In the realm of fuzzy logic, the triangular membership function stands as a fundamental tool for modeling uncertainty and vagueness. Characterized by its triangular shape, this function is defined by three parameters: the lower bound (a), the upper bound (b), and the peak value (c).

The triangular membership function operates as follows:

- For x ≤ a or
*x*≥*b*, the membership value is 0. - For
*a*<*x*≤*c*, the membership value linearly increases from 0 to 1. - For
*c*<*x*<*b*, the membership value linearly decreases from 1 to 0.

The peak value (c) serves as the point of maximum membership within the interval [a, b]. It determines the center of the triangular shape and influences the degree of uncertainty or fuzziness.

Triangular membership functions find widespread application in fuzzy logic systems due to their simplicity and interpretability. They are particularly suitable for modeling variables with symmetric uncertainty or in scenarios where precise measurements are lacking. Moreover, these functions are often integrated into fuzzy inference systems for tasks such as fuzzy logic control, decision-making, and pattern recognition.