Hi Dr. Fahmida Haque,

For the Sugeno-type fuzzy system, you have the choice to select whether the output is a constant-type conclusion or a linear function-type conclusion. In your example, you chose the linear function, which means that the output, u, is determined by:

If X is μA, and Y is μB, and Z is μC, then u = k1·X + k2·Y + k3·Z + k4.

In the "Params" field, the linear output is described by [k1 k2 k3 k4].

If you want to design the fuzzy system manually, why do you bother with ANFIS in the first place?

If you want to train the ANFIS using the data, then it is unnecessary to specify the parameters for [k1 k2 k3 k4], though you need to specify whether the output is a constant-type conclusion (singleton) or a linear-type conclusion in the settings.

Hi Dr. Fahmida Haque,

With the data that you provided, you can train the data in the ANFIS toolbox to obtain the Sugeno-type fuzzy system. Fig. 1 shows the convergence of the training activity. The largest error is 0.45229. Fig. 2 shows the test result against the training data. If you round the outputs to the nearest integers (as seen in the data), then it is believed that the error may be reduced substantially. Fig. 3 shows the core of the Sugeno FIS. Figs 4 and 5 show the MFs of the 1st input (X) and the output, respectively. The linear function-type conclusion was selected for this training.

Dear Dr. Yew-Chung Chak

Thank you so much for your kind response. I have now got the point here.

Thank you.

Regards

Fahmida

Dear Dr. Yew-Chung Chak

I have a few more confusions that I am asking for your kind help.

1. In the above example I have 77 data. To train this with anfis is the data set is enough to Train ANFIS accurately? As with 3 input the number of parameters are much higher then the data? How can I fix this problem? by increasing the number of data or by changing the type and number of membership functions of the inputs?

2.How can I reduce the error ? you said to round the outputs to the nearest integers (as seen in the data). I did not get this point.

3. Whenever I am training my ANFIS I am having 36 rules for the generated FIS. As Anfis is generating the sugeno FIS with 36 rules, but the one you tried with 13 rules. But I am somehow getting the same error value. How the rules are effecting the ANFIS? Is there any scope to improve the sugeno fis?

Looking forward to hearing from you soon.

Thank you.

Hi Dr. Fahmida Haque,

This time I checked your data carefully.

You have to perform due diligence, that is, to reduce the data and ensure no repeating data groups. There are 21 groups of [0, 0, 0, 0], 20 of which are repeating, and therefore redundant for the training.

Have you noticed that some data groups fail the "Vertical Line Test"? In other words, some data groups have one-to-many relationships. For example:

In1 = 4, In2 = 2, In3 = 8, Out = 11

In1 = 4, In2 = 2, In3 = 8, Out = 10 (repeating in #74 and #75)

See the circled data groups (#30, #74, #75) in the figure. The ANFIS cannot produce a good solution and will attempt to find a near mid-point solution. This is why it produces the same error value whether it has 13 rules or 36 rules.

Dear Dr. Yew-Chung Chak ,

Thank you so much for your kind reply. This dataset using for the learning process. But in the real case I can have these types of cases where I can get the similar types of data. In that case should I consider only one case and remove the others from the data to train ANFIS?

Can you let me know how many data required to perfectly train ANFIS if I have 3 outputs? is 77 sets of data is enough to train ANFIS? though here I have almost 20 data which contains 0.

Thank you.

Regards,

Fahmida.

Hi Dr. Fahmida Haque,

I think one of my previous points was missed. Since some of your data contain "one-to-many" relationships, they would violate the definition of a function. Thus, you cannot train a "perfect" ANFIS model.

The integer-valued outputs indicate that your data are discrete. You may eliminate or group the repeating data groups. It does NOT affect the quality of the ANFIS-trained model whether there is one [{0, 0, 0}, 0], or twenty-one of [{0, 0, 0}, 0]'s. However, having lesser data speeds up the training process.

What do you mean by having 3 outputs?

[Injective, Surjective and Bijective]. Retrieved March 27, 2019 from https://www.mathsisfun.com/sets/injective-surjective-bijective.html

You can tune the membership function parameters and rules of your fuzzy inference system using Global Optimization Toolbox tuning methods such as genetic algorithms and particle swarm optimization.

If your system is a single-output type-1 Sugeno FIS, you can tune its membership function parameters using neuro-adaptive learning methods. This tuning method does not require Global Optimization Toolbox software.

For more information, see:

https://fr.mathworks.com/products/fuzzy-logic.html

https://fr.mathworks.com/help/fuzzy/fuzzy-inference-system-tuning.html

https://www.mathworks.com/help/fuzzy/tune-fuzzy-inference-systems.html

https://www.mathworks.com/help/fuzzy/tune-fuzzy-rules-and-membership-function-parameters.html

https://www.mathworks.com/help/fuzzy/evalfis.html