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Travel behaviour depends on the travellers' perception of the trip characteristics. The uncertainty of the journey time is one of the determinants of the choice. Studies of decision behaviour in uncertain conditions show the limited validity of the common assumptions in traffic models. Decision making under uncertainty has to be considered as a contingent process, depending on the objectives and conditions with which the choice is made. Expected utility is one of the many possible criteria used by people to decide. There is a discrepancy between the objective and subjective value of this concept. This is due to the bias with respect to the perception of very likely and very unlikely events. In many cases the expected utility is a less applicable objective, e.g. because people want to arrive before a certain deadline and maximize the probability to achieve that. The fact that probabilities of travel times have to be learned from experiences introduces a dynamic character of choice behaviour.

Most of the reported properties of decision-making under uncertainty still have to be verified for travel behaviour.

How an individual makes a travel decision under uncertain conditions has been one of the critical issues in designing the information that is delivered by Intelligent Transportation Systems (ITS). This has been a difficult problem because a suitable mathematical framework that deals with the interaction among uncertainty, information, and traveler's attitude toward uncertainty is not available. This paper introduces a possibility theory framework, and demonstrates how this framework represents the uncertainty perceived by the traveler, and calculates the feasibility of achieving the travel objective under different degrees of specificity of information. We present this framework in the setting of selecting the time of departure in the face of a not well-defined desired arrival time and estimated travel time. Feasibility of arrival is measured by the possibility and necessity measures; these measures represent two views, optimistic or conservative, respectively. Anxiety that is associated with the departure time, whether to leave now or not is modeled by Yager's anxiety measures. The anxiety measure considers the conflict of impelling forces between “to leave now” and “not to leave yet”; possibility and necessity measures for these outcomes represent these forces. Thus, along the time axis of possible departure time, possibility and necessity measures of arrival and non-arrival are computed and accordingly, the anxiety measure associated with each departure time. The range of time within which a traveler decides to leave is indicated by the anxiety measure. The size of the range is sensitive to the specificity of information. The more specific the information, the smaller the range of time. While the purpose of this paper is to introduce the mathematical framework useful for the analysis of a traveler's decision under uncertainty, the analysis raises an interesting issue of the paradoxical effects of information accuracy also.