T-Norm

A t-norm (triangular norm) is a binary operation on the unit interval [0,1] that generalizes classical logical conjunction to many-valued contexts. Formally, a t-norm is commutative, associative, monotonic, and has 1 as identity. The standard Zadeh t-norm is the minimum, but alternatives — the product t-norm, the Łukasiewicz t-norm, and the drastic t-norm — encode different intuitions about how degrees of truth combine. In fuzzy logic, the choice of t-norm is not merely technical: it determines whether conjunction models conservative evidence combination (minimum), independent sources (product), or bounded rationality (Łukasiewicz). The t-norm family thus reveals that "fuzzy conjunction" is not one operation but a structured space of operations, each carrying distinct inferential commitments.