Abstract
It is well-known that fuzzy number plays a basic role in many fields of fuzzy mathematics, such as fuzzy analysis, fuzzy differential equations, fuzzy probability, and even applications on image processing. In the course of study, some natural metrics on the family of all fuzzy numbers and some natural maps such as weighted mean maps on fuzzy numbers are defined. In the present paper, 16 different topologies on the related sets are defined and compared. Moreover, the continuity of the weighted mean maps as a binary map or a unary map is discussed with respect to these topologies. Finally, an application of the above results is given.
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