Modeling of human choice mechanism has been a topic of intense discussion in the transportation community for many years. The framework of modeling has been rooted in probability theory in which the analyst’s uncertainty about the integrity of the model is expressed in probability. In most choice situations, the decision-maker (traveler) also experiences uncertainty because of the lack of complete information on the choices. In the traditional modeling framework, the uncertainty of the analyst and that of the decision-maker are both embedded in the same random term and not clearly separated. While the analyst's uncertainty may be represented by probability due to the statistical nature of events, that of the decision maker, however, is not always subjected to randomness; rather, it is the perceptive uncertainty. This paper proposes a modeling framework that attempts to account for the decision maker’s uncertainty by possibility theory and then the analyst's uncertainty by probability theory. The possibility to probability transformation is performed using the principle of uncertainty invariance. The proposed approach accounts for the quality of information on the changes in choice probability. The paper discusses the thought process, mathematics of possibility theory and probability transformation, and examples.