Entropy weight method for determining method of index weights

entropy was first introduced into information theory by Shannon's, and it has been widely applied in engineering technology, social economy and other fields.

The basic idea of entropy weight method is to determine the objective weight according to the size of the indicator variability.

Generally speaking, if the information entropy of an indicator is smaller, it indicates that the index is worth more variation, the more information is provided, the greater the function can play in the comprehensive evaluation, the greater the weight. On the contrary, the larger the information entropy of an indicator, the smaller the index is worth, the less information is provided, and the smaller the function in the comprehensive evaluation, the smaller the weight.

Second, the entropy right method to assign the right step

1. Standardization of data

Standardize the data for each metric.

Suppose given a K indicator, where. Assuming that the values for each metric data are normalized, then.

2. seeking information entropy of each index

According to the definition of information entropy, the information entropy of a set of data. Where, if, it is defined.

3. determine the weight of each indicator

According to the calculation formula of information entropy, the information entropy of each index is calculated. The weights of each index are calculated by information entropy:.

Third, an example of the right of entropy weighting method

1. Background information

A hospital in order to improve its own level of care, the 11 departments have carried out a review, the assessment criteria including 9 holistic care, and the care of a better level of the department to reward. The following table is the evaluation results of each department's indicators.

However, due to the different degrees of difficulty in various care, 9 nursing care needs to be empowered so that the level of care in each department can be evaluated more rationally.

2. the right to empower by the entropy method

1 ) Data Normalization

According to the original scoring table, the data can be standardized after the following data normalization table

Table 2 a Department 9 Standardized table of overall nursing Evaluation Index score Table

x2

0.00

1.00

1.00

1.00

0.00

1.00

1.00

1.00

1.00

0.00

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departments	x1	x3	x4	x5	x6	x7	x8	x9
a	1.00	1.00	0.00	0.50	1.00	1.00	1.00	1.00
b	1.00	0.00	1.00	0.50	1.00	1.00	1.00	1.00
c	0.00	0.33	1.00	0.50	1.00	1.00	1.00	1.00
d	1.00	0.00	1.00	0.50	1.00	0.87	1.00	1.00
e	1.00	1.00	1.00	1.00	0.00	1.00	1.00	0.00
f	1.00	1.00	1.00	0.50	1.00	1.00	0.00	1.00
g	1.00	0.00	1.00	0.50	1.00	0.00	1.00	1.00
h	0.50	0.33	1.00	1.00	1.00	1.00	1.00	1.00
i	1.00	0.67	1.00	0.00	1.00	1.00	1.00	1.00
j	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
K	1.00	1.00	0.67	1.00	0.50	1.00	1.00	1.00	1.00

2 ) to find the information entropy of each index

According to the calculation formula of information entropy, the information entropy of 9 nursing indexes can be calculated as follows:

Table 3 9 Item index Information entropy table

 	x1	x2	x3	x4	x5	x6	x7	x8	x9
Information entropy	0.95	0.87	0.84	0.96	0.94	0.96	0.96	0.96	0.96

3 ) Calculate the weights of each indicator

Depending on the calculation formula of the weight of the indicator, the weights of each indicator can be obtained as shown in the following table:

Table 4 9 Item Indicator Weight table

w6

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 	w1	w2	w3	w4	w5	w7	w8	w9
Weight	0.08	0.22	0.27	0.07	0.11	0.07	0.07	0.07	0.07

3. Grading each department

According to the calculated weight of the indicator, as well as the 11 departments of 9 nursing level score. To set Zl as the final score for the section L , the final scores of each department are shown in the following table

Table 5 final scoring table for each department

departments	a	b	c	d	e	f	g	h	i	j	k
Score	95.71	93.14	93.17	92.77	95.84	98.01	90.21	95.17	95.97	97.81	97.02

Entropy weight method for determining method of index weights