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The notion of anti-intuitionistic fuzzy soft a-ideals of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>B</mi> <mi>C</mi> <mi>I</mi> </mrow> </semantics> </math> </inline-formula>-algebras is introduced and several related properties are investigated. Furthermore, the operations, namely; AND, extended intersection, restricted intersection, and union on anti-intuitionistic fuzzy soft a-ideals are discussed. Finally, characterizations of anti-intuitionistic fuzzy soft a-ideals of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>B</mi> <mi>C</mi> <mi>I</mi> </mrow> </semantics> </math> </inline-formula>-algebras are given.