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 CB(X)CB(X) with respect to the completeness of the metric space X  , where CB(X)CB(X) is the class of fuzzy sets with nonempty bounded closed αα-cut sets, equipped with the supremum metric d∞d∞ which takes the supremum on the Hausdorff distances between the corresponding αα-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.