The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model

The unification of indicator types means that different indicators are treated as the same type of indicators. There are four main types of research indicators based on scholarly research, namely ‘maximised’ indicators (the more significant the indicator value is, the better) and the ‘tiny’ indicator (the smaller the indicator value is, the better). Different types of indicators represent the values of different preferences [6]. Therefore, the index type must be uniformised before the evaluation value of the evaluating object can be measured. For ‘minimal’ indicators, we can take the standard method of indicators for ‘minimal ‘indicators to transform them into ‘maximised’ indicators for ‘minimal’ indicators.

Each indicator has its dimension and magnitude. However, they are incommensurable and cannot complete the calculation of the comprehensive index. Therefore, when calculating, we must first make the indicator dimensionless [7]. The dimensionless index is a method to eliminate the influence of the original index dimension and magnitude through mathematical transformation. There are many ways to deal with dimensionlessness. This research adopts the ‘minimum and maximum standardisation method’ widely used by scholars. (1) zij=pij−min{pij}max{pij}−min{pij} {z_{ij}} = {{{p_{ij}} - \min \{ {p_{ij}}\} } \over {\max \{ {p_{ij}}\} - \min \{ {p_{ij}}\} }} In the above formula z_ij is the evaluation index data after the index dimensionless processing. p_ij represents the data after the index type is unified. {p_ij} and min{p_ij} respectively represent the maximum value and the minimum value of the data after the j index unification processing.

The group G2 method is developed based on the single G2 method. The main idea of the single G2 method is to invite experts to compare and judge the same sorting problem under a particular target [8]. Finally, the subjective experience of experts is combined to obtain a more accurate weighing result.

We first invite an expert to establish an order relationship for m evaluation indicators {x₁,x₂, …, x_m}. That is, select the least important one and only one index from the evaluation index set and record it as xm* x_m^* . Then, in the remaining evaluation index set, ask the experts to select the least important one and mark it as xm−1* x_{m - 1}^* . By analogy, we mark the remaining evaluation index as x1* x_1^* to determine the order relationship of the evaluation index set, which we denote as x1*>x2*⋯xm* x_1^* > x_2^* \cdots x_m^* . Then, again invite experts to make a rational judgement on the importance index r_i of a criterion (or target) based on the relevant information on the evaluation index xi* x_i^* and the least essential evaluation index xm* x_m^* , that is, let: r_i = a_j, i = 1,2, …, m − 2, m − 1. Among them, we take the assignment of a_m = 1, r_i. r_i = 1, which shows that both the index xi* x_i^* and the index xm* x_m^* have the same importance. Note that r_i = 1,2 indicates that the index xi* x_i^* is slightly more critical than the index xm* x_m^* ; r_i = 1,4 shows that the index xi* x_i^* is more critical than the index xm* x_m^* ; r_i = 1,6 shows that the index xi* x_i^* is more important than the index xm* x_m^* ; and r_i = 1,8 shows that the index xi* x_i^* is essential than the index xm* x_m^* . Finally, according to the rational assignment of r_i given by experts, the weight coefficient of the evaluation index xi* x_i^* plus i is obtained [9]. The calculation formula is: (2) ωi=ai/∑i=1mai,i=1,2,⋯,m−1 {\omega _i} = {a_i}/\sum\limits_{i = 1}^m {a_i},i = 1,2, \cdots ,m - 1 After making a one-to-one correspondence between the weight coefficient of xi* x_i^* and x_i, we finally obtain the weight coefficient of the single G2 method of the evaluation index set {x₁,x₂, …, x_m}). To compensate the lack of experience and knowledge of a single expert and the interference of personal factors in giving the weight coefficient of the evaluation index more objectively and accurately, we introduce the group G2 method. Based on a single G2 method, we can simultaneously hire L (two or more) experts to judge the order relationship and rationally assign importance to the evaluation indicators [10]. According to the steps of the single G2 method, the weight coefficients of each index are calculated. Then weight coefficients of each index are combined to obtain an ideal weight coefficient. However, there are two situations in which experts have consistent and inconsistent views on the judgement of the index relationship and these two situations should be dealt with.

Suppose that the judgements of L experts on the order relationship in the evaluation index set {x₁,x₂, …, x_m} are entirely consistent and recorded as x1*>x2*⋯xm* x_1^* > x_2^* \cdots x_m^* . Assume that the ratio of the importance of a specific expert q to r_km is assigned as a_q1,a_q2, …, a_q(m−1),q = 1,2, …, L is in order. Calculate the ω_qk obtained under the judgement of each expert according to the calculation formula. Finally, we take the arithmetic average of the L group weight coefficients obtained by the L experts to obtain the combined weight coefficient. The calculation formula is as follows: (3) ωk=∑q=1lωqk/L,k=1,2,⋯,m {\omega _k} = \sum\limits_{q = 1}^l {\omega _{qk}}/L,k = 1,2, \cdots ,m The second one is the inconsistent judgement of the order relationship because L experts from the same field have roughly the same qualitative judgements on the same issue. Therefore, in this case, the qualitative judgements of some experts are consistent, while the qualitative judgements of other experts are inconsistent. Suppose that the ordering relationship given by P experts is consistent and denoted as x1*>x2*⋯xm* x_1^* > x_2^* \cdots x_m^* . At this time, the corresponding weights of the indicators can be calculated as ω1*,ω2*,⋯,ωm* \omega _1^*,\omega _2^*, \cdots ,\omega _m^* according to the sequence mentioned in the above relationship. In addition, suppose that the judgement of the order relationship given by the L-p experts is inconsistent with the above order relationship. The least essential index is different. We set the order relations given by expert k among L-p experts as xk1*>xk2*⋯xkm* x_{k1}^* > x_{k2}^* \cdots x_{km}^* , k = 1,2, …,L − p, respectively. We set the ratio of the importance of expert k to indicators xki* x_{ki}^* and xkm* x_{km}^* as r_ki(k = 1,2, …, L − p;i = m,m − 1, …, 2). We then calculate the weight coefficient under the expert k-order relationship and rational assignment according to formula (4) and record it as ω_ki. Finally, the weights obtained by L-p experts take the arithmetic average as the result of ‘comprehensive weight’ and mark it as ωi** \omega _i^{**} : (4) ωi**=1L−p∑k=1L−pωki,i=1,2,⋯,m \omega _i^{**} = {1 \over {L - p}}\sum\limits_{k = 1}^{L - p} {\omega _{ki}},i = 1,2, \cdots ,m After normalising ωi** \omega _i^{**} , we combine it with the weight ωi* \omega _i^* obtained by P experts. Finally, the weight coefficient ω_i of each evaluation index is obtained: (5) ωi=aωi*+bωi**,i=1,2,⋯,m {\omega _i} = a\omega _i^* + b\omega _i^{**},i = 1,2, \cdots ,m Among them, a > 0, b > 0 and a + b = 1 and we take a = p/L, b = ((L − p)/L.

In our study, five experts were invited and denoted as A1, A2, A3, A4 and A5, and two of them came from the government education department. They are policymakers and supervisors, and they are familiar with the specific practical work of college innovation and entrepreneurship education. The other three experts have come from colleges and universities [11]. Five experts independently judged the order relationship and assigned importance to the 30 evaluation indicators in Table 1. According to the above steps, we assign values according to five experts’ order relationship and importance. Next, apply formulas (2) and (3) to obtain the absolute weight coefficients of the five groups of evaluation indicators, and then substitute weight coefficients of the five groups in formula (5) to obtain the final combined weight coefficient.

On the one hand, the teaching staff of entrepreneurship should achieve crossover and diversity. Entrepreneurship management-related courses mainly involve economic management, even law, and other aspects of knowledge. It is challenging for a single teacher to master relevant field knowledge very professionally. Therefore, we need professional teachers from different professional fields, such as financial management, marketing, human resource management, etc., to build a systematic education team of teachers. On the other hand, in addition to academic teachers who have mastered theoretical knowledge, entrepreneurs or serial entrepreneurs with rich entrepreneurial experience should also be invited to provide special lectures and exchanges, especially for practice and training guidance in industry experience and team management in project financing. Only a team of teachers with comprehensive professional knowledge and different development backgrounds can provide a faculty foundation for cultivating comprehensive college students’ entrepreneurial ability.

Entrepreneurship courses for college students involve knowledge systems in various aspects such as entrepreneurial foundation, innovative thinking and entrepreneurial leadership. Colleges and universities must keep up with the pace of knowledge updates in majors and curriculum following the new needs of the era of ‘mass entrepreneurship and innovation’. However, most colleges and universities currently only offer ‘Undergraduate Entrepreneurship Fundamentals’ as a course of innovation and entrepreneurship modules and is mainly a elective course. The lack of entrepreneurship education curriculum construction is another crucial factor restricting the cultivation of college students’ entrepreneurial ability. Due to the setting of the professional curriculum system and the limit of total credits, students generally lack the study and awareness related to training of economic management and to knowledge in humanities and social sciences. For college students’ entrepreneurial ability, opportunity insight, team management and other competency dimensions require knowledge and skills education outside of the discipline. Therefore, in addition to the systematic innovation and entrepreneurship courses with the theme of ‘entrepreneurship’ for college students, courses related to human geography, interpersonal communication, team management and financial education should also be offered.

The system develops skills through training methods such as sand table simulation and entrepreneurial games. The second is to set up a physical entrepreneurial training base to conduct exercises such as simulation of the establishment process of entrepreneurial enterprises, display of entrepreneurial projects and training of entrepreneurial investment and financing negotiations. The third is the combination of inside and outside the school. Entrepreneurship training is based not only on the use of school-related resources but also on the school to encourage students to participate in entrepreneurial competitions, social research, visiting ‘crowd innovation space’ and communicate with entrepreneurs. The students should watch and participate in various entrepreneurial project road-shows and fund matching activities held by social organisations. Let students ‘learn by doing’ can effectively enhance college students’ social vision and operational skills in entrepreneurship.

Entrepreneurship guidance has both academic and practical requirements. This requires the instructor to have profound entrepreneurial theoretical research and rich experience in entrepreneurial practice. Unfortunately, at present, there are very few such entrepreneurial instructors in Chinese universities. To make up for this shortcoming, it is necessary to employ the new instructors with necessary experience. To cultivate college students’ entrepreneurial ability, the itemisation of entrepreneurial instructors includes two aspects: one is the matching of instructors of technical knowledge and entrepreneurial knowledge. The essence of innovation and entrepreneurship is to use emerging technologies to meet real society's needs to achieve the success of entrepreneurial activities. Therefore, college students must cultivate the ability to effectively match ‘customer pain points’ and ‘market gaps’ with technical resource conditions, which must be completed under the cooperation of technical instructors and entrepreneurial instructors. The second is the matching of instructors of theoretical knowledge and practical knowledge. College students’ learning and mastering the theoretical knowledge of entrepreneurship are the critical foundation for scientific entrepreneurship and a critical way to make up for their lack of experience. Therefore, it is necessary to realise the itemisation of knowledge teachers and experienced teachers in entrepreneurship education.

Entrepreneurship learning in universities is realised in the form of individual students participating in the classroom and practice. However, entrepreneurial activities are a kind of team project that is difficult to complete with high quality only by one person. Therefore, the learning team should be built at the beginning of the student's participation in the entrepreneurial learning process. First, complete all learning and training subjects through teamwork. The second is that students with different professional backgrounds and knowledge structures in the learning team can better learn and communicate with each other to achieve growth and progress in the team. Third, as a team member, especially a team coordinator, it is necessary to coordinate members with different personalities and personality characteristics through effective communication and goal management. This can exercise and accumulate team management skills and experience.

Entrepreneurship education is not a ‘sprint’ in pursuit of speed but a ‘marathon’ that values the process. Since it is a ‘marathon’ of educational activity, some ‘timing points’ should be set during this long process for process control and assessment. The ‘timing point’ of the entrepreneurial education process can be either a homework test in the form of an analysis report or a psychological reflection with cognitive action as the main body. The analysis report includes written materials such as market analysis report, business model canvas, financing plan, business charter and business plan completed by the team as a unit. Cognitive actions include team activities such as visiting business incubators and crowd-creation spaces and interviewing entrepreneurs. Cognitive action needs to be completed as a team but presented in the form of individual summaries.

Educational assessment methods have a decisive guiding role in teaching objectives and the development of teaching activities. The evaluation of the quality of entrepreneurial education results does not lie in the scores of students in the examination papers but a comprehensive reflection of the entrepreneurial knowledge and skills that students have mastered through systematic entrepreneurial learning. Project-based assessment methods can reflect entrepreneurship education's essential characteristics and help cultivate college students’ entrepreneurial ability. The business plan completed by the student team should be an important indicator of the quality of entrepreneurship education. At the same time, students participate in various national and regional entrepreneurship competitions, such as the National College Student E-commerce ‘Innovation, Creativity, and Entrepreneurship’ Challenge, the ‘Creative Youth’ National College Student Entrepreneurship Competition, and the China ‘Internet +’ College Student Innovation and Entrepreneurship Competition, etc. It can be an important way to assess the quality of entrepreneurship education, and can also provide meaningful guidance for the design and implementation of entrepreneurship education.