my 3d fuzzy set looks exactly like a pyramid when using triangular MF. Its a very simple 3d Fuzzy set with x dimension for one variable, y dimention for second variable and z dimension is membership degree.

It could also be a lame excuse from someone who doesn’t want to accept Fuzzy Theory as real mathematics.
Believe it or not, though Zadeh spent years proving the validity of Fuzzy Logic, there are still people who would prefer to be done with the whole thing. (Generally protesting loudly because there is no excluded middle)

Out of curiosity, what was the topic of the thesis? What type of journal were you submitting to?

I agree that with x,y and the membership grade we get the 3d fuzzy set. But i am a bit unsure whether from a 3d fuzzy set we can refer a 3d fuzzy membership function. I think we can but literatures term the traditional fuzzy set as 1d membership function and therefore it makes our 3d fuzzy set having 2d memebrship function.
The following paper mentions 3d f.m.f for a 3d fuzzy set.
A Three-Dimensional Fuzzy Control Methodology for a Class of Distributed Parameter Systems, Han-Xiong Li; Xian-Xia Zhang; Shao-Yuan Li; Fuzzy Systems, IEEE Transactions on Volume: 15 , Issue: 3

However if you follow this link, you will see that they are reffering the traditional fuzzy set having 1d fuzzy membership function. So that woul make our 3d fuzzy set having 2d Fuzzy MF.
http://www.bluerockresearch.com/papers/ieee_kelly.pdf

Both are contradictory. I would appreciete your help on this because i am submiting my paper and I would like to know whether my 3d fuzzy set is developing a 3d or 2d fuzzy membership function.

I would note that if you were to get a 3 Dimensional landscape, you could take the X and Y coordinates of the landscape and get the output of the height of terrain at that particular point.

Just because the function to transform (X, Y) -> (Z) only takes two inputs, the initial system has been prepped with a 3 Dimensional model.

if it was a simple equation
x + y = z
It has two inputs and a singular output, but this would be two dimensional, as it is not referencing an extra plane.

However, ours is
f(x + y) = z
and within the function of f, we actually have a static reference to the 3 Dimensional plane (our fuzzy set)

By a 3 Dimensional Fuzzy Set, I mean a Fuzzy Set with Dimensions (x, y, z (aka. Membership)). It is 3 Dimensional in that it is graphed to a 3D plane denoting memberships.
When we fuzzify an input, what we pass through the set would be two-dimensions of input, but what we receive out is the 3rd dimension.

No, I do not think that we need to use the term “2 Dimensional”. We are not looking at points in a 2D plane, our Fuzzy Set is graphed in a 3D plane because it does have 3 Dimensions of information.
When we add points to our Fuzzy Set, each point (x,y) is given a third value (z) (the membership) which is an extra dimension in and of itself.

Does that sound reasonable enough?

just found this post feed URL from my Technorati Top news Page.Really great post. Keep it up.

Thanks,
Michael

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