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 -continuous posets and fuzzy -algebraic posets are given. Furthermore, we try to find some natural classes of fuzzy -continuous maps under which the images of such fuzzy algebraic structures can be preserved; we also think about fuzzy -continuous closure operators in alternative ways. An extension theorem is presented for extending a fuzzy monotone map defined on the -compact elements to a fuzzy -continuous map defined on the whole set.
Highlights
The concept of continuous lattice was initiated by Scott in [1, 2] in a topological manner as a mathematical tool in computer sciences
We present the definition of fuzzy subset systems, and in such a framework we propose the notions of fuzzy Z-continuous posets and fuzzy strongly Zcontinuous posets and study the relationship between them
Through introducing the concept of fuzzy subset systems, we study fuzzy Z-continuous posets, strongly fuzzy Zcontinuous posets, and fuzzy Z-algebraic posets
Summary
The concept of continuous lattice was initiated by Scott in [1, 2] in a topological manner as a mathematical tool in computer sciences (domain theory). At the end of the paper, the authors suggested an attempt to study the generalized counterpart of continuous poset (lattice) obtained by replacing directed subsets by Z-subsets, where Z is an arbitrary subset system. Yao and Shi [14, 15] studied fuzzy dcpos and their continuity over complete residuated lattices; Su and Li [16] discussed algebraic fuzzy dcpos and exploited their relationship with fuzzy domains. It is natural to give a presentation of these matters in a more general framework For this purpose, we are motivated to introduce the notion of fuzzy subset systems as a structure to study quantitative domain theory.
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