0, 1.5)

Bad (B) (1.25, 2.0, 2.5)

Good (G) (2,25, 3.0, 3.5)

Very good (VG) (3,25, 4.0, 4.5)

Excellent (E) (4.25, 5.0, 5.0)

Table 4: Linguistic variables for the faculty rating of mobility quality

Linguistic variables Fuzzy number (weight)

Very Poor (VP) (0.0,1.5,3.0)

Poor (P) (1.0,3.0,5.0)

Fair (F) (3.0,5.0,7.0)

Good (G) (5.0,7.0,9.0)

Very Good (VG) (8.0,10.0,10.0)

5. Illustrative Example

This example will present the evaluation of student mobility for three faculties.

5.1 Standard crisp evaluation

In the first part of the example, Tables 5 and 6 show quality assessment and final quality rating for faculties F1, F2, F3. The results were calculated in the classical way using arithmetic mean values.

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Table 5: Quality Assessment for Faculties

Table 6: The Final Quality Rating

Faculty Final score Final grade Rating

F1 3,62 Very good 2 F2 3,84 Very good 1 F3 3,48 Good 3

This example shows a situation in which all faculties have nearly equal final grades. The following

evaluation shows how to solve this problem. Later, the example will illustrate how to use Fuzzy-TOPSIS Framework to evaluate the faculty quality with the same assessed results.

5.2 Fuzzy - TOPSIS Framework evaluation

After determining the linguistic variables, the next step is to define the decision matrix based on the same input linguistic variables and criteria values like in the crisp evaluation, as shown in Table 7. This process is part of the fuzzy model that uses defined membership functions [7]. Before calculating the final rating it is necessary to define the weight of each question, what connects the answers with a membership function, characteristics shown in Table 3.

Table 8: Fuzzy Weights of Criteria (question)

Criteria Linguistic term Fuzzy number

C1 Important (5.5, 7.0, 8.5) C2 Very Important (7.5, 9.0, 10.0) C3 Very Important (7.5, 9.0, 10.0) C4 Not very important (3.0, 4.5, 6.0) C5 Not very important (3.0, 4.5, 6.0) C6 Not very important (3.0, 4.5, 6.0) C7 Not very important (3.0, 4.5, 6.0) C8 Very Important (7.5, 9.0, 10.0) C9 Very Important (7.5, 9.0, 10.0)

C10 Important (5.5, 7.0, 8.5) Before the decision matrix is normalized it is necessary to determine linguistic terms with fuzzy weights

for all criteria, shown in Table 8. The next step is construction of the normalized decision matrix [7,8]. Ranking order of all alternatives can be obtained once the closeness coefficient is determined. This method allows the decision makers to select the most feasible alternative. The next step is construction of closeness coefficient CCi of each alternative [9], [10]. Tables 9 and 10 show the final result and faculty rating. According to these closeness coefficients, the ranking order of the three faculties will be F3, F2 and F1.

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Table 9: Fuzzy TOPSIS Results

Faculty dj+ dj

- CCi Rating

F1 43.937 53.380 0.45127 3 F2 46.792 56.203 0.45431 2 F3 46.986 55.443 0.45871 1

Table 10: Final Rating Shown with Linguistic Variables

Faculty Crisp score Fuzzy score Linguistic value

F1 3,62 (3.2, 5.1, 6.8) Fair (F) F2 3,84 (3.4, 5.5, 7.2) Fair (F) F3 3,48 (3.6, 5.5, 6.9) Fair (F)

6. Conclusion

In this paper we presented Fuzzy-TOPSIS Framework structure to determine the quality of student mobility. The basis of the Framework is fuzzy logic and TOPSIS multi-criteria method, their combination has proved to be a good choice and excellent synergy. Modular approach resolves the problem of adaptability to user requirements which gives universality to the Framework and the possibility of evaluating various reports or surveys.

The evaluation is done on three levels: evaluation of individual questions, evaluation of the quality of student mobility and overall rating score of each faculty participating in the Erasmus mobility program. The results show the fuzzy TOPSIS method as a sensible method which provides a very fine quality analysis and ranking. Tests have shown that the concept of frameworks and ways of evaluating the quality are suitable for everyday use. The Framework provides the ability to upgrade and adapt to different user demands, the possibility of Internet access and on-line evaluation.

7. References

[1] European Commission. The ERASMUS Programme – studying in Europe and more (2013.). Retrieved from: http://ec.europa.eu/education/lifelong-learning-programme/erasmus_en.htm

[2] European Union Programmes Agency (EUPA) (2013). Retrieved from: http://llp.eupa.org.mt/files/GfNA-II-C-ERA-HEI mobility grant agreement-Annex V.4-student study final report form.doc"

[3] C. Kahraman. Fuzzy Multi-Criteria Decision Making. Theory & Appl., 2008, Vol.16 : 1931-6828.

[4] I. Mohammadi. Introducing a new method to expand TOPSIS decision making model to fuzzy TOPSIS. The Jurnal of Math. & Comp. Scie. 2011, Vol.2 No 1: 150-159.

[5] G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, M. Izadikhah. Extension of the TOPSIS method for decision-making problems with fuzzy data. Appl . Math. Comput . 2006, 181: 1544–1551.

[6] C. C. Sun, G. T. R. Lin. Using fuzzy TOPSIS method for evaluating the competitive advantages of shopping websites. Expert Syst. Appl. 36, 2009, 11764-11771.

[7] Yi-Li Cheng,Y. Lin, M Tseng. Analysis of Hotel Service Quality Perceptions Using Fuzzy TOPSIS. Progress in Business Innovation & Tech. Management. ,2011, 090-109.

[8] M.Anisseh,R.bt Mohd Yusuff. Developing a fuzzy TOPSIS model in multiple attribute group decision making. Scientific Research and Essays. 2011, Vol. 6(5), pp. 1046-1052.

[9] M.Amiri-Aref, N.Javadian, M.Kazemi. A New Fuzzy Positive and Negative Ideal Solution for Fuzzy TOPSIS. Wseas Transactions on Circuits and Systems. 2012, Issue 3, Volume 11.

[10] Chen-Tung Chena, Ching-Torng Linb, Sue-Fn Huang.A fuzzy approach for supplier evaluation and selection in

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