Research on the standardisation strategy of enterprise economic management mode in the Internet era

In the process of principal component analysis, the first linear combination F_1, called the first principal component, is selected first. F_1 has the largest variance and contains the most information.

If F_1 is not enough to represent the information of the original indicators, then the second linear combination F_2, which is independent of the first principal component F_1, is selected next, and F_2 is the second principal component until the number of selected principal components can replace the original variables, the specific formula is as follows: (1) { F1=a11x1+a12x2+⋯+a1mxmFn=an1x1+an2x2+⋯+anmxm $\left\{ \begin{array}{*{35}{l}} {{F}_{1}}={{a}_{11}}{{x}_{1}}+{{a}_{12}}{{x}_{2}}+\cdots +{{a}_{1m}}{{x}_{m}} \\ {{F}_{n}}={{a}_{n1}}{{x}_{1}}+{{a}_{n2}}{{x}_{2}}+\cdots +{{a}_{nm}}{{x}_{m}} \\ \end{array} \right.$

From the above equation, F the linear combinations are independent of each other, i.e., the covariance is 0, and F the variance between the linear combinations decreases sequentially.

The algorithm for PCA is outlined as follows: let the number of samples be n, the number of sample variables be m, the sample data i = 1,2⋯n, and the sample variables j = 1,2⋯m, then the data set is: (2) T=(x11…x1m⋮⋮⋮xn1…xnm) \[T=\left( \begin{matrix} {{x}_{11}} & \ldots & {{x}_{1m}} \\ \vdots & \vdots & \vdots \\ {{x}_{n1}} & \ldots & {{x}_{nm}} \\ \end{matrix} \right)\]

Support vector machine algorithm in linearly separable solving optimal decision function problem, let the linear classification function be: (14) F(x)=w⋅x+b \[F(x)=w\cdot x+b\]

Assume that the training sample input is (x_i,y_i), where i = {1,2,3…n},x_i∈R,y_i∈{1,–1}, 1 and -1 represent the two sample categories. When H is the optimal surface, F(x) = 0, the function is normalized so that all samples satisfy |H(x)|= 1, i.e: (15) yi[(w⋅x)+b]−1≥0 \[{{y}_{i}}[(w\cdot x)+b]-1\ge 0\]

The classification interval is obtained from the distance public: (16) min{ xi|yi=1 }w⋅xi+b‖ w ‖−max{ xi|yi=−1 }w⋅xi+b‖ w ‖=2‖ w ‖ \[{{\min }_{\left\{ {{x}_{i}}|{{y}_{i}}=1 \right\}}}\frac{w\cdot {{x}_{i}}+b}{\left\| w \right\|}-{{\max }_{\left\{ {{x}_{i}}|{{y}_{i}}=-1 \right\}}}\frac{w\cdot {{x}_{i}}+b}{\left\| w \right\|}=\frac{2}{\left\| w \right\|}\]

Solving the optimal classification function is to maximize the formula while satisfying it, from which we can introduce a Lagrangian function to solve the constraint maximization, which is transformed into a function: (17) L(w,b,ai)=12(‖ w ‖)2−∑i=1nai[ yi(w⋅xi+b)−1 ] \[L\left( w,b,{{a}_{i}} \right)=\frac{1}{2}{{\left( \left\| w \right\| \right)}^{2}}-\sum\nolimits_{i=1}^{n}{{{a}_{i}}}\left[ {{y}_{i}}\left( w\cdot {{x}_{i}}+b \right)-1 \right]\] where a_i is a non-negative Lagrangian coefficient. It can be obtained according to the formula for finding the extreme value of the Lagrangian function: (18) w−∑i=1naiyixi=0 \[w-\sum\nolimits_{i=1}^{n}{{{a}_{i}}}{{y}_{i}}{{x}_{i}}=0\] (19) ∑i=1naiyi=0 \[\sum\nolimits_{i=1}^{n}{{{a}_{i}}}{{y}_{i}}=0\]

It can be obtained from the above equation and the formula carry over: (20) maxQ(a)=∑i=1nai−12∑i=1,j=1naiajyiyj(xiTxj) \[\max Q(a)=\sum\nolimits_{i=1}^{n}{{{a}_{i}}}-\frac{1}{2}\sum\nolimits_{i=1,j=1}^{n}{{{a}_{i}}}{{a}_{j}}{{y}_{i}}{{y}_{j}}\left( x_{i}^{T}{{x}_{j}} \right)\]

The KTT optimization condition is also satisfied: (21) ai[ yi(w⋅xi+b)−1 ]=0, where i=1,2,3…n \[{{a}_{i}}\left[ {{y}_{i}}\left( w\cdot {{x}_{i}}+b \right)-1 \right]=0,\text{ where }i=1,2,3\ldots n\]

The training samples when a_i = 0 do not work for the classification problem, and the samples that satisfy the constraints when a_i ≠ 0 are support vectors to find the weight vectors for the optimal solutions w′ and b′: (22) w′=∑i=1na′iyixi \[w\prime =\sum\nolimits_{i=1}^{n}{{{{{a}'}}_{i}}}{{y}_{i}}{{x}_{i}}\]

Using the original constraints yields (23) b′=1|s|∑i∈s(yi−w′xi) \[b\prime =\frac{1}{|s|}\sum\nolimits_{i\in s}{\left( {{y}_{i}}-w\prime {{x}_{i}} \right)}\] where s is called the set of support vectors. At this point the optimal classification decision function is obtained: (24) F(x)=∑i∈sa′iyixix+b′ \[F(x)=\sum\nolimits_{i\in s}{{{{{a}'}}_{i}}}{{y}_{i}}{{x}_{i}}x+b\prime \]

After finding the optimal classification decision function, the classification result for category x can be obtained: (25) { Category 1H(x)>0Category 1H(x)<0 $\left\{ \begin{array}{*{35}{l}} \text{Category 1} & H(x)>0 \\ \text{Category 1} & H(x)<0 \\ \end{array} \right.$

If F(x) = 0, it means that x is located in the boundary indivisible, and if the training results are acceptable, the region {x|–1<F(x)<1} is a generalized region.

Since the enterprise economic problem is linearly indivisible, this paper uses the Gaussian kernel function, which is formulated as: (26) K(x,xi)=exp(−‖ x−xi ‖2σ2) \[K\left( x,{{x}_{i}} \right)=\exp \left( -\frac{{{\left\| x-{{x}_{i}} \right\|}^{2}}}{{{\sigma }^{2}}} \right)\] Where σ denotes the customized kernel width, which controls the radial range of action of the function.

The introduction of the kernel function has little effect on the computational complexity of the decision function although it maps the vector space into a higher dimensional space, and the decision function formula becomes when linearly indivisible: (27) maxQ(a)=∑i=1nai−12∑i=1,j=1naiajyiyjK(xi,xj) \[\max Q(a)=\sum\nolimits_{i=1}^{n}{{{a}_{i}}}-\frac{1}{2}\sum\nolimits_{i=1,j=1}^{n}{{{a}_{i}}}{{a}_{j}}{{y}_{i}}{{y}_{j}}K\left( {{x}_{i}},{{x}_{j}} \right)\]

Thus the optimal classification decision function is derived: (28) F(x)=∑i=1naiyiK(x,xi)+b′ \[F(x)=\sum\nolimits_{i=1}^{n}{{{a}_{i}}}{{y}_{i}}K\left( x,{{x}_{i}} \right)+b\prime \]

In the practical application of SVM, due to the existence of errors in a few samples, it is not possible to completely separate the two classes of samples with one hyperplane in practical classification, by introducing the relaxation variable ζ_i that solves the linearly indivisible problem, at which time the hyperplane satisfies Eq: (29) yi[ (w⋅xi)+b ]−1+ζi≥0, where i=1,2,3…m \[{{y}_{i}}\left[ \left( w\cdot {{x}_{i}} \right)+b \right]-1+{{\zeta }_{i}}\ge 0,\text{ where }i=1,2,3\ldots m\]

With the introduction of the non-negative relaxation variable ζ_i, sample x_i can still be correctly classified when 0<ζ_i<1 and the sample is misclassified when ζ_i≥1.

In order to obtain the optimal hyperplane without maximum spacing while the number of samples is minimized, it can be transformed into: (30) Q(w)=∑i=1mθ(ζi), where θ(ζi)={ 1ζi>00ζi=0 \[Q(w)=\sum\nolimits_{i=1}^{m}{\theta }\left( {{\zeta }_{i}} \right),\text{ where }\theta \left( {{\zeta }_{i}} \right)=\left\{ \begin{array}{*{35}{l}} 1 & {{\zeta }_{i}}>0 \\ 0 & {{\zeta }_{i}}=0 \\ \end{array} \right.\]

Simplified substitution of the above equation as: (31) minQ(w,b,ζ)=12‖ w ‖2+C∑i=1mζi \[\min Q(w,b,\zeta )=\frac{1}{2}{{\left\| w \right\|}^{2}}+C\sum\nolimits_{i=1}^{m}{{{\zeta }_{i}}}\] (32) s.t.yi[ (w⋅xi)+b ]−1+ζi≥0, where i=1,2,3…m \[s.t.{{y}_{i}}\left[ \left( w\cdot {{x}_{i}} \right)+b \right]-1+{{\zeta }_{i}}\ge 0,\text{ where }i=1,2,3\ldots m\]

In the above formula, C is the penalty factor, which is used to deal with the classification error caused by the maximum interval and the minimum interval, the larger C is, the stricter the error processing of the training samples, the smaller the error, and the smaller C is, the larger the number of errors.

The specific algorithmic process of SVM for business economy recognition is outlined as:

Step1: Identify the positive and negative samples in the training samples, count the total number of samples m and the dimension of feature vectors n, and build the vector matrix of training samples T.

In this paper, we choose the C4.5 algorithm of the decision tree algorithm.The C4.5 decision tree algorithm measures the difference between the categories as the rate of decrease of the information entropy, which indicates that the uncertainty of the information is reduced.

Information entropy, also known as a priori entropy, is the expectation of the amount of information, Let the probability of occurrence of information a_i(i = 1,2…n) be P(a_i), then ΣP(a_i) = 1, then the amount of information is calculated as: (38) I(ai)=log21P(ai)=−log2P(ai) \[I\left( {{a}_{i}} \right)={{\log }_{2}}\frac{1}{P\left( {{a}_{i}} \right)}=-{{\log }_{2}}P\left( {{a}_{i}} \right)\]

From the amount of information, the information entropy is calculated as: (39) H(A)=∑iP(ai)I(ai)=−∑iP(ai)log2P(ai) \[H(A)=\sum\nolimits_{i}{P}\left( {{a}_{i}} \right)I\left( {{a}_{i}} \right)=-\sum\nolimits_{i}{P}\left( {{a}_{i}} \right){{\log }_{2}}P\left( {{a}_{i}} \right)\]

In the C4.5 algorithm, let N be the data sample, x be the target variable, x have y categories, M denotes the number of data samples belonging to x_i in N, and |N| is the number of samples in N. From this, the information entropy of N can be calculated as: (40) H(N)=−∑i=1yM|N|log2M|N| \[H(N)=-\sum\nolimits_{i=1}^{y}{\frac{M}{|N|}}{{\log }_{2}}\frac{M}{|N|}\]

If an attribute variable is z and there are k categories, the information entropy of attribute variable z is: (41) H(z)=−∑i=1kzizH(zi) \[H(z)=-\sum\nolimits_{i=1}^{k}{\frac{{{z}_{i}}}{z}}H\left( {{z}_{i}} \right)\]

Then the information gain of the change attribute variable z of the information entropy is: (42) Gain(z)=H(N)−H(z) \[Gain(z)=H(N)-H(z)\]

Risk assessment and avoidance are crucial parts of enterprise economic management activities.In general, the evaluation indicators of the enterprise economic management model should consist of profitability, turnover operating ability, debt servicing ability, and growth potential.This paper initially selects four major categories of financial indicators based on the principles of operability, comprehensiveness, dynamism, comparability, and the results of previous research.

The Entropy-TOPSIS method combines the Entropy Weight Method and the TOPSIS Superiority Distance Method. Entropy is a thermodynamic concept used to describe the degree of chaos of matter, the concept was first proposed by the German physicist Clausius in 186, and has been widely used in the field of probability theory and number theory. And the entropy weight method is based on the concept and nature of entropy, using the degree of difference of each indicator to empower, the essence is based on the degree of variability of the value of each indicator to determine the weight of the indicator, which is a kind of objective empowerment method. Generally speaking, the smaller the entropy value of the indicator is, the greater the degree of variation of the indicator is, the greater the amount of information it provides, the greater the influence it plays in the evaluation, and the greater the weight of the indicator is. On the contrary, the larger the entropy value of the indicator is, the less information it can provide, and the smaller the weight of the indicator is. Due to the objective assignment of the entropy value method, it reduces the influence of human factors, which results in higher precision and stronger objectivity, and more accurate evaluation results.However, the entropy weight method also has certain shortcomings, such as the inability to deal with strong correlations between indicators and the higher standardization requirements for indicator data.

TOPSIS superiority distance method, also known as the approach to the ideal solution scheme method, is through the use of raw data information, the use of normalized data normalization matrix to calculate the distance between each evaluation target and the positive ideal solution and negative ideal solution, to get the relative closeness of the positive and negative ideal solution of each target and ranked as a basis for evaluating the superiority of the target. If a program is closer to the ideal optimal solution and farther away from the worst solution, it is considered better. This is a commonly used comprehensive evaluation method, which has been successfully applied in a number of decision-making fields, such as enterprise performance evaluation and non-enterprise performance evaluation, and has improved the science, accuracy and operability of multi-objective decision analysis.

In this paper, the entropy weight-TOPSIS method is used in the research of enterprise economic management model strategy, which can effectively correct the calculated weights and carry out comprehensive ranking, and the combination of the two methods helps to improve the accuracy of the evaluation results.

In this paper, the tiers of business economic management are categorized as healthy and strong, with no risk, with mild risk, high risk, and extreme risk, with each tier having a different level of severity.According to the numerical size of the comprehensive score value, enterprises can be divided into the corresponding warning limit interval. Specifically: a composite evaluation score of 80 to 100 is considered strong health, 60 to 80 is no risk, 40 to 60 is mild risk, 20 to 40 is high risk, and 0 to 20 is extreme risk.

According to the model calculation and screening, the evaluation index system of A automobile company has been determined.The screened indicators are used to calculate the weights of each second-level indicator using the entropy value method, and finally, the weights of each first-level indicator are derived.

The results of weight calculation are shown in Table 2. It can be seen that the weights of profitability, turnover operating ability, solvency, and growth ability calculated by the model of this paper are 24.26%, 26.77%, 24.19%, and 24.78% respectively.There is basically no significant difference in the weights of the first-level indicators, which indicates that profitability, turnover, operating ability, debt servicing ability, and growth ability are equally important in managing business risks. Among the second-level indicators, Cash current liability ratio has the lowest weight (7.12%), followed by Times interest earned, Asset current ratio, accounting for 8.51%, 8.56%, so it can be said that the three second-level indicators in solvency have the lowest importance while Total asset growth rate has the highest proportion of 12.61%, followed by Surplus cash guarantee multiple, Revenue growth, the proportion is 12.37%, 12.17%, which shows that revenue growth, asset growth represented by the growth ability of the company’s business development is crucial.

Based on the publicly disclosed financial and operating data, the model was used to calculate the comprehensive evaluation score of Automobile Company A in 2021, and the results are shown in Table 3.

It can be seen that the comprehensive evaluation score of Company A in the model in 2021 is 72.35, which belongs to the risk-free level. Among them, the Times interest earned score is 14.18, which is the highest among the secondary indicators. This indicates that the company’s earned interest multiple performs well and its ability to pay interest on loans is fully guaranteed.This is followed by a accounts receivable turnover score of 9.75, indicating that the operational capacity is somewhat secured.However, the gearing ratio and cash current liabilities ratio are 4.398 and 2.508, respectively, with low scores, which indicate that the pressure on Company A’s liabilities is evident.

Using the model to calculate the comprehensive evaluation score of Automobile Company A in 2022, the results are shown in Table 4. It can be seen that the comprehensive evaluation score of Company A in 2022 in the model is 68.393 points, which is considered risk-free. The first-level indicators of profitability, turnover operations, debt service, and growth capacity scores are 12.43, 21.82, 19.815, and 14.328 points, respectively, which are all declining compared to 2021, indicating that Company A’s production and operations are unfavorable in 2022, and the level of corporate economic management and decision-making is problematic.

Using the model to calculate the comprehensive evaluation score of Automobile Company A in 2023, the results are shown in Table 5. It can be seen that the comprehensive evaluation score of Company A in the model in 2023 is 67.011 points, which continues to decline compared to 2022 and 2021, and although it still belongs to the risk-free level, the downward trend has not significantly improved. The score for profitability, turnover operations, debt service, and growth capacity was 12.768, 21.415, 16.846, and 12.982 points, respectively. Except for a slight increase in profitability, the other three scores continued to decline, of which the debt service capacity dropped sharply by 2.969 points, which indicates that Company A’s solvency deteriorated drastically, dragged down mainly by the significant decrease in the earned interest multiple. From 2021 to 2023, the earned interest multiple declined by more than 5 points, indicating that the pressure to pay interest is gradually having a negative impact on Company A.

The comprehensive model’s enterprise management risk index for Company A in 2021~2023 reveals that although Company A’s comprehensive evaluation score still maintains the risk-free level, its score is declining year by year, and its profitability, debt servicing, turnover, and growth ability are all in the downward channel. Especially the debt servicing ability is declining significantly, and the pressure of Company A’s indebtedness is gradually manifesting itself. It can be assumed that its level of corporate economic management and decision-making is problematic and requires urgent optimization.

In this regard, Company A should take the problem as a guide, optimize the enterprise economic management mode, improve the standardized decision-making level, firstly, start from the solvency, broaden the financing channels, design the debt restructuring or debt replacement plan, try to change the debt structure to avoid further deterioration of the debt problem. Then increase investment in technology research and development, improve product competitiveness, improve profitability and turnover capacity, and strive to reach a healthy and strong level at an early date.

Combining the management analysis model and the risk assessment model, this paper constructs the two points of standardization for enterprise economic management.The results of the research can help the enterprise optimize management decisions and improve the control of risks.