Abstract:

Fuzzy mathematics was introduced by Zadeh in 1965, and the main difference to classical logic is that precise reasoning is only an extreme case of approximate reasoning, and everything is a question of degree. A proposal is no longer true or false, but it can have several intermediate levels: slightly true, quite, very, etc. Furthermore, when alternatives are set out, it is not possible to choose between one and another and each one has to be valued with a level (for instance, quite correct, very correct, etc) and it can be concluded that one proposal is acceptable with its corresponding level.

In this way, several models have been built using fuzzy preferences (Baet & Fodor, 1997; Fodor & Roubens, 1994; García-Lapresta, 2005; Nurmi, 1981; and Tanino, 1984). On the other hand, to capture the lack of precision in human behavior suitably, linguistic preferences are more adequate (Herrera, Herrera-Viedma, & Martínez, 2001; and Zadeh, 1975, 2001).

In short, the main objectives of the present paper are:
•The valuation of a satisfaction degree of a subject through a satisfaction survey of different items, in which a graduation in the responses is considered.
•Next, we must form homogeneous groups of students that present similar degree of satisfaction. For that purpose, we will use the transitive closure algorithm and the inverse transitive algorithm.
•And finally, other algorithm will allow us to put in order the previous homogeneous groups

We are aware of the fact that some steps of the present model are highly elaborate, but some computer programs are very useful for simplifying their operational activity. Anyway, the central element of our model is the correct valuation of the characteristics of the subject for which we will use a survey.

In order to simplify that complex computational activity we propose the usage of Data Mining methods such as Clustering and Classification Rule Sets. Both of them has been successfully applied in previous e-learning works, i.e. Khribi, Jemni & Nasraoui, 2008; Cocea & Weibelzahl, 2009 and Romero, Ventura, Zafra & Bra, 2009.

Keywords:

Fuzzy, Data mining, teaching-learning results, order.