Before starting, I will note that the accuracy of any non-deterministic system is always relative to some dataset.

For a mathematical function, we can prove that y=f(x) is true for all x in R. It's harder to prove that our classifier will identify a cat for all possible cat images.

Instead, we can often start with a public dataset (or one we make public) and validate our algorithm on this data.

For Sugeno, you will have a dataset with n samples containing some linear combination of outputs and a discrete or continuous output. A very standard way of validating your algorithm is K-fold cross validation.

Basically, you should:

1. shuffle the dataset

2. split into k groups

3. Assign 25% (or a percent you choose) as a test data set

4. Fit your model on the remaining data

5. Test the model on the test data

6. Keep the validation score

7. Repeat multiple times with new shuffling. If the accuracy is consistently high for all rounds, then you are done. Otherwise, you'll need to look for what outliers are leading to variance.

https://neptune.ai/blog/cross-validation-in-machine-learning-how-to-do-it-right

https://www.jeremyjordan.me/evaluating-a-machine-learning-model/

https://www.fs.fed.us/r5/rsl/projects/mapping/accuracies/aa-interp.html

Dear Eht E Sham

The accuracy of FIS system can be verified by many means possible depending upon the datasets employed. To begin with you can use the testing datasets to very the developed model. Also there are numerous statistical parameters that can be computed to determine the preciseness of the model.

Go through the following articles for a better understanding and guidance;

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Article A novel liquefaction study for fine-grained soil using PCA-b...

Hope this helps.

Regards

@Nathan Zavanelli Thaks for your response, just want to add here that I have developed rule based FIS consist of 600 rules approx, now to check the performance I have applied five parameters and I am getting one class labeled corresponding to my input. I am getting correct class label as per my rules for the input parameter, one of reviewer have asked to verify its accuracy.

Nathan Zavanelli is their way to test my model. Like standard classification model used to divide the dataset into train and test and based on k fold validation results or accuracy are verified. If you need I may send my .fis model developed in Matlab.