Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Evaluation index of economic benefits of enterprises_

Number	Total output value (ten thousand yuan)	Product sales rate (%)	Sales revenue (ten thousand yuan)	Total profit (ten thousand yuan)	Total profits and taxes (ten thousand yuan)
A	1500	100.6	1172	25	67
B	1002	105.3	954	80	76
C	4890	83.9	2754	198	407
D	20,205	94.2	22082	1021	983
E	589	98.0	674	493	26

The contribution rate of each characteristic value under polynomial kernel function_

	X1 Total output value (ten thousand yuan)	X2 Product sales rate (%)	X3 Sales revenue (ten thousand yuan)
Eigenvalue	1.127	0.063	0.003
Contribution rate	93.98%	4.75%	1.27%
Cumulative contribution rate	93.98%	98.73%	100%

The contribution rate of enterprise economic benefit under Gaussian kernel function when σ = 50_

	Eigenvalue	Contribution rate	Cumulative contribution rate
X1	0.286	45.65%	45.65%
X2	0.203	22.58%	68.23%
X3	0.128	19.59%	87.82%
X4	0.059	7.51%	95.33%
X5	0.012	4.67%	100%

Contribution rate of enterprise economic benefit under neural network kernel function_

	Eigenvalue	Contribution rate	Cumulative contribution rate
X1	0.016	52.38%	52.38%
X2	0.008	41.82%	94.20%
X3	0.001	5.80%	100%

Contribution rate of enterprise economic benefit under mixed kernel function_

	Eigenvalue	Contribution rate	Cumulative contribution rate
X1	0.016	99.80	99.80%
X2	0.008	0.2%	100%

Standardisation results of evaluation index data_

Number	X1 Total output value (ten thousand yuan)	X2 Product sales rate (%)	X3 Sales revenue (ten thousand yuan)	X4 Total profit (ten thousand yuan)	X5 Total profits and taxes (ten thousand yuan)
A	−0.267	0.642	−0.239	−0.593	−0.502
B	0.557	0.901	0.583	−0.237	−0.347
C	−0.429	−1.290	−0.493	−0.320	−0.352
D	3.278	1.829	3.512	3.290	3.200
E	−0.015	−0.483	−0.089	−0.072	−0.126

Ranking of Economic Benefits of Enterprises_

Enterprise number	Evaluation coefficient	Ranking
A	0.837	2
B	−0.509	4
C	−0.378	3
D	3.233	1
E	−0.835	5