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We introduce the concept of fuzzy r-minimal β-open set on a fuzzy minimal space and basic some properties. We also introduce the concept of fuzzy r-M β-continuous mapping which is a generalization of fuzzy r-M continuous mapping and fuzzy r-M semicontinuous mapping, and investigate characterization for the continuity.doi:10.7468/jksmeb.2012.19.3.263 fatcat:7cikthe35rck3b6wmprwg6zdx4