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Fig. 3.9
Point
(
0
.
5
,
0
.
4
,
0
.
7
)
in the 3-dimensional cube; Fig. in [35]
(a)
(b)
Fig. 3.10
(a): Headline of Sadegh-Zadeh's article [64]; (b): Geometrical interpretation of the
count of a fuzzy set
A
as the Hamming length of the vector drawn from the origin of the
hypercube to the point
A
. In the present case we have
c
(
A
)=(
1
.
1
)
for
A
=(
0
.
3
,
0
.
8
)
.Fig.in
[64, p. 315].
In his “Goodbye”-article Sadegh-Zadeh introduced the notion of the basic fuzzy
structure to “shed some light” on Zadeh's creation of fuzzy sets. He emphasized that
this was “a creation and not a discovery of a pre-existent entity.”! Because the young
history of the theory Fuzzy sets and Systems comprises so many controversies and
misinterpretations concerning the question 'What is a fuzzy set?' Sadegh-Zadeh
tried to resolve this problem by using a
structuralist approach
:
13
“the
definition
[of a fuzzy set] subsumes a particular kind of structure under the label 'fuzzy set',
whether they be abstract or concrete, real or unreal, natural or artificial, subjective
or objective, existent or non-existent.” [69, pp. 17f] Therefore he defined the first
structure as follows and following that he re-defined what is a fuzzy set:
13
For more details on this approach in philosophy of science we refer to section 3.9.
