Measuring the Similarity of Different Types of Fuzzy Sets in FRDB

The representation of imprecise, uncertain or inconsistent information is not possible in relational databases, thus they require addonns to handle these types of information. One possible add-on is to allow the attributes to have values that are fuzzy sets on the attribute domain, which result in fuzzy relational databases (FRDB). From the implementational point of view, values are limited to certain types of fuzzy sets, most often trapezoidal. In this paper we measure the similarity of fuzzy sets when they are values of fuzzy attributes in FRDB. We give a similarity fuzzy relation suitable for this task, which is easy to calculate and implement. The ordering 1I over the set of all fuzzy subsets of a universe (F(x)) which is a generalization of the classical ordering ≤ is introduced. This ordering can be used to compare fuzzy sets and it is useful in query implementation. Ordering 1I together with the compatibility fuzzy relation is used to define another fuzzy relation FLQ fuzzy less or equal.