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First, a quick primer on 'Fuzzy Logic'

Lets say you have an apple.  It is what it is ('A' is 'A').

Now take a bite out of it.

Is it still an apple?  Yes.

Now continue eating it until it there is nothing left but the core.

is it still an apple?  No, its just a core.

So here is the crux of how 'Fuzzy Logic' differs from traditional western logic.  In traditional logic, the apple began as 'A', and at the end became 'not A'.

Some indeterminable bite of the apple made it pass precipitously from one absolute, to another.

In 'Fuzzy Logic' the statement 'this object is an apple' would have a degree of truth to it, as opposed to a binary truth value.  In practice, this means that as each bite is taken out of the apple, the truth value is a continuous variable.

Proponents of Fuzzy Logic cast it as a challenge to western logic.  They point out that while traditional formal logic systems declare, at an axiomatic level, that the essence of contradition is to say "A and not A".  Whereas in fuzzy logic, a value can in essence, be both true and not true.  In the example above, once you've eaten roughly half the apple, it is, by degrees, both true and not true that the object is an apple.

For those familiar with logic formalism, it defies the law of the 'excluded middle', in a rather seductive way.

And so, I was curious what the objectivist position on Fuzzy Logic might be.

"Fuzzy logic" is a rigorously defined mathematical structure.

An important application of "fuzzy logic" is in control theory. That is the mathematics of creating a system able to respond to outside perturbation to maintain a stable system.

So an application of "fuzzy logic" would be in creating the "brain" to run an automated aircraft in stable flight.

"Fuzzy logic" is built on "fuzzy set theory" (much as logic can be modelled on set theory). In this conventional set theory an item is either in a set or not. In fuzzy set theory the membership of an item in a set is ranked on some scale (conventionally 0 to 1). So if the membership of an object in a set is "1" it can be thought of as 100% belonging to the set. A membership of "0" has the object not belonging to the set. A membership of "0.5" would have the object belonging 50% to the set. One constructs a rigorous system on this.

Basically it is a logic of making decisions by weighing the information available and is not intended as an alternative to conventional logic.

Put in other terms, fuzzy logic is about answering the question "What should I do given the information I have right now?" At a deeper level fuzzy logic is founded on conventional logic, so it doesn't contradict it.

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Are you familiar with, for instance, fuzzy logic?

The purpose of logic is to identify valid inferences, that is, those ways of thinking which when given true premises will always yield true conclusions. Once you know how to do that, then you can safely calculate the consequences of your observations and plans.

Whatever "fuzzy logic" maybe, it is NOT logic. At best, it is a technique used in control theory. At worst, it is an attempt to destroy logic (and thus reason) by substituting an arbitrary and unreliable method for logic.

I think the people who promote "fuzzy logic" as a new improved logic are either charlatans trying to cheat people or intellectual vandals.

NOT x = (1 - truth(x))

x AND y = minimum(truth(x), truth(y))

x OR y = maximum(truth(x), truth(y))

http://en.wikipedia.org/wiki/Fuzzy_logic

If the fuzzy operators are defined this way, then there are NO tautologies at all; and thus no valid inferences. To see this, just suppose that the fuzzy variables all have the value 1/2, then the formula in question must also have the value 1/2 which is not 1 and thus the formula is not a tautology.

Sometimes people use other fuzzy operators instead of these, but this just shows how totally arbitrary "fuzzy logic" is.

Basically it is a logic of making decisions by weighing the information available and is not intended as an alternative to conventional logic.

Imperfect information is the province of probability and statistics, not logic. They are quite capable of handling it without using "fuzzy logic".

At a deeper level fuzzy logic is founded on conventional logic, so it doesn't contradict it.

This does not follow. "Fuzzy logic" is a stolen concept (in Jennifer Snow's sense: redefining an existing term using a derivative concept which conflicts with the original) and a contradiction of logic.

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The purpose of logic is to identify valid inferences, that is, those ways of thinking which when given true premises will always yield true conclusions.  Once you know how to do that, then you can safely calculate the consequences of your observations and plans.

Whatever "fuzzy logic" maybe, it is NOT logic.  At best, it is a technique used in control theory.  At worst, it is an attempt to destroy logic (and thus reason) by substituting an arbitrary and unreliable method for logic.

I think the people who promote "fuzzy logic" as a new improved logic are either charlatans trying to cheat people or intellectual vandals.

Imperfect information is the province of probability and statistics, not logic.  They are quite capable of handling it without using "fuzzy logic".

This does not follow.  "Fuzzy logic" is a stolen concept (in Jennifer Snow's sense: redefining an existing term using a derivative concept which conflicts with the original) and a contradiction of logic.

You should actually read a book on "fuzzy logic" before deciding what it is. It is a rigorous engineering discipline. It is logic in the sense of a control system making decisions. Think of it as being "logic" in the way a computer operates is "logic", rather than "logic" in the sense of the way we decide what is true or false of the world around us. That is the logic of a flow-diagram.

There may be models of probability theory able to handle the same problem, but there is also the issue of which system is more graceful and capable of handling complex situations in elegant ways. There are *always* going to be multiple ways to solve any engineering problem, the key is finding the one that handles it in a simple and robust way.

At the base of "fuzzy set theory" there is the issue to assigning the membership number of an element in a set in a consistent and systematic fashion (i.e. given an element which we are saying has 0.5 membership in set A, and 0.25 membership in set :P. Any system which we give to assign these numbers will end up following the laws of conventional logic. So the very basis of "fuzzy set theory" requires conventional logic to be made systematic.

"Fuzzy logic" makes then doesn't use "true" or "false" (0 or 1 set membership), rather it uses a continuous scale from 0.00 to 1.00 to assign shades of "truth-hood".

The real issue is what a set/proposition is in "fuzzy logic" and conventional logic.

In conventional logic a set/proposition will be something like "brown dog" and the elements a bunch of dogs. A brown dog will have membership 1 and a dog of a different color will have membership 0.

In "fuzzy logic" a set/proposition will be something like "the engine is too hot", and the elements various states of the system. Now based on the degree of membership of the current state of the system in "the engine is too hot" and its membership in various states of a similar nature the system will make a decision to make certain will-defined changes to itself.

This isn't anything philosophical, it is just the logic of a flow-diagram which dictates what the machine will do when in certain states. The sets are those aspects of the system chosen because they are deemed important to control of the system by engineers.

The alternative using conventional logic for machine control would be to create a whole slew of sets/propositions like "the engine is between 100 and 150 degree", "the engine is between 150 and 200 degrees", etc. and have the state of the system be reflected in a strict true/false, 0/1 membership in these states. The machine then makes strict decisions based on these states.

The point of "fuzzy logic" is that it is less cumbersome than conventional logic for these sorts of things.

Edited by punk
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I agreed with punk. Also, a lot of human concepts/categories dont have the 'all or nothing' structure which classical set theory demands, which is why fuzzy set theory/logic has been used within artificial intelligence as a modelling tool. Personally I dont think any formal logic is suitable for this purpose, but fuzzy set theory does seem vaguely better than classical.

To clarify something, probabilty theory is a tool for modelling uncertainty. Fuzzy logic/set theory is for modelling vagueness. It isnt 'uncertain' whether someone with 21% bodyfat is fat - its not like there's a right answer lurking out there which we just dont happen to know.

The purpose of logic is to identify valid inferences, that is, those ways of thinking which when given true premises will always yield true conclusions.
On a side note, this is false - inductive logic wouldnt class as 'logic' by this standard. Logic, in Ayn Rand's definition, is the art of non-contradictory identification. However formal (symbolic) logic is a tool for, amongst various other things, analysing the structure of arguments and modelling human reasoning. Since a lot of human reasoning is based on concepts which arent 'all or nothing', fuzzy set theory can be a useful tool. Edited by Hal
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I forgot the part that makes it analogous to logic....

For conventional logic take 0 to be false and 1 to be true. Let us define a function CAND (conventional AND) so that we get the right answers for AND"

For function CAND(*,*) we take:

CAND(x,y) = x*y (here * is multiplication, above it was a placeholder, sorry)

We then can define a fuzzy AND (FAND) as:

FAND(x,y) = x*y

Except that where for CAND, the inputs could only be 0 or 1, for FAND the inputs are any number between 0 and 1 (including 0 and 1), so for x =0.5 and y =0.5

FAND(x,y) = 0.25

Similarly for other logical operators. (Note though, it has been a while so this might not be the conventional fuzzy definition of AND).

We then can track these fuzzy truth values through our fuzzy control diagram to determine what the system does for various truth values.

Again, the point of this is to make, say, a computer program operating a system more easy to program, understand, and debug, while controlling the system correctly. That is making the ENGINEERING more transparent.

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The purpose of logic is to identify valid inferences, that is, those ways of thinking which when given true premises will always yield true conclusions. Once you know how to do that, then you can safely calculate the consequences of your observations and plans.

I should have said that I was talking about DEDUCTIVE logic here.

Induction is not expected to be exact, unlike deduction.

I have seen nothing in Fuzzy which claims to be or appears to be inductive, that is, it is not producing universals.

["fuzzy logic"] is logic in the sense of a control system making decisions. Think of it as being "logic" in the way a computer operates is "logic", rather than "logic" in the sense of the way we decide what is true or false of the world around us.

.........

The real issue is what a set/proposition is in "fuzzy logic" and conventional logic.

.........

The point of "fuzzy logic" is that it is less cumbersome than conventional logic for these sorts of things.

You are contradicting yourself. First you say that Fuzzy is not in competition with conventional logic. Then you say that it is.

...  probabilty theory is a tool for modelling uncertainty. Fuzzy logic/set theory is for modelling vagueness.

Vagueness is reducible to uncertainty -- how likely is it that a vague thing will be considered to be in the set rather than outside it.

FAND(x,y) = x*y

Notice that this fuzzy operator will still lead to NO tautologies; and thus no valid inferences are possible.

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I should have said that I was talking about DEDUCTIVE logic here.

Induction is not expected to be exact, unlike deduction.

I have seen nothing in Fuzzy which claims to be or appears to be inductive, that is, it is not producing universals.

You are contradicting yourself.  First you say that Fuzzy is not in competition with conventional logic.  Then you say that it is.

Vagueness is reducible to uncertainty -- how likely is it that a vague thing will be considered to be in the set rather than outside it.

Notice that this fuzzy operator will still lead to NO tautologies; and thus no valid inferences are possible.

I'm starting to think you are being willfully obtuse.

Okay, lets construct a *very* simple fuzzy control system:

Lets have an engine and suppose we want to set the throttle based on the temperature and rpms.

Let X by the temperature value, Y be the rpm value, and Z be the throttle value (which for ease will set between 0 and 10).

Let us define a function f to map the temperature into a value between 0 and 1 (i.e. that gives the fuzzy truth value for the set "engine is too hot"):

f(x) = x/200 for 0 <= x <= 200

f(x) = 1 for x > 200

Let us define a function g to map the rpm into a value between 0 and 1

g(x) = x/500 for 0<= x <= 500

g(x) = 1 for x > 500

Let us finally define a function h to map from values between 0 and 1 to throttle values (i.e. takes a fuzzy truth value, or fuzzy control bit, as in put and generates a throttle value):

h(x) = 10*x

We can construct a fuzzy control system in which the throttle value is given by the observed temperature and rpm values as follows:

Z = h(AND(f(X),g(Y))

Recalling that AND is here defined as:

AND(x,y) = x*y

So as the engine's temperature and rpm measurements fuzzy inclusion in the sets/conditions "engine too hot", and "engine rpms too high" change the system adjusts by setting the throttle to different values.

This is the sort of problem fuzzy logic was intended to solve. That's it, right there, everything fuzzy logic is about. In fact if I write the last equation above in more purely mathematical form it is innocuous:

Z = h(f(X)*g(Y))

But the thinking behind the control system is much less obvious.

I didn't contradict myself. I was trying to make a distinction between logic as rules of inference and deduction, and logic as the basic structure which makes computers work. Hopefully this has made it clear that fuzzy logic is meant to be a logic in the sense of a basic structure which makes a machine work, and is not intended to operate as a set of rules of inference and deduction.

In fact all the mathematical definitions which underlie fuzzy logic make appeal to conventional logic in their definitions (the same way all mathematics does). Fuzzy logic is just a bunch of mathematical objects. Maybe it should really have been called "fuzzy control theory", and we wouldn't be having this discussion, but again the creators understood "logic" to refer to the NAND and NOR gates which underlie computer computation, so fuzzy logic is a logic in that sense.

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Maybe it should really have been called "fuzzy control theory", and we wouldn't be having this discussion, but again the creators understood "logic" to refer to the NAND and NOR gates which underlie computer computation, so fuzzy logic is a logic in that sense.

I have no problem with Fuzzy as long as it is properly labelled as "fuzzy control theory".

But remember that this discussion of Fuzzy began when Hal gave "Fuzzy logic" as an example of a non-Aristotelian logic which he claimed was not inherently dishonest. That context clearly puts Fuzzy at odds with Aristotelian logic.

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But remember that this discussion of Fuzzy began when Hal gave "Fuzzy logic" as an example of a non-Aristotelian logic which he claimed was not inherently dishonest.  That context clearly puts Fuzzy at odds with Aristotelian logic.

I was using non-Aristotelian to mean 'non-classical' logic. However, this was poor terminology on my part - I had reason to believe the terms were generally taken to be synonymous, but it seems the phrase 'non-Aristotelian' is only really used by those involved in General Semantics.

But anyway, by 'non-Aristolean' I explicitly mean non-classical. The term 'non-Aristolean' is very vague and should be avoided, since pretty much ALL of modern logic is technically 'non-Aristotlean' (predicate calculus, for instance, rejects most of the reasoning behind the syllogistic forms - Aristotle's logic was inherently non-quantificational and functioned by terms like "all Greeks" as referring to an entity in the same way as a name like "John Smith").

Edited by Hal
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Vagueness is reducible to uncertainty -- how likely is it that a vague thing will be considered to be in the set rather than outside it.

I'm not quite sure what you mean - how would you go about determining this probability? It seems like you'd have to perform some kind of statistical survey; "79% of people said they'd call Peter Evans fat". Of course, this survey would be completely flawed because you'd have to ask participents "Is Peter Smith fat? - answer either yes or no", and most of them would complain because you arent allowing them to say natural things like 'I suppose hes a bit fat but not really', for reasons that dont seem to make much sense.

Edited by Hal
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First, a quick primer on 'Fuzzy Logic'

Lets say you have an apple.  It is what it is ('A' is 'A').

Now take a bite out of it.

Is it still an apple?  Yes.

Now continue eating it until it there is nothing left but the core.

is it still an apple?  No, its just a core.

So here is the crux of how 'Fuzzy Logic' differs from traditional western logic.  In traditional logic, the apple began as 'A', and at the end became 'not A'.

Some indeterminable bite of the apple made it pass precipitously from one absolute, to another.

In 'Fuzzy Logic' the statement 'this object is an apple' would have a degree of truth to it, as opposed to a binary truth value.  In practice, this means that as each bite is taken out of the apple, the truth value is a continuous variable.

Proponents of Fuzzy Logic cast it as a challenge to western logic.  They point out that while traditional formal logic systems declare, at an axiomatic level, that the essence of contradition is to say "A and not A".  Whereas in fuzzy logic, a value can in essence, be both true and not true.  In the example above, once you've eaten roughly half the apple, it is, by degrees, both true and not true that the object is an apple.

For those familiar with logic formalism, it defies the law of the 'excluded middle', in a rather seductive way.

And so, I was curious what the objectivist position on Fuzzy Logic might be.

Again, I think this problem arises from a misuse of the term logic. Fuzzy logic is really just a cute name: It is not a form of logic in the philosophical sense, and is only vaguely a form of logic in the mathematical sense. What it really is is a probablistic algorithm that uses elements of formal logic and probablitity theory to deal with complicated problems that defy exact identification in the time allowed.

Fuzzy Logic really should be called Probablistic Procedure Using Some Machinery of Mathematical Logic.

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Again, I think this problem arises from a misuse of the term logic. Fuzzy logic is really just a cute name: It is not a form of logic in the philosophical sense, and is only vaguely a form of logic in the mathematical sense.

How is it not logic in both the philosophical and the mathematical senses? And what do you mean by it being only 'vaguely' mathematical logic - surely it either is mathematical logic, or it isnt. Unless you want to say that 'mathematical logic' is a fuzzy set with fuzzy logic having a lower membership value than classical logic.

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How is it not logic in both the philosophical and the mathematical senses? And what do you mean by it  being only 'vaguely' mathematical logic - surely it either is mathematical logic, or it isnt. Unless you want to say that 'mathematical logic' is a fuzzy set with fuzzy logic having a lower membership value than classical logic.

To answer that question we would need to get down to what the main point of logic is.

From a mathematical standpoint the purpose of logic is to insure that the truth values we apply to our whole set of mathematical propositions is consistent.

So fuzzy logic is a "logic" in the sense that it insures that all of our truth values (on a range 0 to 1) are applied consistently to our whole set of fuzzy propositions.

From a philosophical standpoint logic is used to infer new statements from existing statements. In this contexts generating new vague propositions from an existing set of vague propositions doesn't seem terribly useful, so one might begrudge it the label "logic".

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Fuzzy logic is not an attack on A is A. You can't attack it. It's just that if you only have two choices like 'The fish is raw' and 'The fish is cooked', then you cannot put a half-cooked fish into one of the two possibilities you have created. It is neither cooked nor raw. Saying a half-cooked fish is cooked is false. Saying a half-cooked fish is raw is false. A half-cooked fish is a half-cooked fish. A is A. Period.

What Fuzzy Logic does is to try to put the half-cooked fish somewhere into the realm of cooked and raw. But then still it is clearly defined in fuzzy logic, since you don't keep it in floppy language but say: The fish is 80% cooked and 20% raw. Clear numbers that can be true or false. It is neither fully cooked nor fully raw. It just allows you to fully allocate the areas in between your categories. It doesn't deny reality. The problem is that you don't have enough categories to fully categorize it. And fuzzy allows you to do just that. Precisely say to which degree the fucking fish is cooked. That's not bad, that's good.

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Fuzzy logic is not an attack on A is A.  You can't attack it. It's just that if you only have two choices like 'The fish is raw' and 'The fish is cooked', then you cannot put a half-cooked fish into one of the two possibilities you have created. It is neither cooked nor raw. Saying a half-cooked fish is cooked is false. Saying a half-cooked fish is raw is false. A half-cooked fish is a half-cooked fish. A is A. Period.

What Fuzzy Logic does is to try to put the half-cooked fish somewhere into the realm of cooked and raw. But then still it is clearly defined in fuzzy logic, since you don't keep it in floppy language but say: The fish is 80% cooked and 20% raw. Clear numbers that can be true or false. It is neither fully cooked nor fully raw. It just allows you to fully allocate the areas in between your categories. It doesn't deny reality. The problem is that you don't have enough categories to fully categorize it. And fuzzy allows you to do just that. Precisely say to which degree the fucking fish is cooked. That's not bad, that's good.

Ummm, then we have always had "fuzzy logic", or atleast since numbers were invented. So really fuzzy logic is what we call "arithmetic".

I like the original, 2,000 year old name better.

1/2 cooked, 1/3 cooked, .999 cooked, .5 cooked, etc.... This is what all these PHD computer scientists are refering to when they discuss fuzzy logic???

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1/2 cooked, 1/3 cooked, .999 cooked, .5 cooked, etc.... This is what all these PHD computer scientists are refering to when they discuss fuzzy logic???

Yup! That's it.

Arithmetic. Never thought about it, but you're right! :)

I'm an engineering student and took a course on fuzzy logic and even programmed a robot and wrote a simulation of ants (which is going to be published :) ) with fuzzy logic, plus I supervised practical exercises on fuzzy and explained it. I know this stuff. And in the end ... this is it.

At least the part of identifying what's going on in the world (called fuzzification to make it sound complicated). Then follows inference (processing in a 'fuzzy' way) and defuzzification so you get a clear number out. But in the end it's just a clear mathematical formula. The reason people like fuzzy logic so much is because it allows you to model simple human behavior and get a clear mathematical formula without having to do much modeling. It's an easy way to build an efficient control mechanism.

You just say: if the fish is not cooked, then apply heat. And since it is fuzzy this also means that you apply less and less heat the more the fish is cooked. This is just a simple version, but in the end ... that's how it works.

Edited by Felix
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Ummm, then we have always had "fuzzy logic", or atleast since numbers were invented. So really fuzzy logic is what we call "arithmetic".

I like the original, 2,000 year old name better.

1/2 cooked, 1/3 cooked, .999 cooked, .5 cooked, etc.... This is what all these PHD computer scientists are refering to when they discuss fuzzy logic???

Surprisingly, quarter-cooked is a relatively modern invention, Babylonian and later. Numbers have been invented many times in human history and date back minimally 10's of thousands of years into the past. Fractions are quite rare in human history, once you go beyond the simple concept "a part" (i.e. invoking specifically "a third").
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Surprisingly, quarter-cooked is a relatively modern invention, Babylonian and later. Numbers have been invented many times in human history and date back minimally 10's of thousands of years into the past. Fractions are quite rare in human history, once you go beyond the simple concept "a part" (i.e. invoking specifically "a third").

You're quite right.

It just occured to me, that my argument is just a special case of a more general argument that could be leveled against any new formalism.

Since the church-turing thesis claims that all formal systems can be mapped to number theory, then EVERY formal system claim can be countered by saying it is just artithmetic? (Which was essentially my previous argument)

So unless an advocate of a new formalism can disprove the church-turning thesis, their new formalism is just number theory with different symbols.

Is this right?

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So unless an advocate of a new formalism can disprove the church-turning thesis, their new formalism is just number theory with different symbols.

Is this right?

As a formalism, yes, but that just emphasises the emptiness of empirically detached formalism. Physics is about something quite real and we certainly don't know everything about the universe, but we can formally reduce the entire universe to something we know, number theory. The interesting stuff then resides in the part that isn't number theory, namely the actual physical laws and the nature of the existents that we're talking about. That's why I'm neither a formalist nor a reductionist.
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You're quite right.

It just occured to me, that my argument is just a special case of a more general argument that could be leveled against any new formalism.

Since the church-turing thesis claims that all formal systems can be mapped to number theory, then EVERY formal system claim can be countered by saying it is just artithmetic? (Which was essentially my previous argument)

So unless an advocate of a new formalism can disprove the church-turning thesis, their new formalism is just number theory with different symbols.

Is this right?

No, since you've used the terms 'Church-Turing thesis', 'formal systems', 'mapped', 'number theory', and 'formalism' incorrectly and incoherently.

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First, a quick primer on 'Fuzzy Logic'

Lets say you have an apple.  It is what it is ('A' is 'A').

Now take a bite out of it.

Is it still an apple?  Yes.

Now continue eating it until it there is nothing left but the core.

is it still an apple?  No, its just a core.

I always think of pure mathematical logic as something that does not take time into account. The apple clearly changed through time, as you have taken a bite out of it. However, the law of identity states that an apple is an apple, not that an apple will always be an apple and its properties won't change.

Another thing, a professor at college told me that fuzzy logic deals with things like the following:

a number approximately equal to 2 + a number between 3 and 3.5 = a number approximately equal or greater than 5 and less or approximately equal to 5.5

Edited to quote my professor.

Edited by source
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