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Fig. 3.17
Headline of article [70]
3.8
Prototype Resemblance Structures
In the last section we arrived at the definition of what is a disease in Sadegh-Zadeh's
“Prototype Resemblance Theory of Disease”. In this section we will briefly report
the science-theoretical framework of this theory, i.e. the structures that build its
bases. The first structure that Sadegh-Zadeh defined in [70] is the fuzzy prototype
resemblance frame:
Definition 24.
ξ
is a fuzzy prototype resemblance frame iff there are
Ω
,A
1
,A
n
,B,s,
and f such that:
1.
ξ
=
Ω
,{
A
1
,...,
A
n
},
B
,
f
,
s
.
2.
Ω
is a nonempty set referred to as the universe of discourse.
3.
{
A
1
,...,
A
n
}
is a subset of
Ω
with n
>≥
1
.
4. B is a fuzzy set in
.
5. f is a similarity function that maps pairs of
Ω
Ω
to
[
0
,
1
]
as function similar in
definition 19 in section 3.5.3.
6. s is a human society.
7. Each member of
is a member of B to the extent
1
if it is considered
a prototype in B by the society s.
8. A member X of
{
A
1
,...,
A
n
}
Ω
is a member of B to the event
ε
iff
ε
is the maximum degree
ε
=
of its similarity with the prototype in B, and
0
; that is iff there is a prototype
(
,
)=
ε
A
i
in B such that f
X
A
i
, and there is no prototype A
j
in B such that
f
(
X
,
A
j
)
>
ε
To illustrate this structure Sadegh-Zadeh went back to his example of birds: Let us
assume that
•
Ω
is the class of animals.
•{
A
1
,...,
A
n
}
=
{
robin, sparrow, blackbird, crow
}
with
n
=
4,
•
B
is the class of birds, i.e. a fuzzy set in
Ω
as we know from the last section.
•
f
is our similarity function
similar
.
•
s
is the society of West Europeans.
