Ranking fuzzy numbers in the setting of possibility theory

The arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood. Equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals, which is addressed in this paper. A complete set of comparison indices is proposed in the framework of Zadeh's possibility theory. It is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers. Moreover, this approach is related to previous ones, and its possible extension to the ranking of n fuzzy numbers is discussed at length. Finally, it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities.