Transformation between probability and possibility has been studied by many researchers, since Zadeh proposed Possibility theory. In most of those studies, conditions that must be satisfied for the transformation are examined, and the transforming equation devised heuristically is proved to satisfy the conditions. Therefore, it is not guaranteed that the proposed transforming equation is the only one satisfying the conditions. The paper devises and examines three new transformation methods between probability and possibility. Every method first gives principles that must be satisfied in the transformation, and conducts the transformation in the only way derived from the principles. One of the three methods (T1) considers that possibility is an ordinal scale of uncertainty, and obtains an ordinal structure of possibility from a given probability distribution. The remaining two (T2, T3) regards possibility as a ratio scale, and transforms a probability distribution into a possibility one. Especially, the principles used for T3 lead to an equation transformable in both directions, which is the same as an equation devised heuristically by Dubois and Prade. These three methods create the identical ordinal structure of possibility when the transformation is in the direction from probability to possibility. However, possibility distributions derived by T2 and T3 are different. Thus, the paper examines which of T2 or T3 is more desirable from the point of the given principles, when a possibility distribution is obtained from a probability one. The examination suggests that T3 is more desirable.
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