Fuzzy Z -Continuous Posets

Abstract

The aim of this paper is to generalize fuzzy continuous posets. The concept of fuzzy subset system on fuzzy posets is introduced; some elementary definitions such as fuzzy $Z$-continuous posets and fuzzy $Z$-algebraic posets are given. Furthermore, we try to find some natural classes of fuzzy $Z$-continuous maps under which the images of such fuzzy algebraic structures can be preserved; we also think about fuzzy $Z$-continuous closure operators in alternative ways. An extension theorem is presented for extending a fuzzy monotone map defined on the $Z$-compact elements to a fuzzy $Z$-continuous map defined on the whole set.