The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics

We assume that the uncertain parameter matrix B = (b_ij) is an interval matrix, and the mean matrix or midpoint matrix of the uncertain parameter matrix is as follows: (1) Bc=(bij,c)=m(Bl)=(B+B)2bij,c=(bij+bij)2(i,j=1,2,⋯,n) \matrix{ {{B_c} = ({b_{ij,c}}) = m({B_l}) = {{(B + B)} \over 2}} \hfill \cr {{b_{ij,c}} = {{({b_{ij}} + {b_{ij}})} \over 2}(i,j = 1,2, \cdots ,n)} \hfill \cr } The deviation magnitude matrix or uncertainty matrix of the uncertainty parameter matrix is defined as follows: (2) ΔB=(Δbij)=(B+B)2,Δbij=(bij−bij)2(i,j=1,2,⋯,m) \matrix{ {\Delta B = (\Delta {b_{ij}}) = {{(B + B)} \over 2},} \hfill \cr {\Delta {b_{ij}} = {{({b_{ij}} - {b_{ij}})} \over 2}(i,j = 1,2, \cdots ,m)} \hfill \cr } According to interval mathematics, the uncertainty parameter matrix B is expressed as follows: (3) B=Bc+δB,|δB|≤ΔB B = {B_c} + \delta B,|\delta B| \le \Delta B We carry out the first-order Taylor series expansion of the eigenvalue at B_c, (4) λj(B)=λj(Bc+δB)=λj(Bc)+∑j=1m∂λj(Bc)∂bijδbij {\lambda _j}(B) = {\lambda _j}({B_c} + \delta B) = {\lambda _j}({B_c}) + \sum\limits_{j = 1}^m {{\partial {\lambda _j}({B_c})} \over {\partial {b_{ij}}}}\delta {b_{ij}} (5) δbij∈Δbij,l=[−Δbij,Δbij](i,j=1,2,⋯,m) \delta {b_{ij}} \in \Delta {b_{ij,l}} = [ - \Delta {b_{ij}},\Delta {b_{ij}}](i,j = 1,2, \cdots ,m) It can be obtained from the natural expansion of the interval that (6) λjl(B)=λj(Bc+δB)=λj(Bc)+∑i=1m∂λj(Bc)∂bijδbij,l(j=1,2,⋯,n) \lambda _j^l(B) = {\lambda _j}({B_c} + \delta B) = {\lambda _j}({B_c}) + \sum\limits_{i = 1}^m {{\partial {\lambda _j}({B_c})} \over {\partial {b_{ij}}}}\delta {b_{ij,l}}(j = 1,2, \cdots ,n) The upper and lower bounds of the eigenvalue interval can be obtained by interval operation: (7) λj(B)=λj(Bc)+∑i=1m|∂λj(Bc)∂bij|Δbij=λj(Bc)+|∂λj(Bc)∂(csB)T|Δ(csB)(j=1,2,⋯,n)λj(B)=λj(Bc)−∑i=1m|∂λj(Bc)∂bij|Δbij=λj(Bc)+|∂λj(Bc)∂(csB)T|Δ(csB)(j=1,2,⋯,n) \matrix{ {{\lambda _j}(B) = {\lambda _j}({B_c}) + \sum\limits_{i = 1}^m \left| {{{\partial {\lambda _j}({B_c})} \over {\partial {b_{ij}}}}} \right|\Delta {b_{ij}} = {\lambda _j}({B_c}) + \left| {{{\partial {\lambda _j}({B_c})} \over {\partial {{(csB)}^T}}}} \right|\Delta (csB)(j = 1,2, \cdots ,n)} \hfill \cr {{\lambda _j}(B) = {\lambda _j}({B_c}) - \sum\limits_{i = 1}^m \left| {{{\partial {\lambda _j}({B_c})} \over {\partial {b_{ij}}}}} \right|\Delta {b_{ij}} = {\lambda _j}({B_c}) + \left| {{{\partial {\lambda _j}({B_c})} \over {\partial {{(csB)}^T}}}} \right|\Delta (csB)(j = 1,2, \cdots ,n)} \hfill \cr } where ∂λj∂B {{\partial {\lambda _j}} \over {\partial B}} is the eigenvalue sensitivity matrix.

According to the nature of mean value calculation, the mean value λ_i0 of the eigenvalue is obtained, and the ith eigenvalue and eigenvector can be expressed as follows: (8) λi=λi0+Δλi(i=1,2,⋯,n) {\lambda _i} = {\lambda _{i0}} + \Delta {\lambda _i}(i = 1,2, \cdots ,n) We expand the first-order Taylor series of λ_i near csB_c and combine it with the properties of variance calculation to get (9) var[λi]=E[(Δλi)2]=[∂λi∂(csB)T]2var(csB) \mathop {{\rm{var}}} [{\lambda _i}] = E[(\Delta {\lambda _i}{)^2}] = [{{\partial {\lambda _i}} \over {\partial {{(csB)}^T}}}{]^2}{{\rm{var}}}{(csB)} Here, var(csB) = (ξμ_B)². We combine the sensitivity matrix of the eigenvalues to obtain the first-order approximation of the variance of the eigenvalues. The mean and variance of the feature vector can also be calculated accordingly. Figure 1 shows the flow of the perturbation method of probability theory [5]. We write the mean and variance of the eigenvalues obtained by the probability method in interval form, and the result is shown in the following formula: (10) λj¯(B)=E(λj)+kσλj=μλj+kvar(λj)=μλj+kξ∑i=1m(∂λj∂bij)2(j=1,2,⋯,n)λj(B)=E(λj)−kσλj=μλj−kvar(λj)=μλj+kξ∑i=1m(∂λj∂bij)2(j=1,2,⋯,n) \matrix{ {\overline {{\lambda _j}} (B) = E({\lambda _j}) + k{\sigma _{{\lambda _j}}} = {\mu _{{\lambda _j}}} + k\sqrt {{{\rm{var}}} ({\lambda _j})} = {\mu _{{\lambda _j}}} + k\xi \sqrt {\sum\limits_{i = 1}^m {{\left( {{{\partial {\lambda _j}} \over {\partial {b_{ij}}}}} \right)}^2}} (j = 1,2, \cdots ,n)} \hfill \cr {{\lambda _j}(B) = E({\lambda _j}) - k{\sigma _{{\lambda _j}}} = {\mu _{{\lambda _j}}} - k\sqrt {{{\rm{var}}}({\lambda _j})} = {\mu _{{\lambda _j}}} + k\xi \sqrt {\sum\limits_{i = 1}^m {{\left( {{{\partial {\lambda _j}} \over {\partial {b_{ij}}}}} \right)}^2}} (j = 1,2, \cdots ,n)} \hfill \cr }

Fig. 1

We introduce the coefficient of variance ξ=var(B)E(B) \xi = {{\sqrt {{{\rm{var}}}(B)} } \over {E(B)}} and combine B¯=Bc+kσB \overline B = {B_c} + k{\sigma _B} , B = B_c − kσ_B (where k is a constant coefficient) and interval mathematics to get (11) Δbij=kσbij=kξμbij \Delta {b_{ij}} = k{\sigma _{{b_{ij}}}} = k\xi {\mu _{{b_{ij}}}} We substitute the sensitivity matrix and the variance expression into Eq. (7) to obtain the upper and lower bounds of the nonprobability interval analysis eigenvalue interval. (12) λj(B)=λj(Bc)+∑i=1m|∂λj(Bc)∂bij|kξμbij(j=1,2,⋯,n)λj(B)=λj(Bc)−∑i=1m|∂λj(Bc)∂bij|kξμbij(j=1,2,⋯,n) \matrix{ {{\lambda _j}(B) = {\lambda _j}({B_c}) + \sum\limits_{i = 1}^m \left| {{{\partial {\lambda _j}({B_c})} \over {\partial {b_{ij}}}}} \right|k\xi {\mu _{{b_{ij}}}}(j = 1,2, \cdots ,n)} \hfill \cr {{\lambda _j}(B) = {\lambda _j}({B_c}) - \sum\limits_{i = 1}^m \left| {{{\partial {\lambda _j}({B_c})} \over {\partial {b_{ij}}}}} \right|k\xi {\mu _{{b_{ij}}}}(j = 1,2, \cdots ,n)} \hfill \cr }

This article attempts to construct a more comprehensive model of the entrepreneurial ability of college students based on the research of domestic and foreign scholars on the entrepreneurial ability models and the connotation and characteristics of college students’ entrepreneurial ability [6]. According to the statistical analysis of the entrepreneurial ability model, we summarize entrepreneurial ability into six dimensions of ability: self-efficacy, knowledge and professional skills, learning and innovation ability, opportunity recognition ability, interpersonal relationship ability, and organization and management ability. The frequency statistics of these capacity dimensions in the above research results are shown in Table 1.

Based on the above engineering research, we construct a college students’ entrepreneurial ability model, as shown in Figure 2. The model is a pyramid-structured capability model. The lower the level of competence, the more basic and extensive it is. This is a necessary condition for college students to succeed in starting a business [7]. On the other hand, the higher-level ability elements are the comprehensive abilities needed by college students to succeed in entrepreneurship. Their ability elements tend to be specialized, unique, and practical. This is the decisive factor that determines the level of entrepreneurial achievement of college students. It is also an important distinction between the levels of entrepreneurial ability of different college students.

Fig. 2

Self-efficacy is an essential component in the structural model of college students’ entrepreneurial ability. It reflects an individual's ability to work or deal with problems and is an individual's judgment on self-ability and beliefs. Personal effectiveness is mainly composed of five abilities: self-management ability, adaptability, commitment ability, self-motivation, and breakthrough ability.

Self-management ability is also called self-control ability. It refers to the individual's ability to control negative emotions and actions and remain calm in the face of frustration, pressure, and temptation. Some scholars put forward the terms self-control and willpower [8]. Emotional control ability and frustration resistance ability belong to the category of self-management ability.

Self-adaptability refers to the adaptability and flexibility that an individual exhibits when working with different people or groups in different environments. It includes specific abilities such as stress resistance and emotional control. Self-adaptability is necessary for college students in the process of entrepreneurship. It helps college students change their ways of doing things according to actual conditions and quickly adapt to changes in the environment.

Entrepreneurship quality refers to a person's ability and willingness to adjust individual behavior to conform to the organization's needs and goals, act according to the organization's needs, and assist the organization in achieving its goals. It includes specific abilities such as commitment ability, self-motivation, and self-breakthrough. Some scholars believe that commitment ability is necessary for entrepreneurial ability, and it is also a manifestation of excellent entrepreneurial quality.

In addition, college students will inevitably encounter many difficulties in the process of starting a business. Therefore, they must have the ability for self-motivation and breakthrough, with firm entrepreneurial beliefs, be positive, dare to take risks, and – through the continuous overcoming of difficulties and self-improvement–successfully start a business.

Entrepreneurship knowledge and professional skills are necessary conditions for entrepreneurs. It includes specific abilities such as knowledgeability and professional technical ability.

Knowledgeability is an important indicator reflecting the efficiency of knowledge absorption and transformation. Its meaning refers to synthesizing various abilities with knowledge as the core possessed by the knowledge holder. Some scholars believe that college students should have a ‘T’ knowledge structure in entrepreneurship [9]. Some scholars believe that the knowledge element system necessary for college students to start a business should be based on finance, business, law, marketing, marketing management, finance, taxation, business establishment procedures, and macroeconomic policies. This is the social knowledge formed by entrepreneurial ability. Basically, in addition, students must have the necessary knowledge of natural sciences.

Professional technical ability refers to mastering the profession-related knowledge, being proficient in the industry's business, and having specialized skills, as well as engaging experienced workers. It is the skill that people must possess to engage in a particular social occupation. Entrepreneurs should pay attention to accumulating professional and technical experience and undergoing vocational skills training in the process of starting a business.

Learning and innovation ability is a comprehensive ability, including learning ability and innovation ability.

Learning ability refers to the ability to actively learn and change one's behavior from past experiences and critical events of oneself or others. It consists of limited learning ability, conceptual ability, and analytical ability (logical thinking ability), as well as the ability to reflect on and solve problems. Concept and analysis ability is the ability to look at the overall situation, recognize the development of things, and grasp the direction of progress [10]. Entrepreneurs can perceive the interaction between the enterprise and the environment. Concepts and analytical skills help college students to simplify the complex situation in the entrepreneurial process, extract and abstract a lot of trivial information, and make objective decisions by weighing different options, thereby leading the development direction of the enterprise. Introspection and problem-solving ability can check one's errors, sum up experience, and obtain solutions to problems from it. Entrepreneurship is a process of constant exploration. Undergraduate entrepreneurs must constantly conduct self-reflection, learn from failures, and summarize successful experiences. Through comparative research, some scholars have found that entrepreneurs and college teachers place more emphasis on learning ability than college students. It can be seen that college students have not yet realized the importance of learning ability. The importance and cultivation of the learning ability of college students must be strengthened [11]. An enterprise needs to continuously develop and innovate to continue to develop and remain invincible. Entrepreneurship itself is the beginning of innovation, so the ability to innovate is essential for entrepreneurs. Some scholars have proved through empirical evidence that the innovation ability of entrepreneurs has a strong positive correlation with the growth of enterprises. New ventures must grow and develop new products, all of which require entrepreneurs to have the ability to innovate.

Entrepreneurship opportunities refer to the existence and perception of opportunities available in the market. Opportunity is a necessary condition for starting a business, but this alone is not enough. Entrepreneurs must have the necessary abilities (motivation and skills) to create a new business.

Some scholars believe that identifying opportunities refers to the ability to discover potential market opportunities and make objective assessments. However, we believe that the ability to identify opportunities is the ability to discover opportunities and the ability to grasp opportunities [12]. In other words, the ability to identify opportunities refers to the ability to objectively analyze the surrounding environment and various types of information, explore potential market opportunities, and transform potential opportunities into reality.

Some scholars decompose the ability to identify and develop opportunities to identify viable niche markets, develop products and services suitable for selected niche markets, generate ideas, conduct environmental observations, identify and conceive how to use opportunities, and develop relevant strategies. We believe that information analysis is the most important manifestation of the ability to identify and develop opportunities. Some scholars have found through research that there is a significant positive correlation between the entrepreneur's ability to identify opportunities and the growth of enterprises. Recognizing and using opportunities is the central concept of entrepreneurship, which distinguishes entrepreneurship from management.

Interpersonal relationships can have a rich social network, facilitating communication with people and handling of the interaction between people and between individuals and organizations. Establishing good interpersonal relationships is the essential ability of people to maintain interpersonal relationships and maintain survival in daily life. Unlike the ability of learning and innovation, interpersonal relationship ability is different from abstract thinking ability [13]. It has a strong practicality and tends to be more concrete.

Some scholars have pointed out – by comparing the entrepreneurial ability reflected by entrepreneurs at home and abroad – that the relationship ability is affected by the entrepreneur's personality, behavior, attitude, and cultural background. Although relationship skills are capabilities that domestic and foreign entrepreneurs possess, domestic entrepreneurs are more inclined to use their interpersonal networks. From the perspective of Chinese social and cultural traditions and college students, interpersonal skills are essential for college entrepreneurs, including interpersonal relationship-processing skills, expression skills (written and oral expression skills), and communication skills.

Entrepreneurs must communicate with investors, government departments, customers, and consumers during the entire process of starting a business. Whether it is oral interviews or providing written documents, such as business plans or other corporate announcements, they need good language skills. Some scholars conducted a questionnaire survey of 100 significant entrepreneurs and the chief executive officers (CEOs) of the fastest-growing startups in the United States and found that written and oral expression skills are more critical to these successful entrepreneurs.

Organization and management ability is a comprehensive entrepreneurial ability. It contains many specific skills, such as organization ability, management ability, team-building ability, marketing ability, operation management ability, resource integration ability, etc. Therefore, we can divide these skills into two categories: broad organizational skills and management skills.

Organizational capabilities include organizational capabilities and resource integration capabilities in a narrow sense. Organizational ability in a narrow sense refers to the internal and external resources (human, financial, material, and technical resources) of the organization and includes team building, leadership of subordinates, training, and monitoring skills. Many scholars believe that organizational ability is an integral part of entrepreneurial ability, which is of great significance to the entrepreneurial activities of college student entrepreneurs. Resource integration ability refers to the ability to acquire and organize various required resources [14]. Entrepreneurs always engage in entrepreneurial activities when resources are scarce at the beginning of their business. They must borrow external forces and use their resources to integrate the resources of others to achieve the effect of 1 + 1 > 2. Thus, the cultivation of the ability to integrate resources is an important component of entrepreneurial ability. Through empirical research, some scholars have found that college teachers, entrepreneurial entrepreneurs, and college students themselves believe that organizational management capabilities and resource integration capabilities are important components of entrepreneurial capabilities.

Management capabilities include management capabilities, leadership capabilities, decision-making capabilities, marketing capabilities, business and management capabilities, and many other specific skills. Some empirical studies have found that management ability plays an essential role in college students’ entrepreneur-ship: leadership communication ability is the most influential ability on entrepreneurship; Li Fanning found that college students pay more attention to cultivating their leadership inspiring ability. Some scholars have found that most entrepreneurs in the United States believe that leadership is the most critical entrepreneurial ability. Foreign entrepreneurs pay more attention to organizational ability than domestic entrepreneurs and tend to manage organizations. It shows that domestic college student entrepreneurs need to strengthen their organization and management awareness.