Fuzzy Z-Continuous Posets

Abstract EN

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.