ON THE PROBABILITY/POSSIBILITY TRANSFORMATIONS:A COMPARATIVE ANALYSIS

Abstract

In this paper, we investigate some of the most common probability/possibility transformations found in the literature. Some meaningful criteria, on which the performance of these transformations are evaluated and compared, will be proposed. It concerns respectively the specificity order, i.e., the specificity value of the resulting distributions, the strength of the preference preservation, or in other words, how is the behavior of the result when initial points are close to each other with some strength or according to some function. The third one is related to the result of the transformation where initial distribution tends towards the ignorance state. Finally, we study the influence of incomplete data (subnonnal distribution) to the result of each transformation. This analysis will be illustrated with some theoretical foundation and followed with some numerical examples.

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