# Research and Development Talents Training in China Universities—Based on the Consideration of Education Management Cost Planning

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## Abstract

**:**

## 1. Introduction

- The BRB expert system takes into consideration the IF-THEN rule with embedding belief structure into THEN part for knowledge representation, in which the IF- THEM rule is one of the most common forms for expressing various types of know- ledge [10]; therefore, it makes the EBRB expert system more powerful in keeping human knowledge. Moreover, the use of belief structure further extends the ability of traditional IF-THEN rules to represent a variety of uncertain information [11].
- The BRB expert system is a data-driven, knowledge-driven, or hybrid-driven model, and its rule base is constructed using historical data and expert knowledge. Meanwhile, the BRB expert system takes the ER algorithm [12] as an inference engine for rule reasoning; therefore, it can not only achieve knowledge fusion with uncertain information but also have transparent rule integration process. All these components form a powerful expert system for handling complex practical problems.
- The BRB expert system belongs to a “white box” model, which mainly refers to the visible modeling and inference processes, especially because of the fact that domain experts can participate in these processes. The inferential results of the BRB expert system have good traceability and interpretability so that decision makers can fully understand and explain its working principle more easily when applying BRB expert systems.

## 2. Preliminaries for Education Management Cost Prediction

#### 2.1. Brief Review of the BRB Expert System

_{m}; m = 1,…, M} denotes a set of M antecedent attributes; {${A}_{m}^{k}$; m = 1,…, M} denotes a set of referential values used to describe the kth (k = 1,…, L) belief rule; L is the total number of belief rules in the BRB; ${A}_{m}^{k}$ belongs to {A

_{m}

_{,j}; j = 1,…, J

_{m}} that is a complete set of J

_{m}referential values used to describe the mth antecedent attribute; and {(D

_{n}, β

_{n}

_{,k}); n = 1, …, N} denotes belief structure in consequent attribute D, in which β

_{n}

_{,k}is the belief degree to which the consequent D

_{n}is believed to be true.

#### 2.2. Optimization of BRB Expert System

**x**) denotes the inference output of a BRB expert system to predict the input data

_{t}**x**, here

_{t}**x**= (x

_{t}_{1t}, x

_{2t}, …, x

_{Mt}); y

_{t}is the actual output of the input data

**x**; T is the total number of historical data used to train the BRB expert system; Equation (2b,c) are constraints on the belief degree; Equation (2d,e) are constraints on the antecedent attribute weights and the rule weights, respectively; and Equation (2f–i) are the constraint on the utility values of the referential values used for antecedent attributes and the consequents used for consequent attribute. Note that the global parameter learning model can be solved by using the MATLAB optimization toolbox [15], clonal selection algorithm [16], and differential evolution algorithm [17].

_{t}#### 2.3. Inference of BRB Expert System

**x**= (x

_{1}, x

_{2}, …, x

_{M}) is the input vector, and x

_{i}denotes the input data of the ith antecedent attribute. The following steps should be performed to obtain an inference output.

**Step 1**: To calculate individual matching degrees. The individual matching degree can be transformed from the input data

**x**using utility-based equivalence transformation techniques, i.e., the individual matching degrees of x

_{i}are calculated by

_{i}

_{,j}represents the jth referential value for the ith antecedent attribute; u(A

_{i}

_{,j}) represents the utility value of A

_{i}

_{,j}; and ${\alpha}_{i,j}$ represents the individual matching degree of the given input x

_{i}to A

_{i}

_{,j}. As a result, the distribution of the individual matching degree for the ith antecedent attribute is represented as follows:

**Step 2**: To calculate activation weights. While the BRB expert system is constructed under the conjunctive assumption, the activation weight for the kth belief rule is calculated as follows:

**Step 3**: To integrate belief rules for producing an inference output. After calculating activation weights for all belief rules in the BRB, the combined belief degree ${\beta}_{i}$ can be calculated using the ER algorithm:

**x**) can be obtained as follows:

_{i}) denotes the utility value of the consequent D

_{i}.

## 3. Education Management Cost Prediction Based on the BRB Expert System

_{t}(t = 1,…, T) is x

_{t}∈ [100, 200], which also means that the input data needed to predict must be x ∈ [100, 200]. In other words, the BRB expert system cannot produce an inference output for the input data x = 210 because of 210 > 200.

**Definition**

**1**

**.**Consider a case of a M-dimensional function y = f(

**x**) with

**x**= {x

_{1},…, x

_{M}} and its definition domain [

**a**,

**b**], where

**a**and

**b**are all M-ary vectors, respectively. When there exists an input–output data pair <

**x**,

_{0}**y**> in the function y = f(

_{0}**x**), for any

**x**∈ [

_{1}**a**,

**b**], the data increment regarding the input and output data can be written as Δ

**x**=

**x**−

_{1}**x**and Δy = f(

_{0}**x**) − f(

_{1}**x**) = f(

_{0}**x**+ Δ

_{0}**x**) − f(

**x**), respectively.

_{0}_{t}

_{,l}= x

_{t}− x

_{l}and Δx

_{t}

_{,l}∈ [−100, 100] (t, l = 1,…, T) for historical data x

_{t}and x

_{l}; therefore, it is possible for BRB expert system to produce an inference output when x = 210 because data increment is Δx = x − x

_{t}and Δx ∈ [−100, 100]. Based on the above viewpoint, Figure 1 provides a framework of the BRB expert system for education management cost prediction.

**Step 1**: To determine antecedent and consequent attributes. Suppose that one certain education management cost D is related with M education management indicators {U

_{i}; i = 1,…, M}. In order to construct a BRB expert system, all these D and U

_{i}are regarded as antecedent and consequent attributes of the BRB expert system. Moreover, this gives J

_{i}referential values {A

_{i}

_{,j}; j = 1,…, J

_{i}} for the ith antecedent attribute and N consequents {D

_{n}; n = 1,…, N} for consequent attribute.

**Step 2**: To generate data increments. Suppose that there are S input–output education management data pairs <

**x**, y

_{t}_{t}> (t = 1,…, S) for the M antecedent attributes {U

_{i}; i = 1,…, M} and consequent attribute D, where

**x**= {x

_{t}_{t}

_{,1},…, x

_{t}

_{,M}}. Based on Definition 1, the data increments of any two input–output data pairs, e.g., <

**x**, y

_{t}_{t}> and <

**x**, y

_{s}_{s}> (t, s = 1,…, S; t≠s), are generated as follows:

**Step 3**: To train parameter value of BRB expert system. Based on the parameter learning model shown in Section 2.2 and the T input data increment pairs shown in Equations (10)–(11), the parameters of the BRB expert system, including rule weights, attribute weights, belief degrees, and utility values, can be trained to obtain their optimal values; therefore, the resulting BRB expert system is able to accurately predict the cost of education management.

**Step 4**: To predict education management cost for any given input data. Suppose that there are a new input data

**x**= {x

_{i}; i = 1, …, M} and a recent input–output historical data pair <

**x**, y

_{k}_{k}>. Hence, the data increment of

**x**and

**x**can be calculated, and it is denoted as

_{k}**Δx**= {Δx

_{i}; i = 1,…, M}. Furthermore, based on the three steps detailed in Section 2.3, an inference output of the BRB expert system f(

**Δx**) can be obtained to produce a final predicted education management cost by y

_{k}+ f(

**Δx**).

**x**, y

_{1}_{1}> = <x

_{1,1}= 12142, x

_{1,2}= 5695.28, y

_{1}= 1137.18>, <

**x**, y

_{2}_{2}> = <x

_{2,1}= 11010, x

_{2,2}= 4957.82, y

_{2}= 1025.51> and <

**x**, y

_{3}_{3}> = <x

_{3,1}= 10490, x

_{3,2}= 4486.89, y

_{3}= 964.62>, the resulting data increments can be calculated, and they are <Δx

_{1,1}= 1132, Δx

_{1,1}= 737.46, Δy

_{1}= 111.67>, <Δx

_{2,1}= −1132, Δx

_{2,1}= −737.46, Δy

_{2}= −111.67>, <Δx

_{3,1}= 1652, Δx

_{3,1}= 1208.39, Δy

_{3}= 172.56>, <Δx

_{4,1}= −1652, Δx

_{4,1}= −1208.39, Δy

_{4}= −172.56>, <Δx

_{5,1}= 520, Δx

_{5,1}= 470.93, Δy

_{5}= 60.89>, and <Δx

_{6,1}= 520, Δx

_{6,1}= 470.93, Δy

_{6}= 60.89>. Thirdly, all these six data increments are used to optimize the parameter values of nine belief rules to improve the performance of the BRB expert system, in which the parameter learning model is introduced in Section 2.2. Finally, when a new input datum

**x**= <x

_{1}= 13142, x

_{2}= 6695.28> is given, the data increment regarding <

**x**, y

_{1}_{1}> should be calculated by Δx

_{1}= 13142 − 12142 = 1000 and Δx

_{2}= 6695.28 − 5695.28 = 1000. Afterward, the three steps detailed in Section 2.3 are used to produce f(Δ

**x**), e.g., f(Δ

**x**) = 300, and the final predicted cost is f(

**x**) = 300 + 1137.18 = 1437.18.

## 4. Empirical Analysis on China Education Management Cost Planning

#### 4.1. Data Collection and Indicator Explanation

#### 4.2. Analysis of Education Management Cost Investments during 2001–2019

#### 4.3. Verification of BRB Expert System for Cost Prediction

#### 4.4. Analysis of Future Education Management Cost Planning

## 5. Discussions

## 6. Conclusions

#### 6.1. Theoretical Implications

- (1)
- Due to the problem of sparse data in the field of education management cost prediction, the system modeling has to suffer from the over-fitting problem. The data increment of education management input and output indicators were used to enrich data for modeling expert system, and the resulting BRB expert system is able to overcome the over-fitting problem.
- (2)
- To overcome the subjectivity of parameters given by experts, the global parameter learning model was introduced to enhance the BRB expert system construction, so that the parameter values of the BRB expert system can be optimized according to the historical education management input and output data.
- (3)
- The results of comparative studies demonstrated that the data increment and parameter learning could effectively improve the performance of the BRB expert system. The government expenditures on education, science, and technology predicted by the BRB expert system were much lower than the other prediction models.

#### 6.2. Policy Suggestions

- (1)
- To optimize the setting of professional knowledge learning in universities based on the demand of economic market and social development, the course learning in universities for R&D talents should be improved and designed according to the current market environment and industry demand, so that they can better understand the market demand and master relevant professional technology through school–enterprise cooperation and exchange, so as to make up for the shortage of professional technicians in relevant fields in the market.
- (2)
- To advocate expanding teaching and to cultivate R&D talents’ basic quality and professional skills for social practice by relying on the practice carrier outside the universities professional classroom, so that they can train professional skills and improve practical ability in expanding teaching.
- (3)
- To establish a diversified training mode for R&D talents, and adopt a variety of talent training methods to improve the innovation of scientific and technological capability is an important strategy for R&D talents training in China universities. Decision makers of education management should also pay attention to improve the professional and technical level of R&D talents so as to ensure that the talents trained in universities can be truly applicable to new products and technologies innovation of actual economic activities.

#### 6.3. Limitations and Future Researches

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Rule No. | Rule Weight | Antecedent Attributes (Weights) | Belief Distribution of Consequent Attribute | |||
---|---|---|---|---|---|---|

TMTV (δ_{1}) | NNP (δ_{2}) | Low | Middle | High | ||

R_{1} | θ_{1} | Low | Low | β_{1,1} | β_{2,1} | β_{3,1} |

R_{2} | θ_{2} | Low | Middle | β_{1,2} | β_{2,2} | β_{3,2} |

R_{3} | θ_{3} | Low | High | β_{1,3} | β_{2,3} | β_{3,3} |

R_{4} | θ_{4} | Middle | Low | β_{1,4} | β_{2,4} | β_{3,4} |

R_{5} | θ_{5} | Middle | Middle | β_{1,5} | β_{2,5} | β_{3,5} |

R_{6} | θ_{6} | Middle | High | β_{1,6} | β_{2,6} | β_{3,6} |

R_{7} | θ_{7} | High | Low | β_{1,7} | β_{2,7} | β_{3,7} |

R_{8} | θ_{8} | High | Middle | β_{1,8} | β_{2,8} | β_{3,8} |

R_{9} | θ_{9} | High | High | β_{1,9} | β_{2,9} | β_{3,9} |

Indicator Name | Abbr. | Corresponding Relationship |
---|---|---|

Number of R&D employees | NRDE | Antecedent |

Number of new products | NNP | Antecedent |

Number of invention patent applications | NIPA | Antecedent |

Technical market transaction volume | TMTV | Antecedent |

Government expenditure on education | GEE | Consequent |

Government expenditure on science and technology | GEST | Consequent |

Predicted Costs | MAE | MAPE | ||||
---|---|---|---|---|---|---|

BRB | FRBS | ANFIS | BRB | FRBS | ANFIS | |

GEE | 82.40 (1) | 164.17 (2) | 2683.36 (3) | 9.62% (1) | 17.57% (2) | 400.76% (3) |

GEST | 18.59 (1) | 38.81 (2) | 446.91 (3) | 12.99% (1) | 22.74% (2) | 245.18% (3) |

Predicted Costs | MAE | MAPE | ||||||
---|---|---|---|---|---|---|---|---|

BRB | AR | MA | GM | BRB | AR | MA | GM | |

GEE | 82.40 (2) | 56.27 (1) | 384.16 (4) | 256.94 (3) | 9.62% (2) | 4.45% (1) | 35.22% (4) | 27.43% (3) |

GEST | 18.59 (1) | 25.27 (2) | 76.82 (4) | 54.86 (3) | 12.99% (1) | 13.21% (2) | 36.92% (4) | 23.09% (3) |

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**MDPI and ACS Style**

Yang, L.-H.; Liu, B.; Liu, J. Research and Development Talents Training in China Universities—Based on the Consideration of Education Management Cost Planning. *Sustainability* **2021**, *13*, 9583.
https://doi.org/10.3390/su13179583

**AMA Style**

Yang L-H, Liu B, Liu J. Research and Development Talents Training in China Universities—Based on the Consideration of Education Management Cost Planning. *Sustainability*. 2021; 13(17):9583.
https://doi.org/10.3390/su13179583

**Chicago/Turabian Style**

Yang, Long-Hao, Biyu Liu, and Jun Liu. 2021. "Research and Development Talents Training in China Universities—Based on the Consideration of Education Management Cost Planning" *Sustainability* 13, no. 17: 9583.
https://doi.org/10.3390/su13179583