Abstract
Using the concept of a neutrosophic quadruple number to a fuzzy duplex number, we introduce the concept of a fuzzy duplex UP-algebra, and investigate some related properties. Also, we find the necessary condition for a fuzzy duplex UP-set to be a fuzzy duplex UP-algebra. Furthermore, we study the relationship between special subsets of a UP-algebra and special subsets of a fuzzy duplex UP-set.