A new approach for modelling fuzzy time primitives

As our knowledge about time is usually vague and not precise, the fuzzy set theory and the possibility theory represent a convenient framework for modeling in temporally rich domains. In many models, temporal reasoning depends on the chosen primitives (fuzzy or nonfuzzy) time instant or/and time interval. This paper presents a new approach for modeling fuzzy time primitives. By a new definition of the fuzzy time interval, introduced in this paper, the fuzzy time interval is represented as a single fuzzy set. This simplifies reasoning process allowing to define a temporal interval forms two possibility distributions and vice versa it allows converting the membership function of an interval into the possibility distribution of an instant. This definition of an interval extends the set of temporal linguistic expressions that can be modelled in the system.