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The concept of quasi-coincidence of a fuzzy point with a fuzzy subset has played a vital role in generating various fuzzy algebraic substructures. In this article, we introduce the notions of (∈, ∈ ∨q k)-fuzzy soft near-ring and (∈, ∈ ∨q k)-fuzzy soft ideal over a near-ring which are generalization of (∈, ∈ ∨q)-fuzzy soft near-ring and (∈, ∈ ∨q)-fuzzy soft ideal respectively and study some of their properties with examples. We also introduce the notion of (∈, ∈ ∨q k)-fuzzy soft subnear-ring (resp. ideal) of an (∈, ∈ ∨q k)-fuzzy soft near-ring and obtain some related results. Keywords (∈, ∈ ∨q k)-fuzzy soft near-ring, (∈, ∈ ∨q k)-fuzzy soft ideal, (∈, ∈ ∨q k)-fuzzy soft subnear-ring.

In this paper, we introduce some new kind of fuzzy subsets of a semigroup by using fuzzy magnified translation, fuzzy translation, fuzzy multiplication and extension of a fuzzy subset. Using these kinds of fuzzy subsets, we obtain some results on fuzzy semiprime ideals of semigroups.

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