Membership Function
A function, typically bounded between 0 and 1, that maps an input to its degree of membership in a fuzzy set.
A fuzzy set does not need a hard inside/outside boundary. A membership function quantifies how strongly a value belongs to the concept represented by that set:
μA(x) ∈ [0, 1]For example, a temperature does not need to jump from “not high” to “high” at one exact threshold. The transition can be represented by a triangular, trapezoidal, Gaussian, or problem-specific curve.
A membership grade is not a probability. A value of 0.7 describes degree of membership in the selected fuzzy set, not the probability that an event will occur.
The function shape is therefore part of the model: it changes how strongly rules activate across the input space.
Background: Fuzzy Logic.