👉 Turing t-norms (t-norms) are mathematical functions that generalize the logical AND operation in Boolean algebra and are used extensively in fuzzy logic, approximation theory, and various computational fields. Formally, a t-norm is a function \( T: [0, 1] \times [0, 1] \to [0, 1] \) that satisfies four key properties: \( T(a, b) \geq T(a, c) \) (monotonicity), \( T(a, b) = T(a \land c) \) (associativity), \( T(1, b) = b \) (identity element), and \( T(a, T(b, c)) = T(a, T(b \land c)) \) (commutativity). These properties ensure that t-norms behave similarly to the logical AND operation, but they can be more flexible and robust than traditional AND operations, allowing for a broader range of applications in dealing with uncertainty and approximate reasoning.
