Place of possibility theory in transportation analysis

The transportation phenomena, as a manifestation of the complex human, social, economic, and political interactions, are filled with uncertainties. In order for the analysis of transportation to be scientifically credible, uncertainty must be accounted for properly. Traditionally, probability theory has been used as the only paradigm for dealing with uncertainty without much thought being given to its limits of application. In recent years, a systematized framework of uncertainty theory that handles different types of uncertainty has emerged. In this framework, possibility theory offers a useful way of handling the uncertain situations that often arise in transportation analysis, particularly when incomplete data and perception are involved. This paper describes possibility theory for its mathematical structure, and discusses the reasons why its use is justified for analysis of certain transportation problems. It is shown that the use of a particular theoretical framework depends on the type of information available and the nature of the predicate of the proposition. Probability theory is justified when the propensity of occurrence of well-defined events is the issue. Possibility theory, on the other hand, is justified when the information is partially perceived and evidence points to the nested sets. The dual measures of possibility theory, possibility and necessity, evaluate the truth, optimistically and conservatively. This paper advocates the use of a proper analysis framework that is consistent with the type of information. Such an attitude not only enhances the scientific credibility of the field but also allows the analyst to express how much is known and how much is not known honestly.