Image Processing Reference

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essentially in the fact that linguistic characterizations can be less specific than numer-

ical ones and therefore require less information to be used and handled in reasoning

systems.

8.6.1.
Definition

,G,M
) where
x
is the

variable's name,
T
(
x
) the set of values of
x
(referred to as terms),

A linguistic variable is defined by a quintuple (
x, T
(
x
)
,

S

S

is the domain or

the universe in which the values of the variable are defined,
G
is a syntactic rule which

makes it possible to generate the name
X
of each value of
x
and
M
is a semantic

rule, since
M
(
X
) is the fuzzy set defined in

S

that represents the meaning of
X

[DUB 80, ZAD 75, ZIM 91].

This definition represents a symbolic-numerical conversion and establishes ties

between language and numerical scales.

8.6.2.
An example of a linguistic variable

Let us consider the example of an object's size. In numerical terms, this size can be

expressed using a value that varies inside a domain

+
).

In linguistic terms, size can be expressed by using terms such as very small, small,

medium, large, very large, etc. The semantics of these terms are defined by fuzzy sets

in

S

(typically,

S

is a subset of

R

S

. Figure 8.11 illustrates the concept of the linguistic variable “size”.

linguistic variable

size

syntactic rules

terms

{very small, small, medium, large, very large}

semantic rules

M

membership

functions

S

Figure 8.11.
Illustration of the linguistic variable “size”, its terms and the associated fuzzy

sets. The arrows drawn from the linguistic variable to the term set represent syntactic

rules. The second set of arrows represents the semantic rules and translates

the terms into membership functions

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