How to draw the transfer behavior of a fuzzy controller

[Elias_HH]

Homework Statement

A fuzzy controller is given with one input and one output variable. For both
variables, we have fuzzy sets dened according to the upper drawing in the gure. Furthermore, the following fuzzy relations hold:

IF x IS low THEN y IS high
IF x IS medium THEN y IS medium
IF x IS high THEN y IS low

Mark some important points and sketch the transfer behavior (characteristic
curve) from the input to the output of the fuzzy controller! After that, do the
same for the following cases:

a) The medium and the right fuzzy set of the input variable are shifted to
the right, so that the fuzzy sets don't overlap anymore.

b) The medium and the right fuzzy set of the output variable are shifted to
the right, so that the fuzzy sets don't overlap anymore.

c) The outer fuzzy sets of the input variable are changed as shown in the
right drawing.

d) The outer fuzzy sets of the output variable are changed as shown in the
left drawing.

Relevant Equations

N/A

Hey Guys, i try to solve the question mentioned above. But I'm hones...i have no idea to solv this. I need a kind advice. I tryed to find help in the internet but it's impossible. You can see the hole exercise in the figure.

 

[haruspex]

You may have trouble getting help with this. Few of us oldies will have had any exposure to fuzzy logic, and I cannot even find any free access info on the net that explains "transfer behaviour" or "characteristic curve" in this context.
If you can post a link or quote some text that defines these I'll take a look.

 

[Elias_HH]

You may have trouble getting help with this. Few of us oldies will have had any exposure to fuzzy logic, and I cannot even find any free access info on the net that explains "transfer behaviour" or "characteristic curve" in this context.
If you can post a link or quote some text that defines these I'll take a look.

Hey, Thank you for your reply. Thats the problem for me too. I can't find any example for this task in the internet or in the lectures. I'v a similar exercises with solution. maybe the solutions can help to get a better understanding of how it works ?

 

[haruspex]

Hey, Thank u for your reply. Thats the problem for me too. I can't find any example for this task in the internet or in the lectures. I'v a similar exercises with solution. maybe the solutions can help to get a better understanding of how it works ?

I see the question but don’t see the solution.

 

[Elias_HH]

I see the question but don’t see the solution.

The Solution is there, for example here:

 

[haruspex]

The Solution is there, for example here:View attachment 268987

I'm using an iPad. When I downloaded the PDF yesterday it behaved as though there was only one page. Today it has decided there are several. Strange.

I think I can see the logic.
In a) and c):
Between T1 and T2, it could be cold, but can't be hot, so the output is large only (u2).
Going from T2 to T3, it is decreasingly likely cold and increasingly likely hot, so the output slides from u2 to u1.
Between T3 and T4, it could be hot, but can't be cold, so output u1.
Outside of T1 to T4, no possible input, so no output line.

This seems to work for all the others except e). The question specifies four T coordinates but there are only 3 in the answer, and the output changes at points not labelled. I think the answer should be the same as for a) and c), and it is except for the labels on the axis.

 

[Tom.G]

I used fuzzy logic for one project a few decades ago, but unfortunately don't recall the details... and it was on a dedicated Industrial Control processor with its own language. But here is what I could remember/find.

There are several possible transfer curves mapping Inputs to Output, they have various names which I don't recall. Some are mentioned in the results of the following searches. IIRC, one maps the output to the Highest (resp. Lowest) of overlapping input memberships. Another averages the overlapping memberships.

I used two Google searches to find the below (and many others):
https://www.google.com/search?&q=fuzzy+logic+examples
https://www.google.com/search?q=fuzzy+logic+algorithm

For a different (more complete?) explanation see:
https://towardsdatascience.com/a-ve...to-fuzzy-logic-and-fuzzy-systems-d68d14b3a3b8

This one seems more applicable to your present problem:
http://cs.bilkent.edu.tr/~zeynep/files/short_fuzzy_logic_tutorial.pdf

An article by the inventor of Fuzzy Logic, L.A. Zadeh:
https://www.sciencedirect.com/scien...ff02680&pid=1-s2.0-S0019995868902118-main.pdf

Hope it helps.

Cheers,
Tom