Table 5.

The subordinate function of cadmium tolerance of bermudagrass collected from different areas of Hunan province.

Sampling sites	Soil type	Subordinate function value					Order
		TQ	Chl	TR	GR	Average
Liuyang	Polluted	0.73	0.69	0.61	0.38	0.60	2
	Un-polluted	0.68	0.60	0.42	0.32	0.50	6
Zhuzhou	Polluted	0.68	0.60	0.57	0.67	0.67	1
	Un-polluted	0.57	0.54	0.36	0.53	0.53	4
Xiangtan	Polluted	0.66	0.57	0.33	0.57	0.57	3
	Un-polluted	0.47	0.29	0.19	0.39	0.39	8
Yueyang	Polluted	0.74	0.63	0.45	0.23	0.51	5
	Un-polluted	0.47	0.40	0.24	0.44	0.44	7

TQ, Chl, TR, and GR mean turf quality, chlorophyll content, transpiration rate, and growth rate, respectively. The subordinate function value of each index of each accession was evaluated by the following equation: $\mathit{X}\mathrm{\left(}\mathit{\mu }\mathrm{\right)}\mathit{=}\frac{\mathit{X}\mathit{-}{\mathit{X}}_{\mathit{min}\mathit{}}}{{\mathit{X}}_{\mathit{max}\mathit{}}\mathit{-}{\mathit{X}}_{\mathit{min}\mathit{}}}\mathit{}\mathit{\left(}\mathit{1}\mathit{\right)}\mathit{,}$$\mathit{X}\mathrm{\left(}\mathit{\mu }\mathrm{\right)}\mathit{=}\mathit{1}\mathit{-}\frac{\mathit{X}\mathit{-}{\mathit{X}}_{\mathit{min}\mathit{}}}{{\mathit{X}}_{\mathit{max}\mathit{}}\mathit{-}{\mathit{X}}_{\mathit{min}\mathit{}}}\mathit{}\mathit{\left(}\mathit{2}\mathit{\right)}\mathit{,}$$\overline{{\mathit{X}}_{\mathit{1}}}\mathit{=}\frac{\mathit{1}}{\mathit{n}}{\mathit{\Sigma }}_{\mathit{j}\mathit{=}\mathit{1}}^{\mathit{n}}{\mathit{X}}_{\mathit{i}\mathit{j}}\mathit{}\mathit{\left(}\mathit{3}\mathit{\right)}\mathit{,}$X(μ) is the subordinate function value of the μth indicator, X is the observed value of an indicator, X_max represents the maximum value of the indicator, and X_min is the minimum value. X₁ is the mean of fuzzy subordinate function value, and n is the number of indicators. If an index was negatively correlated with Cd tolerance, membership value of Cd resistance was estimated by anti-membership function (formula 2). Otherwise it was calculated by formula 1. Mean value was counted following the accumulation of all membership values of Cd tolerance (formula 3).