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Recently, researches have contributed a lot towards fuzzification of Soft Set Theory. In this paper, we introduce the topological structure of fuzzyfying soft sets called fuzzy parametrized fuzzy soft sets. We define the notion of quasi-coincidence for fuzzy parametrized fuzzy soft sets and investigated basic properties of it. We study the closure, interior, base, continuity and compactness in the content of fuzzy parametrized fuzzy soft topological spaces.doi:10.20852/ntmsci.2016115658 fatcat:qvmys4sfmfasdhkezzk2djil6y