This paper is devoted to describe the notion of a parameterized degree of continuity for mappings between L-fuzzy soft topological spaces, where L is a complete De Morgan algebra.The degrees of openness, closedness, and being a homeomorphism for the fuzzy soft mappings are also presented.The properties and characterizations of the proposed notions are pictured. Besides, the degree of continuity for a fuzzy soft mapping is unified with the degree of compactness and connectedness in a natural way.
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