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Soft set theory is considered as one of the best effective toolwhich provides parameterization approach to tackle the inadequacy offuzzy set. So far, it has been applied to different mathematical conceptssuch as set operations, algebraic structure (e.g., group and ring theory)and topological spaces. Many researchers have studied classical conceptof convex and concave set under fuzzy-like, soft-like and fuzzy soft-likeenvironments. In this paper, new notions of (m; n)-convex and (m; n)-concave fuzzy soft sets are developed first and then their versions for firstand second senses are established. Further some known classical resultsand properties are generalized under fuzzy soft set environment. Moreover,special cases of (m; n)-convexity on fuzzy soft sets are established.