Information Technology Reference
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The animals in subset
{
A
1
,...,
A
n
}
=
{
robin, sparrow, blackbird, crow
}
of all ani-
mals (universe of discourse
) are considered prototype birds by West Europeans
and therefore they are members of the class
B
of birds with membership value1.
Any other species
X
in
Ω
ε
=
(
,
)=
ε
is the
maximum degree of this species' similarity to the four prototype birds. Therefore,
Ω
is to an extent
0abirdiff
similar
X
A
i
animals
,{
robbin
,
sparrow
,
blackbird
,
crow
},
birds
,
similar
,
West Europeans
is
a
fuzzy prototype resemblance frame.
From definition 24 of a
fuzzy prototype resemblance frame
we can vice versa
define what is a
fuzzy prototype resemblance category
:
Definition 25.
B is a fuzzy prototype resemblance category iff there are
Ω
,A
1
,A
n
,
s, and f such that
Ω
,{
A
1
,...,
A
n
}
B
,
f
,
s
is a fuzzy prototype resemblance frame.
Sadegh-Zadeh referred to the fact that these definitions are dependent from the so-
ciety
s
as part of the fuzzy prototype resemblance frame: “For example, it may
be that what Australians view as the category of birds, vegetables, fruits, furniture,
or cloths is not identical with what Siberians do because the focal members of an
Australian category differ from those of the Siberian category. an Australian cate-
gory may partially overlap a Siberian one, though, they need not match completely.”
[70, p. 133]
With these structures we have now all requirements to get the goal of Sadegh-
Zadeh's article [70]:
Hypothesis 1
The category of diseases in Western medicine, denoted
D
, is a fuzzy prototype re-
semblance category.
To support this hypothesis he considered the following points:
1.
H
, the class of all fuzzy human conditions, is the universe of discourse.
2.
{
D
1
,...,
D
n
}
is a subset of
H
, that comprises e.g.
D
i
=
heart attack,
D
j
=
breast cancer,
D
k
=
small pox, etc. and some of these human
conditions are prototype diseases in Western societies.
measles,
D
r
=
3.
.
4.
s
may be the human society of West Europeans.
5.
D
is a family of fuzzy sets in
H
f
is the similarity function
similar
.
With these premises he came to the next hypothesis:
Hypothesis 2
H ,{
D
1
,...,
D
n
},H ,
similar
,
West Europeans
is a fuzzy prototype resemblance
frame.
For every class
H
of all fuzzy human conditions holds:
