On Fuzzy Arithmetic, Possibility Theory and Theory of Evidence

This paper explores the existing relationship between Possibility Theory and Theory of Evidence, when they are both applied to fuzzy arithmetic. Possibility Theory arithmetic is based on the extension principle (projection of the joint possibility distribution), while in Theory of Evidence, the consonant bodies of evidence obtained from each operand are combined into a new joint body of evidence, which can in general be non consonant. Identical behaviour is found when the joint possibility distribution is calculated using the min operator, while Possibility Theory gives more specific results when others T-norms are used. This has been considered by some authors as a Theory of Evidence drawback (Dubois & Prade 1989). This paper shows that Theory of Evidence may be a more realistic uncertainty model when input data are obtained from random experiments with imprecise outcomes.