Abstract:

 A new order structure is introduced on the class of subsets of an m-dimensional positive Euclid space. In the new order structural sense, the relationships between (pseudo-) almost everywhere convergence and (pseudo-) almost uniform convergence in set-valued fuzzy measures are studied. Furthermore, the Egoroff theorems and their corresponding reverse theorems by depicting the sequence of measurable functions with set-valued fuzzy measure are obtained.
 

Key words: set-valued fuzzy measure; almost everywhere convergence; almost uniform convergence; Egoroff theorems