Probability-possibility transformation based on evidence theory

The transformation between probability and possibility has been studied by many researchers. Most of those studies examined the principles that must be satisfied for the transformation, and devised an equation satisfying them in a heuristic way. They did not show that the proposed transformation was the only one satisfying the principles. The paper devises three new transformation methods based on evidence theory. Each starts from some principles in the same way as the previous research, but finds the only transformation satisfying the principles. One of them considers that possibility is an ordinal scale of uncertainty, and obtains the possibilistic order from a given probability distribution. The remaining two regard possibility as a ratio scale, and transforms a probability distribution into a possibility distribution. All of the three generate the same ordinal structure of possibility. However, two of them generate different possibility distributions. Thus, the paper examines which of the two is more valid from the point of view of the given principles.