Fuzzy Logic

[quddusaliquddus]

What is fuzzy logic? Why would we want to make logic fuzzy? Applications-uses? Criticisms? Basically any thioughts on the subject - kindly post here :smile:

[Hurkyl]

Lots of questions one might wish to answer involve imperfect data and vague categories. For example, consider the question "Is it hot in here?"

Making a hard decision to this question, i.e. simply answering "yes" or "no", is unsatisfactory for many applications. In this example, the only (sensible) way to make a hard decision is to pick a cutoff temperature, say, 72 degrees. Any temperature above 72 is then "hot" and anything below 72 is not "hot". This has some undesirable features, such as that the temperatures 71.9 and 72.1 are almost identical, but are classified differently.

The solution is not to make a soft decision instead of a hard decision. One technique for making soft decisions is to use fuzzy logic instead of binary logic. With 1 meaning absolutely true and 0 meaning absolutely false, in this case when asked "Is it hot?" when it's 72.1 degrees, one might say "0.51" and when it's 71.9 degrees, one might say "0.49".

[quddusaliquddus]

......... Thanks .........

[Hurkyl]

Also, Fuzzy Logic earns the term "logic" because it has direct translations of connectives like "not", "and", and "or".

For some soft decisions, just knowing the answers to question P and question Q doesn't mean you can get an answer to the question "P and Q". Fuzzy logic is a "logic", though, because you can give the answer.

For example, in one version, "and" just means minimum and "or" means maximum. So, for example:

If "Is it hot?" has the answer 0.41
and "Is it humid?" has the answer 0.79
Then "Is it hot and humid?" has the answer 0.41.

[quddusaliquddus]

Nice. I like it. Do you know any weaknesses, strengths, and applications of it?

[Hurkyl]

Anything sort of automated intelligence would be a potential application. I'm not particularly qualified to discuss strengths and weaknesses though.

[wuliheron]

Fuzzy logic and multivalue logics in general have found specific applications for a number of real world problems. For example, fuzzy logic is now used to regulate the temperature of buildings more accurately and enables modern elevators to move at high speeds without throwing their occupants around.

Neutrosophy is an extention of the original fuzzy logic which provides some interesting examples of how they fundamentally differ from traditional logistics. Instead of merely true or false truth values, Neutrosophy also uses "indeterminate" truth values. This makes it much more compatable with Quantum Mechanics than traditional logic.

The mathematics that have evolved out of such multivalued logics are very complex. In the case of Neutrosophy, it incorporates recursive matrices. In other words, such logics are relatively new, on the cutting edge of mathematics, and related to the continuing efforts to reconcile QM and Relativity and mathematics in general.

[jeffceth]

Any multivalued logic with a truth set mappable to the integers is still, unfortunately, subject to defeat at the hands of godel's incompleteness theorem, and any logic that is of a higher cardinality can cause problems with the well-ordering principle. As useful as these systems are, they still fall short of a complete one. It seems it might be impossible to construct a complete logical system that would meet all needs. Call me old-fashioned, but I feel somehow this is not right. Shouldn't we be able to come up with something?

jeffceth

[wuliheron]

Any multivalued logic with a truth set mappable to the integers is still, unfortunately, subject to defeat at the hands of godel's incompleteness theorem, and any logic that is of a higher cardinality can cause problems with the well-ordering principle. As useful as these systems are, they still fall short of a complete one. It seems it might be impossible to construct a complete logical system that would meet all needs. Call me old-fashioned, but I feel somehow this is not right. Shouldn't we be able to come up with something?

jeffceth

I'd call you a dreamer rather than old fashioned. :tongue2:

Context is paramount. Every formal logic devised to date has proven to be context sensitive. I would no more expect a single logic to be applicable to every context than I would expect a single tool from Sears to replace all others.

[phoenixthoth]

you can use three valued logic to circumvent russell's paradox which has the nasty implication of there being no largest set, a universal set of all sets. one doesnt' need fully fuzzy logic for that; just 3 truth values are sufficient.

here's an article on fuzzy logic:
http://plato.stanford.edu/entries/logic-fuzzy/

[rgoudie]

Discrete logic may be viewed as a special case of Fuzzy logic. That is, Fuzzy logic theory may be applid to discrete logic.

Go ahead and replace the OR truth table with the MAX function, and replace the AND truth table with the MIN function.

-Ray.