Unable to understand the concept of fuzzy logic

Re: fuzzy logic..????

Here is one analogy. Think of boolean logic as statements about a 2D point and various circles. A point either is or is-not contained in the circle. You have to specify whether you count the perimeter of the circle as "in" the circle or not. Once you have done that, a point either is or is-not "in" the circle. Think of fuzzy logic as dealing with statements about how much circles overlap. Instead of statements about a "point", it deals with statements about a circle. A circle can overlap another circle so its covers 0%, 20%, 30% etc. of the other circle.

That is only a rough analogy. The specific implementation of fuzzy logic must obey certain mathematical laws. In practical applications, the engineer has a great freedom of choice about how he defines the "degree of membership". He doesn't not have to use the overlap of circles as his model. For example, if we want "the room is hot" to be a fuzzy input to a temperature control system, we must define how to convert some objective measurement (like degrees Farenheight) to a "degree of hotness". There are many mathematical functions of f(x) that are 0 when x is, say, 40 F and 1 when x is, say 102 F. The mathematical definitions of fuzzy logic do not tell the engineer how to invent such a function. So he has freedom of choice.

Re: fuzzy logic..????

tashirosgtHere is one analogy. Think of boolean logic as statements about a 2D point and various circles. A point either is or is-not contained in the circle. You have to specify whether you count the perimeter of the circle as "in" the circle or not. Once you have done that, a point either is or is-not "in" the circle. Think of fuzzy logic as dealing with statements about how much circles overlap. Instead of statements about a "point", it deals with statements about a circle. A circle can overlap another circle so its covers 0%, 20%, 30% etc. of the other circle.

That is only a rough analogy. The specific implementation of fuzzy logic must obey certain mathematical laws. In practical applications, the engineer has a great freedom of choice about how he defines the "degree of membership". He doesn't not have to use the overlap of circles as his model. For example, if we want "the room is hot" to be a fuzzy input to a temperature control system, we must define how to convert some objective measurement (like degrees Farenheight) to a "degree of hotness". There are many mathematical functions of f(x) that are 0 when x is, say, 40 F and 1 when x is, say 102 F. The mathematical definitions of fuzzy logic do not tell the engineer how to invent such a function. So he has freedom of choice.

k..i think i got..a bit about it..
well i hv one more ques to ask..
as we hv freedom of choice in fuzzy..if we implement or apply fuzzy logic to some system..then..the probablity of the system failure must be nil..??

Fuzzy logic itself does not involve the theory of probability. For example, if we say "This neighborhood is somewhat expensive to live in", that statement might be implemented in fuzzy logic as: This neigborhood belongs to the set of expensive neighborhoods to the degree 0.8. That statement does NOT mean that the neighborbood has a 0.8 chance of being expensive to live in and a 0.2 chance of not being expensive to live in. It must be interpreted as a given "degree" of being expensive, not something that happens at random, jumping between expensive and inexpensive.

Re: fuzzy logic..????

imnitsyk..i think i got..a bit about it..
well i hv one more ques to ask..
as we hv freedom of choice in fuzzy..if we implement or apply fuzzy logic to some system..then..the probablity of the system failure must be nil..??

Please donot use SMS language on CE!!

k = Ok , hv = have ques can be question!!

Dont use long trailing dots (....) on CE!!

ok
thanx for telling such things.

tashirosgtFuzzy logic itself does not involve the theory of probability. For example, if we say "This neighborhood is somewhat expensive to live in", that statement might be implemented in fuzzy logic as: This neigborhood belongs to the set of expensive neighborhoods to the degree 0.8. That statement does NOT mean that the neighborbood has a 0.8 chance of being expensive to live in and a 0.2 chance of not being expensive to live in. It must be interpreted as a given "degree" of being expensive, not something that happens at random, jumping between expensive and inexpensive.

could you please give one more example

The application of fuzzy logic is often an attempt to replace skilled human management with computer controls. For example, suppose there is a building and the building supervisor controls the air conditioning. He is is skilled at keeping the building comfortable. We interview him and ask about his methods. He makes such statements as "When it is not very humid and somewhat hot, I turn the fans on a little and set the thermostat only slightly low". "When it is very humid and very hot , I turn the fans on very high and set the thermostat very low".

It is the task of the control designer to translate words like "not very humid", "very humid", "hot" , "very hot", etc. into numerical quantities. These quantities can include the outputs of the controller ( such as "fans on high", "thermostat set slightly low"). These quantities do not represent probabilities.

tashirosgtThe application of fuzzy logic is often an attempt to replace skilled human management with computer controls. For example, suppose there is a building and the building supervisor controls the air conditioning. He is is skilled at keeping the building comfortable. We interview him and ask about his methods. He makes such statements as "When it is not very humid and somewhat hot, I turn the fans on a little and set the thermostat only slightly low". "When it is very humid and very hot , I turn the fans on very high and set the thermostat very low".

It is the task of the control designer to translate words like "not very humid", "very humid", "hot" , "very hot", etc. into numerical quantities. These quantities can include the outputs of the controller ( such as "fans on high", "thermostat set slightly low"). These quantities do not represent probabilities.

does it means that we can operate the AC or we can maitain the comfortablity of building in any circumstances using fuzzy logic ??😒

As an empirical (not theoretical) matter, If a human being can control the AC so it works, it is reasonable to expect that a fuzzy logic control system can duplicate his methods.

Were you looking for a mathematical proof that a controller based on fuzzy logic will work under a given set of conditions? I think there are mathematical proofs for the stability of "Takagi-Sugeno" controllers under certain conditions.

well i have something again to ask about the illustrations of fuzzy logic,

suppose an aircraft is designed in which the landing and take off operation is automatic, now can we implement fuzzy logic in these operations such that we take our parameters as,
lenght of the run way,
speed of the aircraft,
direction of wind.

and according to these parameters we implement fuzzy logic to give the wings an angle so that the take off and landing operation is done successfully!!!

is it possible to implement fuzzy logic in above case, as the parameters chosen above will be diffrent for different places and different locations ?????


please suggest some tutorials for fuzzy logic.

In my opinion, it is not possible to implement automatic landing for a real aircraft with so few input parameters. Futhermore, you did not specify any outputs of the controller ( flaps down, rudder movement etc.).

In addition to the names of parameters, there must be a description of the opinions of a human expert about how he controls the task.

I studied fuzzy sets and fuzzy control from a book, so i don't know about online sources. If I happen find any good ones, I will post the links.

Your questions concern the topic of "fuzzy control". One would study "fuzzy sets" and "fuzzy logic" first, as a background to learning "fuzzy control".

ok thanks for helping a lot over the most confusing topic.

I am not able to understand what is the use of fuzzy logic . Have some practical applications of it?

Nikhil AgrawalI am not able to understand what is the use of fuzzy logic . Have some practical applications of it?

refer above post!!

there are some illustrations!!!

Search on the web for the keywords: fuzzy control tutorial. You will find things like this:
#-Link-Snipped-#

tashirosgtIt is the task of the control designer to translate words like "not very humid", "very humid", "hot" , "very hot", etc. into numerical quantities. These quantities can include the outputs of the controller ( such as "fans on high", "thermostat set slightly low"). These quantities do not represent probabilities.

Yes, but just to be clear (because such explanations are so often misunderstood): The items such as "hot", "very hot" etc. are not bins (or ranges)- they are fuzzy sets which have graded membership. This means that, as one moves up the temperature scale, there is not suddenly a jump from "hot" to "very hot". Rather, the fuzzy truth (a graded value ranging from 0.0 to 1.0) of "hot" decreases, as the fuzzy truth of "very hot" increases.