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Advances in Fuzzy Systems

Advances in Fuzzy Systems / 2018 / Article / Alg 2

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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