Research Article
A Method Based on Extended Fuzzy Transforms to Approximate Fuzzy Numbers in Mamdani Fuzzy Rule-Based System
Algorithm 2
Extended F-transform approximation.
| Description: Approximate a fuzzy number with an extended iF- | | transform | | Input: Initial fuzzy partition size n0 | | Threshold parameter | | A set of m points and their membership function value | | | Output: RMSE error | | Extended Direct F-transform components | | n≔ n0 | | Read the dataset of points | | Create a h-uniform fuzzy partition by using the basic functions (36) | | Calculate the extended direct F-transform components | | WHILE the dataset is sufficiently dense with respect to the fuzzy partition | | Calculate the RMSE approximation error (37) | | IF (RMSE approximation error ≤ threshold) THEN | | Store the extended direct F-transform components and the RSME error | | RETURN “Success” | | END IF | | n≔n+1 | | Create a h-uniform fuzzy partition by using the basic functions (36) | | Calculate the extended direct F-transform components | | END WHILE | | Store the extended direct previous F-transform components (n = n-1) and the | | RMSE error | | RETURN “ERROR: Dataset non sufficiently dense” | | END |
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