This paper presents a comprehensive framework for ranking fuzzy numbers within the context of possibility theory. The authors propose a complete set of comparison indices that enable the precise characterization of the relative positions of two fuzzy numbers. These indices are derived from Zadeh's possibility theory and are shown to be both necessary and sufficient for describing the relationships between fuzzy numbers. The paper also discusses the relationships between these indices and previous approaches, highlighting their advantages in terms of discrimination power. The authors demonstrate that the proposed indices can be used to rank fuzzy numbers in a way that is consistent with the principles of possibility theory. The paper also explores the relationship between these indices and Zadeh's compatibility index, showing that the values of the introduced scalar indices can be recovered from the knowledge of the compatibility index. The paper concludes that possibility theory provides a natural framework for the derivation of comparison indices aimed at ranking fuzzy numbers.This paper presents a comprehensive framework for ranking fuzzy numbers within the context of possibility theory. The authors propose a complete set of comparison indices that enable the precise characterization of the relative positions of two fuzzy numbers. These indices are derived from Zadeh's possibility theory and are shown to be both necessary and sufficient for describing the relationships between fuzzy numbers. The paper also discusses the relationships between these indices and previous approaches, highlighting their advantages in terms of discrimination power. The authors demonstrate that the proposed indices can be used to rank fuzzy numbers in a way that is consistent with the principles of possibility theory. The paper also explores the relationship between these indices and Zadeh's compatibility index, showing that the values of the introduced scalar indices can be recovered from the knowledge of the compatibility index. The paper concludes that possibility theory provides a natural framework for the derivation of comparison indices aimed at ranking fuzzy numbers.