Jack Teller wrote:
> I think that in these words about Waclaw, and the fuzzy logic discussed in
>earlier paragraphs, at least IMHO, the probabilities we are discussing
>measure the certainty/uncertainty with which WE KNOW the actual height of
>Waclaw. That is NOT the SAME as Waclaw's probability of actually being xx.xx
>cm tall. (01)
Charles D Turnitsa wrote:
> Stating that Waclaw is 0.73 within the set of tall people seems somewhat
> of statement with a lot of precision but not a lot of certainty. After
> all, by applying the determinant of 0.73 to the determinable "set of
> tall people" we apply a nice determinant with at least an (somewhat)
> objective value attached to it (0.73). The problem is that we are
> pairing this with a determinable of "set of tall people". What exactly
> is that? Is there some range - and is the range weighted. What is the
> mean, the median, some measures of standard deviation, etc - what does
> it mean to be 0.73 tall? Truth is in the eye of the perceiver. If I am
> 130cm tall, then tall means something, but on the other hand if I am
> 185cm tall, then tall means something else - subject to my viewpoint.
> Without objective scale, truth is relative. (02)
I think there can be different interpretations. Of course, there is the
reading that W is precisely .73 in the set of tall people, but as
Charles notes, the set itself is not defined precisely. Or, it is
defined precisely to have vague boundaries. (03)
As to whether we speak of uncertainty or probability or anything else,
depends on what the reason for fuzzyifying was. (04)
One may want to use the term 'tall', but is not determined as to whether
people with height of 160-170 should be called 'tall' or not. A person
of 175 would be classified as 'tall' with some hesitation. In the fuzzy
set lingo, the person belongs .75 to the set. The membership functions
reflects one's indetermination wrt. 'tallness' and the range 160-180.
But there is no uncertainty in the probabilistic sense: it is rather
the level of contentment one has calling a person with height between
160 and 180 'tall'. (05)
But one may want to use the term 'tall' based on how it is used by other
people. Some would say that a 175-high person is tall, some would not.
All would say a 180 or higher person is tall, and all would say a 160
or lower person is not. The .75 membership of a 175-person can in this
case be seen as a measure of probability: it is the probability of a
randomly chosen person classifying the 175-er as tall. (And of course,
each of the members of the population may have only a vague idea what
'tall' means.) (06)
That is, a fuzzy set may reflect the subjective view of one person, or
it may reflect the distribution of subjective views in the population. (07)
What a fuzzy set reflects is not a property of the fuzzy set, but rather
of a person's interpretation of it. To say that fuzzy sets are not
about probability may be correct strictly speaking, but to say that a
fuzzy set cannot reflect probability is wrong, in that it depends on the
interpretation, which may be probabilistic. My view. (08)
We were talking about fuzzy encoding. In fuzzy logics, there is also
the other part, decoding. If based on some input a fuzzy controller
answers that a machine should 0.75 go ahead and 0.25 go backwards, the
machine may be 0.75 in the set of machines moving forwards and 0.25 in
the set of machines moving backwards, but it won't simultaneously go
ahead and backwards. (09)
vQ (010)
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