Distinction between several subsets of fuzzy measures

Abstract In this paper, we place several fuzzy measure subsets in relation one with the other. The subsets under study are those corresponding to the definitions of probability measure. Sugeno's g λ -measure, Shafer's belief function and Zadeh's possibility measure. We study the intersection of these subsets and we show the particular role of Dirac's measures in this comparison. We limit ourself to the case of mappins whose domain is the collection of all subsets of a finite set. Finally, the obtained partial results are summarized in only one figure which shoul clarify the specificity of each of the above definitions.