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 (m^2)
Fuzzy number	a	c	d	b	RMSE
Low	20	20	45	70	9.11×10^-3
Mean Low	45	70	75	90	9.91×10^-3
Mean	75	90	95	100	9.17×10^-3
Mean High	95	100	115	125	9.76×10^-3
High	110	120	150	150	9.34×10^-3

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

x2
Fuzzy number	a	c	d	b	RMSE
Low	0	0	1	4	9.18×10^-3
Mean Low	0.5	3	6	8	9.43×10^-3
Mean	2	7	12	20	9.19×10^-3
Mean High	8	12	15	25	9.57×10^-3
High	15	25	50	50	9.15×10^-3

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

x3
Fuzzy number	a	c	d	b	RMSE
Low	0	0	0.5	1	9.21×10^-3
Mean Low	0.4	0.6	1	1.5	9.35×10^-3
Mean	1	2	4	6	9.33×10^-3
Mean High	2	4	7	10	9.02×10^-3
High	6	10	30	30	9.26×10^-3

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

x4
Fuzzy number	a	c	d	b	RMSE
Low	0	0	30	40	9.24×10^-3
Mean Low	30	50	60	70	9.29×10^-3
Mean	60	65	70	80	9.49×10^-3
Mean High	75	80	85	90	9.35×10^-3
High	85	95	100	100	9.08×10^-3

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

x5
Fuzzy number	a	c	d	b	RMSE
Low	0	0	10	15	9.30×10^-3
Mean Low	7	15	20	25	9.52×10^-3
Mean	20	25	30	35	9.25×10^-3
Mean High	30	35	40	50	9.31×10^-3
High	40	50	100	100	9.37×10^-3

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

x6
Fuzzy number	a	c	d	b	RMSE
Low	0	0	10	15	9.32×10^-3
Mean Low	7	15	25	30	9.19×10^-3
Mean	22	28	32	35	9.24×10^-3
Mean High	30	40	45	55	9.48×10^-3
High	50	60	100	100	9.28×10^-3