In the simplest case, if you provide two membership functions on each of the 10 inputs, then the ANFIS will generate 210 = 1024 fuzzy rules, and too many fuzzy rules will result in a very long training time. If you cut the number of inputs into half, there will be only 25 = 32 fuzzy rules.

First things first, are all these 10 inputs fundamentally different and independent variables? If they are, then you probably want to select only the input variables that cause a significant change in the output.

To do this, you need to carry out the sensitivity analysis to the output (dependent variable). The idea is to analyze and understand how the different values of a set of independent variables affect the output. The task is to select a k-combination (in a group of 5) of a set of independent variables that gives the highest sensitivity index with low RMSE.

Note: It doesn't have to be 5 inputs. You can select 4 or 6, that suits your needs and the computational capability.

Dear Dr. Yew-Chung Chak ,

Thank you so much for your kind reply!

This is definitely very helpful for me.

This is my first time listening to the sensitivity analysis.

So would like to check with you, for the k-combination.

So I should randomly selecting 5 (or more or less variables) to determine the best combination with the lowest RMSE?

Is there any sample documents/research that I can refer?

Thank you so much for your kind reply sir!

Have a great day.

Best Regards,

Jacky

Hi Jacky Wong,

Here are some papers for your references. The idea of sensitivity analysis is to determine the most influential k-combination (not permutation) of a set of independent variables.

http://www.wolframalpha.com/input/?i=10+choose+5

Article Sensitivity Analysis of Adaptative Neuro Fuzzy Inference Sys...

Article Reliability and Sensitivity Analysis of Structures Using Ada...

Article Performance Evaluation of Two ANFIS Models for Predicting Wa...

Article SENSITIVITY ANALYSIS OF LASER WELDING PROCESS BY ANFIS METHODOLOGY

You can also watch a video here: “Sensitivity analysis for the parameter identification of a PEM fuel cell” by Giovanni Petrone.

https://www.youtube.com/watch?v=JjuyEZL9MmU

Dear Dr. Yew-Chung Chak ,

Thanks for your kind reply.

I have gone through the materials, however I am still trying my very best in understanding the concept. Will try to read more and hoping can find a way for it.

Thanks for your time in sharing with me the methods too!

Best Regards,

Jacky

Hi Jacky,

Some of the chapters related to Neural Nets and ANFIS in these four books maybe helpful:

Dear Dr. Yew-Chung Chak

That's definitely a great help Dr!

Thank you for the kind sharing!

Best Regards,

Jacky