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In this paper, the concepts of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras and (∈, ∈)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are introduced and studied. The UP (BCC)-homomorphic image and inverse image are investigated in (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras. Characterizations of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are discussed.