On the Roots of Fuzzy Sets - Fuzzy Logic: An Introductory Course for Engineering Students - page 29

={ }

- For buildings, Height low, high, medium, very high, not very low, …

={ }

- For people, Height tall, short, medium, very tall, more or less short, …

• }

Although the number of terms in a Linguistic Variable can be large, usually it is
comprised between 5 and 9 (7

LV = Speed, is Speed ={ fast, slow, very slow, more or less fast, not fast, …

2) since, in a lot of cases, less than 5 shades is poor
and more than 9 is excessive. Anyway in a good number of applications there only
appear the three terms P , aP , and MP .
Usually, in the applications, the variables range in the set of real numbers and,
because of this, the predicate P acts in some interval of the real line. For example,
the linguistic variable 'Temperature' in the interval between

±

− 10, and 50 degrees Celsius, is often represented by only the three terms μ cold , μ hot ,

μ w arm , with warm =

not cold and not hot.
Analogously, 'Height' for people, can be represented in

[ , ]

0 2 meters by the lin-

guistic variable with the four terms μ tall , μ short , μ v er y shor t , μ more or less tall in the

following figure,

1.5.1 Fuzzy Partition

It is sometimes useful in the applications that, once ordered in some sequence, the
fuzzy sets in a linguistic variable LV ={ μ 0 , μ 1 ,...,μ n } do form what is called a

fuzzy partition (or a unit's partition), that is, verifying

n

0 μ j (

x ) = 1 , ∀ x ∈ X .

j =