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We introduce the concept of fuzzy r-minimal α-open set on a fuzzy minimal space and some basic properties. We also introduce the concepts of fuzzy r-M α-continuous and fuzzy r-M (M * ) α-open mappings, and investigate characterization for such mappings. words and phrases. r-minimal semiopen, r-minimal α-open, fuzzy r-M continuous, fuzzy r-M α-continuous, fuzzy r-M semicontinuous, r-M (M * ) α-open mappings.doi:10.4134/ckms.2012.27.3.603 fatcat:h2idmunad5hlnaxo52o7t5ni2u