A Method Based on Extended Fuzzy Transforms to Approximate Fuzzy Numbers in Mamdani Fuzzy Rule-Based System

Algorithm 1

Approximation of a set of data by using the extended inverse F-transform.

n≔n_{0}

Create the fuzzy partition

Calculate the direct F-transform components

WHILE the dataset is sufficiently dense with respect to the fuzzy

partition

Calculate the approximation error

IF (approximation error ≤ threshold) THEN

Store the direct F-transform components

RETURN“SUCCESS”

END IF

n≔n+1

Calculate the extended direct F-transform components

END WHILE

RETURN“ERROR: Dataset not sufficiently dense”

END

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