14.2. Linguistic Variables and Membership Functions
In 1973, Professor Lotfi Zadeh proposed the concept of linguistic or ‘fuzzy’ variables, like temperature, defined by fuzzy sets and linguistic values such as hot and cold. A fuzzy set is an extension of a classical set and includes the possibility of partial membership of its elements. The input space is referred to as the universe of discourse (UOD). If X is the UOD and its elements are denoted by x, then a fuzzy set A in X is defined as a set of ordered pairs.
A = {x, μA(x)|x ε X}
where μA(x) is called the membership function (or MF) of x in A. The MF associated with a given fuzzy set X, maps each element of X to a membership value between 0 and 1. A MF is a curve that defines how each
Get MATLAB® and Its Applications in Engineering: [Based on MATLAB 7.5 (R2007b)] now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
