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theories for the last 2300 years, i.e. the Aristotelian disciplinary matrix, because it
contains the two-valued, classical logic whith which researchers reason and defend
their work.” [69, p. 4]
3.1.2
“Hello” to the “Fuzzy Revolution”
Saying “Goodbye to the Aristotelian Weltanschauung” Sadegh-Zadeh stated that
the Aristotelian disciplinary matrix “is being eradicated by fuzzy theory” [69, p. 4].
In his article he said not only a “Goodbye” but also a “Hello” because its subti-
tle is headed by “The Fuzzy Revolution:”. Consequently, Sadegh-Zadeh was also
intended to show that there is a new scientific view that revolutionized our “Weltan-
schauung”. He stated that the Fuzzy-view removes the fundamental principles (A)
- (F) of the Aristotelian Weltanschauung: “The treatment of truth in fuzzy theory
as a many-valued linguistic variable wiht a colorful and invigorating term set such
as
true, not true, very true, completely true, more or less true, fairly true, false,
very false, ..., etc. ...
{
, and the treatment of these terms as labels of fuzzy sets
over the unit interval
3
, is an ingenous andhighly esthetic dethronement of all exist-
ing theories of truth and oaf all simplistic semantics, including Aristotle's, Tarskis's
Carnap's, and Kripke's perspectives, It goes without saying that whenever the sim-
plistic concept of truth is lost, everything dependent will also vanish. That means
that following the fall of A above, B - G will automatically collapse. Fortunately,
there is a complete substitute for all of that, the fuzzy theory, which is capable of
reigning immediately as the new disciplinary matrix. Its availablility as a more than
perfect substitute is, thus, the reason of its success.” [69, p. 6]
Sadegh-Zadeh replaced concept F, that he also named “Aristotelian ontology”
and “Aristotelian doctrine of crisp existence”, i.e. he replaced the refusal of the
existence of something between being and nonbeing by the “Fuzzy ontology” that
is on the contrary the permission of the existence of something between being and
nonbeing. To this purpose he introduced the “fuzzy existence operator” as a new
fuzzy quantifier:
}
that denotes “there is to some extent”
∃
.
(3.1)
Therefore, let (P,
μ
P
) be a fuzzy set and its membership function and let
P
be the
corresponding predicate that signifies P, and
x
∃
(
Px
)
means that
there is to some
extent
an
x
such that
x
is
P
if and only if
.
He named such an object
x
a “fuzzy object” and to measure the fuzzy existence
of fuzzy objects he introduced the another operator:
∃
r
(
μ
P
(
x
)=
r
)
r
x
∃
(
Px
)
relative to
P there is to the extent r
.
(3.2)
P
Therefore we have:
r
x
∃
(
Px
)
if and only if
∃
r
(
μ
P
(
x
)=
r
)
.
(3.3)
P
3
Here Sadegh-Zadeh refered to Zadeh's series of articles [112].
