Knowledge-Based Systems

136 Chapter 5 Fuzzy LogiC

5.6.3 Trapezoidal Fuzzy Membership Function

This membership function follows a trapezoidal curve. A trapezoidal curve

is a function of (A = (a, b, a, b)) with tolerance interval [a, b], left width a,

and right width b, if its membership function has the following form (see

Figure 5.10):

A(x) = 1 − (a − x)/a if a − a ≤ x ≤ a

= 1 if a ≤ x ≤ b

= 1 − (x − b)/b if a ≤ x ≤ b + b

= 0 otherwise.

Figure 5.10

Trapezoidal fuzzy

membership

function

1

0

a – aaba + β

5.7 LINGUISTIC VARIABLES

The power and strength of fuzzy logic comes from its ability to deal with

vague linguistic variables. A linguistic variable is a var ...