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This article deals about an interval-valued neutrosophic Ẑ-algebra is a mathematical framework which incorporates the concepts of interval-valued neutrosophic sets, Ẑ-algebra and algebraic operations. This innovative algebraic structure addresses the challenges posed by uncertain, imprecise, and indeterminate information in various fields. In this work, we presented the fundamentals of Ẑ-algebra and int_val neutrosophic sets, as well as several of their attributes such as homomorphism and cartesian product.