Advances in Fuzzy Systems / 2018 / Article / Tab 2

Research Article

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

Table 2

(a) Parameters and RMSE of the approximation for fuzzy sets of x1

x1 (m2)
Fuzzy numberacdbRMSE

Low202045709.11×10-3
Mean Low457075909.91×10-3
Mean7590951009.17×10-3
Mean High951001151259.76×10-3
High1101201501509.34×10-3

(b) Parameters and RMSE of the approximation for fuzzy sets of x2

x2
Fuzzy numberacdbRMSE

Low00149.18×10-3
Mean Low0.53689.43×10-3
Mean2712209.19×10-3
Mean High81215259.57×10-3
High152550509.15×10-3

(c) Parameters and RMSE of the approximation for fuzzy sets of x3

x3
Fuzzy numberacdbRMSE

Low000.519.21×10-3
Mean Low0.40.611.59.35×10-3
Mean12469.33×10-3
Mean High247109.02×10-3
High61030309.26×10-3

(d) Parameters and RMSE of the approximation for fuzzy sets of x4

x4
Fuzzy numberacdbRMSE

Low0030409.24×10-3
Mean Low305060709.29×10-3
Mean606570809.49×10-3
Mean High758085909.35×10-3
High85951001009.08×10-3

(e) Parameters and RMSE of the approximation for fuzzy sets of x5

x5
Fuzzy numberacdbRMSE

Low0010159.30×10-3
Mean Low71520259.52×10-3
Mean202530359.25×10-3
Mean High303540509.31×10-3
High40501001009.37×10-3

(f) Parameters and RMSE of the approximation for fuzzy sets of x6

x6
Fuzzy numberacdbRMSE

Low0010159.32×10-3
Mean Low71525309.19×10-3
Mean222832359.24×10-3
Mean High304045559.48×10-3
High50601001009.28×10-3

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