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Fuzzy Logic

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Re: Fuzzy Logic

#11

Post by tlarkworthy »

tehsauce wrote: post #8

"Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1 both inclusive. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false." Can someone explain how this is different than bayesian statistics?

Bayesian statistics has to follow Bayes rule. There is a fairly specific framework behind the numbers in Bayes (i.e. probability). Fuzzy logic is looser.

You could say Bayesian statistics is a subset of Fuzzy logic.

Given how informal people have to be in Bayesian statistics to come up with reasonable priors (e.g. uniform), and how well it works by just guessing reasonable values, it could be argued that the power of Bayes is not in the inference but from the slack in the system it permits. Fuzzy logic is pure slack.

I think modern neural networks with activations like leaky relu look more at home in a fuzzy logic textbook than in a statistics text book.

Re: Fuzzy Logic

#12

Post by a_imho »

tlarkworthy wrote: post #11
tehsauce wrote: post #8

"Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1 both inclusive. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false." Can someone explain how this is different than bayesian statistics?

Bayesian statistics has to follow Bayes rule. There is a fairly specific framework behind the numbers in Bayes (i.e. probability). Fuzzy logic is looser. You could say Bayesian statistics is a subset of Fuzzy logic. Given how informal people have to be in Bayesian statistics to come up with reasonable priors (e.g. uniform), and how well it works by just guessing reasonable values, it could be argued that the power of…

Back when I was in school neural networks, fuzzy logic and genetic algorithms were all taught in the same course called soft computing.

Re: Fuzzy Logic

#13

Post by jblazevic »

A team I was a part of at the uni made a fuzzy logic-based robot for a soft computing course, almost 20 years ago it seems. I rember that we were able to accomplish seemingly complex behavior (light tracking with obstacle avoidance) with only a few very simple fuzzy logic rules. Seems the project page is still up, along with the source code, schematics and documentation (in Croatian): http://www.zemris.fer.hr/predmeti/nenr/

Re: Fuzzy Logic

#14

Post by pjbk »

Back in the 90s when neural networks and fuzzy logic were the rage and were going to solve all problems of human mankind (déjà vu?), I stumbled upon this nice course put together by Texas A&M in the form of an "ebook" (aka Win3.1 application). Lofti Zadeh himself was a contributor. I looked it up in my bookmarks and I cannot believe that the site is still up:

http://faculty.petra.ac.id/resmana/private/fuzzy

I was very interested in training neural networks to find out optimal fuzzy parameters for robotic control systems as an alternative to gain scheduling. There were some cool small companies making nifty scientific apps that I remember evaluating (Aptronix and Neuralogix come to my mind).

Re: Fuzzy Logic

#16

Post by tr352 »

js8 wrote: post #9
tehsauce wrote: post #8

"Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1 both inclusive. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false." Can someone explain how this is different than bayesian statistics?

Bayesian statistics is one approach to modelling fuzziness and uncertainty, but fuzzy logic explores other approaches. For example, see https://en.wikipedia.org/wiki/Possibility_theory Also fuzzy logic builds a "traditional" logical framework for deduction on terms, again this is a bit different from Bayesian approach, which is more abductive reasoning.

Apart from the other answers, there is also one important technical difference. Fuzzy logic is truth functional but probability is not. That is, in fuzzy logic, if you know the fuzzy truth value of A and of B, you can calculate the fuzzy truth value of “A and B” “A or B” and so on. Not in probability. If you know, let’s say, A and B both have probably 0.9, you don’t know enough to calculate the probability of “A and B”, which lies somewhere between 0.8 and 0.9, or “ A or B”, which lies between 0.9 and 1.

Re: Fuzzy Logic

#17

Post by elcomet »

tr352 wrote: post #16
js8 wrote: post #9

Earlier quoted context omitted.

Bayesian statistics is one approach to modelling fuzziness and uncertainty, but fuzzy logic explores other approaches. For example, see https://en.wikipedia.org/wiki/Possibility_theory Also fuzzy logic builds a "traditional" logical framework for deduction on terms, again this is a bit different from Bayesian approach, which is more abductive reasoning.

Apart from the other answers, there is also one important technical difference. Fuzzy logic is truth functional but probability is not. That is, in fuzzy logic, if you know the fuzzy truth value of A and of B, you can calculate the fuzzy truth value of “A and B” “A or B” and so on. Not in probability. If you know, let’s say, A and B both have probably 0.9, you don’t know enough to calculate the probability of “A and…

Yeah but in the real world it doesn't matter does it?

you cannot compute the probability A and B for a reason: they might be related (what if they're mutually exclusive for instance? )

So how does fuzzy logic deals with this?

Re: Fuzzy Logic

#18

Post by regularfry »

a_imho wrote: post #12
tlarkworthy wrote: post #11

Earlier quoted context omitted.

Bayesian statistics has to follow Bayes rule. There is a fairly specific framework behind the numbers in Bayes (i.e. probability). Fuzzy logic is looser. You could say Bayesian statistics is a subset of Fuzzy logic. Given how informal people have to be in Bayesian statistics to come up with reasonable priors (e.g. uniform), and how well it works by just guessing reasonable values, it could be argued that the power of…

Back when I was in school neural networks, fuzzy logic and genetic algorithms were all taught in the same course called soft computing.

Which is odd, because GA isn't like the others at all. We had a similar arrangement. I think the criterion wasn't "these things are similar in approach", more "these things are similar in lack of available rigour."

Re: Fuzzy Logic

#19

Post by airbreather »

I built a fuzzy logic controller for a very large sag mill in a gold plant (top ten in the world by size).

But at the end of it managed to reduce it to a one line formula I could get almost identical results from when simulating in Excel.

I don't think this is an unusual case looking at other examples I found on the net - really it is just a form of non linear control and probably the easiest way to deal with a second order system that reverses action over the peak.

Re: Fuzzy Logic

#20

Post by tr352 »

elcomet wrote: post #17
tr352 wrote: post #16

Earlier quoted context omitted.

Apart from the other answers, there is also one important technical difference. Fuzzy logic is truth functional but probability is not. That is, in fuzzy logic, if you know the fuzzy truth value of A and of B, you can calculate the fuzzy truth value of “A and B” “A or B” and so on. Not in probability. If you know, let’s say, A and B both have probably 0.9, you don’t know enough to calculate the probability of “A and…

Yeah but in the real world it doesn't matter does it? you cannot compute the probability A and B for a reason: they might be related (what if they're mutually exclusive for instance? ) So how does fuzzy logic deals with this?

Fuzzy logic deals with this in the exact same way as classical logic. Note that in classical logic, the truth value of "A and B" and "A or B" is also a function of the truth values of A and of B. When using fuzzy logic you have to make a choice as to which function you use. Typically these functions generalise the classical logic ones in the sense that they behave like the classical ones when using 0 and 1. These functions are defined by a so called T-norm.
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