Possibility distribution introduced by Zadeh ["Fuzzy sets as a basis for a theory of possibility theory", Fuzzy Sets Syst. 1 (1978) 3-28] in his introductory paper of possibility theory assumes a normal distribution, in the sense that it supposes the existence of at least one element s 0 of the universe of discourse U , for which the distribution ~ is fully compatible with the context of interest: ~ (s 0 )=1. However, when such element does no longer exist, it leads to a subnormal possibility distribution. This situation may arise from incomplete data, inconsistent statements, or contradictory beliefs. To deal with such case, many authors like Yager ["On the relationships of methods of aggregation evidence in expert systems", Cybern. Syst. , 16 (1985) 1-21; "A modification of the certainty measure to handle subnormal distributions", Fuzzy Sets Syst. , 20 (1986) 317-324], Dubois and Prade ["An alternative approach to the handling of subnormal possibility distributions--A critical comment on a proposal of Y...
['Mourad Oussalah']
On the normalization of subnormal possibility distributions: New investigations