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## Re: [ontolog-forum] {Disarmed} Reality and Truth

 To: "[ontolog-forum]" Waclaw Kusnierczyk Thu, 17 May 2007 18:55:29 +0200 <464C8901.6050103@xxxxxxxxxxx>
 ``` Kathryn Blackmond Laskey wrote: >> Suppose that we have the linguistic variable 'tall'. Suppose you assign >> to it a fuzzy set with a membership function f such that f(x) = 0 if x < >> 160, f(x) = 1 if x > 180, and f(x) is linearly increasing from 0 at 160 >> to 1 at 180. Suppose my height h is 170. Thus, f(h) = 0.5. Would you >> say that it is 50% true that I am tall? That the truth of 'wk is tall' >> is a 50% truth? > > This brings me to Waclaw's "degree of tallness". Fuzzy logic enables > us to attach a number "degree of tallness" to Waclaw's height, and to > relate Waclaw's degree of tallness to his degree of heaviness, to his > father and mother's degrees of tallness, etc. Fuzzy logic provides a > calculus for manipulating these "degrees of set membership" > (equivalently, "degrees of truth" or "degrees of having a property") > consistently. Actually, there isn't one single calculus -- there are > several, depending on what combination operators one chooses to > employ. There is an enormous literature on fuzzy logic, a number of > implemented fuzzy reasoning systems, and a proliferation of > applications of fuzzy logic. Many people find fuzzy logic > interesting and useful, and it has a passionate community of > adherents. > > The fuzzy logic community has agreed to use the terminology "degree > of membership", "degree of truth", etc. for the numbers fuzzy systems > manipulate. The fuzzy community has agreed to use this terminology > because things that have 100% "degree of truth" correspond to things > that satisfy the clarity-test definition of true statements, and the > terminology has intuitive resonance for many people. > > Suppose we say that Waclaw's degree of tallness is 0.73. Does this > mean Waclaw "really" has membership level 0.73 in the set of tall > people, or that it "really is" 73% true that he is tall? I don't know > what that means. Waclaw's "degree of tallness" doesn't satisfy the > clarity test. > > So then, should we follow Waclaw's suggestion and say that the number > 0.73 reflects our uncertainty about whether he is tall? I would > argue against this. It is too easily confused with subjective > probability. Assigning a subjective probability of 73% to the > statement that Waclaw is tall is very different from assigning a > fuzzy degree of truth of 73%. In the former case, I am asserting > that: (1) there IS a fact of the matter, in the clarity test sense, > of whether or not Waclaw is tall; but (2) I am uncertain about the > facts; and (3) the odds at which I would bet that he is tall are > 73:27; and (4) in principle, I could find out the truth of the matter > and settle the bet. But whether Waclaw is tall does not satisfy the > clarity test, because I have not provided a precise definition of > what it means for him to be tall, that could in principle be verified > by anyone with access to the facts of the matter. Therefore, it is > not appropriate to assign a probability to the statement that he is > tall. > > I personally think, therefore, that it is misleading to say I am > uncertain about whether Waclaw is tall. I think it is less > misleading to say that (according to a given system of assigning > fuzzy memberships) he has membership degree 0.73 in the set of tall > people. The consumer of such statements must, of course, bear in > mind the rules by which fuzzy memberships are assigned and > manipulated, and think carefully about whether the resulting > mathematics applies to the problem at hand. But this is the case > with any application of any theory.    (01) Indeed, it is not always uncertainty that we acknowledge with degrees; in an earlier post I used the term 'satisfaction' -- it would fit better in this example. I did not use the term 'uncertainty' with this particular example. That I am in 73% in the set of tall people (weird) may be interpreted as that the one who defined the set is 73% satisfied (how do we measure satisfaction?) with calling me 'tall'. He/she is not uncertain whether I am in the set -- he/she is 100% sure I am 73% in the set.    (02) But this still seems to me to be far from degrees of truth, even if the fuzzy logic community agreed to use the term 'degree of truth'. It either is that I am 73% in the set, or it is not.    (03) vQ    (04) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (05) ```
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