The objective of this study is to generalize the roughness of a fuzzy set-in three-dimensional structure by introducing ternary multiplication. Many results and theorems of rough fuzzy ideals have been extended from semigroup and semiring, to ternary semiring by introducing the definition of a rough fuzzy subset of ternary semiring. By using the concept of set-valued homomorphism and strong set-valued homomorphism, it is proved generalized lower and upper approximations of (∈,∈∨q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\in , \\in \\vee q)$$\\end{document}-fuzzy ideals (semiprime and prime ideals) of ternary semirings are (∈,∈∨q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\in ,\\in \\vee q)$$\\end{document}-fuzzy ideals (semiprime and prime ideals) respectively.