2.2 Scalar Properties of Fuzzy Time Intervals........................... 5

Abstract

The FuTIRe library is a collection of classes and methods for representing and manipulating fuzzy time intervals and relations between them. Time intervals like ‘tonight’, which are usually not very precise, can be modeled as fuzzy sets. But this causes the problem that the relations between points and intervals and between two intervals, which are usually very trivial, become very complex when the intervals are fuzzy sets. Moreover, there are many different possibilities to define such relations. In FuTIRe it is not only possible to represent fuzzy time intervals, but one can define customized fuzzy point-interval and interval-interval relations. These relations can even yield fuzzy values when the intervals are in fact crisp. As an example for an application, consider a database with, say, a cinema timetable, and you query the timetable “give me all performances ending before midnight”. The usual ‘before ’ relation will exclude the performances ending a second after midnight. With the fuzzy before relation in FuTIRe you can get instead of a sharp drop to 0 at midnight decreasing fuzzy values after midnight, and these can be used to order the results of the query. FuTIRe is an ope