Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings

This paper generalizes a classical result about the space of bounded closed sets with the Hausdorff metric, and establishes the completeness of image with respect to the completeness of the metric space X, where image is the class of fuzzy sets with nonempty bounded closed image-cut sets, equipped with the supremum metric image which takes the supremum on the Hausdorff distances between the corresponding image-cut sets. In addition, some common fixed point theorems for fuzzy mappings are proved and two examples are given to illustrate the validity of the main results in fixed point theory.