Many of the new fuzzy structures with complete MV-algebras as value sets can be transformed into one type of fuzzy sets,  the R-fuzzy sets, with values in a special structure, called R-algebra. We use this algebraic structure to define standard power set theory of R-fuzzy sets and related transformations of R-power set structures, including lower and upper approximations of R-fuzzy sets by R-relations or rough R-fuzzy sets and we show that these constructions (including their properties) can be universally applied to any of fuzzy type structures that is transformable to R-fuzzy sets.