Advanced CoCoSo method for uncertain MAGDM: Evaluating college students’ entrepreneurial skills

Abstract

With the in-depth implementation of the innovative development-driven strategy of “mass innovation and entrepreneurship” put forward by the state, colleges and universities, as the main positions for cultivating innovative and entrepreneurial talents, have set up a multi-level and all-round training system for college students’ innovative and entrepreneurial ability according to the relevant policies and implementation opinions of the state for deepening innovation and entrepreneurship education in colleges and universities, and actively promoted the improvement of college students’ innovative and entrepreneurial ability. The college students’ innovation and entrepreneurship ability evaluation could be regarded as the classical multiple attribute group decision making (MAGDM) issue. The PULTSs could well depict uncertain information during the college students’ innovation and entrepreneurship ability evaluation and the combined compromise solution (CoCoSo) method is appropriate to stable the decision-making results. In this paper, the probabilistic uncertain linguistic combined compromise solution (PUL-CoCoSo) method based on the probabilistic uncertain linguistic sets (PULTSs) and combined compromise solution method is proposed for multiple attribute group decision making (MAGDM). The weights of attribute based on the CRITIC method are obtained under PULTSs. Finally, an application related to the college students’ innovation and entrepreneurship ability evaluation is utilized to demonstrate the usage of the developed algorithms.

Keywords

Multiple attribute group decision making (MAGDM) issues probabilistic uncertain linguistic sets (PULTSs)CoCoSo method CRITIC method college students’ innovation and entrepreneurship ability evaluation

1. Introduction

Many researchers at home and abroad, as well as front-line educators, have carried out research on cultivating college students’ innovative and entrepreneurial ability, and have achieved remarkable results so far. Professor Terman of Stanford University took the lead in proposing to cultivate college students’ entrepreneurial ability. He believes that scientific research and industrial fields can be effectively combined, and his views run through teaching practice, training a certain number of college students with innovative and entrepreneurial ability for the United States [1, 2, 3]. In 2002, the Ministry of Education established nine colleges and universities as pilot institutions for innovative education, which marked the official implementation of innovative entrepreneurship education in China [1, 2, 3, 4, 5, 6]. After that, more colleges and universities have devoted themselves to the practical activities of cultivating college students’ innovative and entrepreneurial ability. Many colleges and universities have established business incubation bases and opened scientific and technological platforms for college students to support and encourage college students to start businesses, which has effectively eased the severe situation of college students’ employment difficulties and promoted the transformation of scientific and technological achievements in colleges and universities into industrial fields [7, 8, 9, 10]. However, on the whole, there are still the following problems in college students’ innovation and entrepreneurship education: First, students’ awareness of innovation and entrepreneurship needs to be improved. Students lack social practical experience, so they often don’t know the positive significance of innovation and entrepreneurship, and they lack corresponding interest in innovation and entrepreneurship. Although some students have the desire to innovate and start a business, they are tired of the corresponding practical activities and think that innovation and start a business is very simple and do not need relevant training and practice [11, 12, 13, 14]. Some students lack self-confidence in innovation and entrepreneurship, and at the same time it is difficult to get some help and guidance through smooth channels. Second, the credit recognition of innovation and entrepreneurship education is not uniform. Because of the differences in training objectives, there are some differences in the evaluation of innovation and entrepreneurship education and the distribution of credit scores [15, 16, 17, 18]. For example, some colleges and universities not only require students to participate in training courses, but also require students to participate in corresponding practical activities or related competitions held by schools, so as to obtain credit for innovation and entrepreneurship education; Some colleges and universities also count students’ innovation achievements or professional skills scores into innovation and entrepreneurship education credits, such as computer scores and English scores. Third, the environment for cultivating innovation and entrepreneurship is not good. At present, there is a serious shortage of full-time teachers engaged in innovation and entrepreneurship education in colleges and universities, and the number of teachers who have received entrepreneurship training is small. In addition, due to the limitations of funds and venues, there is a phenomenon that theory and practice are out of touch in innovation and entrepreneurship education. Fourth, a systematic innovation and entrepreneurship training system has not yet been established. The course of innovation and entrepreneurship education is different from the general course, and it needs to adopt new educational methods [19, 20, 21, 22]. However, some colleges and universities still adopt the traditional teaching mode, and the courses are relatively single, and the teaching is not systematic and scientific, resulting in poor training effect of innovative and entrepreneurial talents. Fifth, there is no perfect quality supervision system. The purpose of innovation and entrepreneurship education is to cultivate students’ quality and ability, not to let students take credits. The quality supervision system of innovation and entrepreneurship education in some colleges and universities is not perfect, which causes innovation and entrepreneurship education to become a mere formality [23, 24, 25].

In numerous multi-critieria decision analysis (MCDA) issues, decision information is regularly described through crisp numbers [26, 27, 28, 29, 30, 31, 32]. However, in more and more routine multiple attribute group decision making (MAGDM) issues, most subjective assessment information is always imprecise because of growing uncertain complexity and human subjective preferential fuzziness [33, 34, 35, 36, 37, 38]. The college students’ innovation and entrepreneurship ability evaluation could be regarded as the classical MAGDM issue. The PULTSs [39] could well depict uncertain information during the college students’ innovation and entrepreneurship ability evaluation. The combined compromise solution (CoCoSo) method was introduced by Yazdani et al. [40], which was viewed as a great compromise solution for MAGDM issues by integrating the compromise DM algorithm with several aggregation strategies. In this paper, the probabilistic uncertain linguistic combined compromise solution (PUL-CoCoSo) method based on the probabilistic uncertain linguistic sets (PULTSs) and CoCoSo method is proposed for multiple attribute group decision making (MAGDM). The weights of attribute based on the CRITIC method [41] are obtained under PULTSs. Finally, the college students’ innovation and entrepreneurship ability evaluation is given to demonstrate the PUL-CoCoSo for MAGDM under PULTSs and some good comparative analysis is done to demonstrate the advantages of PUL-CoCoSo under PULTSs.

The reminder of our paper proceeds as follows. In Sect. 2, some necessary theories of PULTSs are provided. In Sect. 3, the conventional CoCoSo method is integrated with PULTSs to tackle MAGDM issues with CRITIC method and the calculating procedures are simply depicted. In Sect. 4, a numerical case related to college students’ innovation and entrepreneurship ability evaluation is offered and some existing comparative analysis are made. The work ends up with some favorable conclusions in Sect. 5.

2. Preliminaries

Herrera and Martinez [42] proposed the LTSs and Gou et al. [43] proposed the mathematical transformation between LTSs and [0, 1].

Definition 1 [43]. Let $L=\{l_{a}\mid\alpha=-\theta,\ldots,-2,-1,0,1,2,\ldots\theta\}$ be the given LTS, the given linguistic terms $l_{a}$ depict the information to $\beta$ which is depicted through function $g$ :

$\displaystyle g:[l_{-\theta},l_{\theta}]\rightarrow[0,1],g(l_{\alpha})=\frac{% \alpha+\theta}{2\theta}=\beta$ (1)

$\beta$ could be depicted the information to the given $l_{\alpha}$ through function $g^{-1}$ :

$\displaystyle g^{-1}:[0,1]\rightarrow[l_{-\theta},l_{\theta}],g^{-1}(\beta)=l_% {(2,\theta-1)\theta}=l_{\alpha}$ (2)

In order toenhance the HFLTSs, Pang, Wang and Xu [44] designed the PLTSs.

Definition 2 [44]. Given the LTS $L=\{l_{j}|j=-\theta,\ldots,-2,-1,0,1,2,\ldots\theta\}$ , the given PLTS is designed:

$\displaystyle L(p)=\left\{l^{(\phi)}(p^{(\phi)})\left|l^{(\phi)}\in L,p^{(\phi% )}\geqslant 0,\phi=1,2,\ldots,\#L(p),\mathop{\sum}\limits_{\phi=1}^{\#L(p)}p^{% (\phi)}\leqslant 1\right.\right\}$ (3)

where $l^{(\phi)}(p^{(\phi)})$ is the $\phi$ th linguistic term $l^{(\phi)}$ with the given probability $p^{(\phi)}$ , and $\#L(p)$ is the put forward length of $L(p)$ . The $l^{(\phi)}$ of $L(p)$ are aligned through ascending order.

In order to fully depict the uncertainty, Lin et al. [39] put forward the PULTS based on ULTSs [45] and PLTSs [44].

Definition 3 [39]. The PULTSis designed:

$\displaystyle\textit{PULTS}(p)=\left\{[L^{\phi},U^{\phi}](p^{\phi})\left|p^{% \phi}\geqslant 0,\phi=1,2,\ldots,\#\textit{PLTS}(p),\mathop{\sum}\limits_{\phi% =1}^{\#\textit{PULTS}(p)}p^{\phi}\leqslant 1\right.\right\}$ (4)

where $[L^{\phi},U^{\phi}](p^{\phi})$ depicts the ULTS $[L^{\phi},U^{\phi}]$ associated with probability $p^{\phi},L^{\phi},U^{\phi}$ are LISt, $L^{\phi}\leqslant U^{\phi}$ , and $\#\textit{PULTS}(p)$ is length of $\textit{PULTS}(p)\phi$ .

Furthermore, Lin et al. [39] normalized $\textit{PULTS}(p)$ as

$\displaystyle\textit{NPULTS}(p)=\left\{[L^{\phi},U^{\phi}](\tilde{p}^{\phi})% \left|\tilde{p}^{\phi}\geqslant 0,\phi=1,2,\ldots,\#\textit{NPULTS}(\tilde{p})% ,\mathop{\sum}\limits_{\phi=1}^{\#\textit{NPULTS}(\tilde{p})}\tilde{p}^{\phi}=% 1\right.\right\},$

where

$\displaystyle\tilde{p}^{(\phi)}=p^{(\phi)}\left/\mathop{\sum}\limits_{\phi=1}^% {\#L(p)}p^{(\phi)}\right.$

for all $\phi=1,2,\ldots,\#\textit{NPULTS}(\tilde{p})$ .

Definition 4 [39]. Let $\textit{PULTS}_{1}(p)=\{[L_{1}^{\phi},U_{1}^{\phi}](p_{1}^{\phi})|\phi=1,2,% \ldots,\#\textit{PULTS}_{1}(p)\}$ and $\textit{PULTS}_{2}(p)=\{[L_{2}^{\phi},U_{2}^{\phi}](p_{2}^{\phi})|\phi=1,2,% \ldots,\#\textit{PULTS}_{2}(p)\}$ be two PULTS, $\#\textit{PULTS}(p)$ and $\#\textit{PULTS}_{2}(p)$ are the put forward numbers of $\textit{PULTS}_{1}(p)$ and $\textit{PULTS}_{2}(p)$ . If $\#\textit{PULTS}_{1}(p)\geqslant\#\textit{PULTS}_{2}(p)$ , then $\#\textit{PULTS}_{1}(p)-\#\textit{PULTS}_{2}(p)$ linguistic terms are added to $\textit{PULTS}_{2}(p)$ . The added ULTSs should be the smallest ULTSs in $\textit{PULTS}_{2}(p)$ and the probabilities of these added ULTSs should be zero.

Definition 5 [46]. Let $\textit{PULTS}_{1}(p)=\{[L_{1}^{\phi},U_{1}^{\phi}](p_{l}^{\phi})|\phi=1,2,% \ldots,\#\textit{PULTS}(p)\}$ and $\textit{PULTS}_{2}(p)=\{[L_{2}^{\phi},\linebreak U_{2}^{\phi}](p_{2}^{\phi})|% \phi=1,2,\ldots,\#\textit{PULTS}_{2}(p)\}$ be two PULTSs with given length $\#\textit{PULTS}_{1}(p)=\#\textit{PULTS}_{2}(p)=\#\textit{PULTS}(p)$ , then put forward Hamming distance $HD(\textit{PULTS}_{1}(p),\textit{PULTS}_{2}(p))$ between $\textit{PULTS}_{1}(p)$ and $\textit{PULT}S_{2}(p)$ is put forward below:

$\displaystyle HD(\textit{PULTS}_{1}(p),\textit{PULTS}_{2}(p))$ (5) $\displaystyle=\frac{\mathop{\sum}\limits_{\phi=1}^{\#\textit{PULTS}(p)}(|g(L_{% 1}^{\phi})p_{1}^{\phi}-g(L_{2}^{\phi})p_{2}^{\phi}|+|g(U_{1}^{\phi})p_{1}^{% \phi}-g(U_{2}^{\phi})p_{2}^{\phi}|)}{2\#\textit{PULTS}(p)}$

Defmition 6 [46]. For the $\textit{PULTS}(p)=\{[L^{\phi},U^{\phi}](p^{\phi})|\phi=1,2,\ldots,\#\textit{% PULTS}(p)\}$ , the put forward expected value $EV(\textit{PULTS}(p))$ and put forward deviation degree $DD(\textit{PULTS}(p))$ of $\textit{PULTS}(p)$ is put forward:

$\displaystyle EV(\textit{PULTS}(p))=\frac{\mathop{\sum}\limits_{\phi=1}^{\#% \textit{PULTS}(p)}\left(\frac{g(L^{\phi})p^{\phi}+g(U^{\phi})p^{\phi}}{2}% \right)}{\mathop{\sum}\limits_{\phi=1}^{\#\textit{PULTS}(p)}p^{\phi}}$ (6) $\displaystyle DD(\textit{PULTS}(p))=\frac{\sqrt{\mathop{\sum}\limits_{\phi=1}^% {\#\textit{PULTS}(p)}\left(\frac{g(L^{\phi})p^{\phi}+g(U^{\phi})p^{\phi}}{2}-% EV(\textit{PULTS}(p))\right)^{2}}}{\mathop{\sum}\limits_{\phi=1}^{\#\textit{% PULTS}(p)}p^{\phi}}$ (7)

3. CoCoSo method for probabilistic uncertain linguistic MAGDM with CRITIC method

In such section, we devise the PUL-CeCeSe method for MAGDM issue. The following notations depict the PUL-MAGDM Let $A=\{A_{1},A_{2},\ldots,A_{m}\}$ be altematives and $G=\{G_{1},G_{2},\ldots,G_{n}\}$ with weight $w=(w_{1},w_{2},\ldots,w_{n})$ , where $w_{j}\in[0,1],j=1,2,\ldots,n,\mathop{\sum}\limits_{j=1}^{n}w_{j}=1$ , and a group of experts $E=\{E_{1},E_{2},\ldots,E_{q}\}$ . Suppose that there are $n$ qualitative attribute values are evaluated by uncertain linguistic information $[L_{\xi}^{k},U_{ij}^{k}](i=1,2,\ldots,m,j=1,2,\ldots,n,k=1,2,\ldots,q)$ .

Then, PUL-CeCeSe method is put forward to solve PUL-MAGDM through CRITIC weight. The concrete calculating steps are shown:

Step 1. Shift the put forward cost attribute into beneficial attribute. If the cost attribute is depicted as $[l_{\alpha},l_{\beta}]$ , then the beneficial value could be depicted as $[l_{-\beta},l_{-\alpha}]$ .

Step 2. Convert the ULTSs $[L_{i}^{k},U_{ij}^{k}]$ into PUL-matrix $\textit{PULDM}=(\textit{PULDM}_{ij}(p))_{m\times n}$ , $\textit{PULDM}_{ij}(p)=\{[L_{ij}^{\phi},U_{ij}^{\phi}](p_{ij}^{\phi})|\phi=1,2% ,\ldots,\#\textit{PULDM}_{i}(p)\}$ .

Step 3. Derive the nomalized PUL-matrix $\textit{NPULDM}=(\textit{NPULDM}_{ij}(p))_{m\times n}$ , $\textit{NPULDM}_{ij}(p)=\{[L_{ij}^{\phi},\linebreak U_{ij}^{\phi}](p_{ij}^{% \phi})|\phi=1,2,\ldots,\#\textit{NPULDM}_{ij}(p)\}$ . Thus, nomalized PUL information for altemative $A_{i}\in A$ could be designed as: $\textit{NPULA}_{i}=([L_{i1}^{\phi},U_{i1}^{\phi}](p_{i1}^{\phi}),[L_{i2}^{\phi% },U_{i2}^{\phi}](p_{i2}^{\phi}),\ldots,[L_{in}^{\phi},U_{in}^{\phi}](p_{in}^{% \phi}))$ , $\phi=1,2,\ldots,\linebreak\#\textit{NPULDM}_{ij}(p)$ .

Step 4. Compute the weight through CRITIC.

The CRITIC method [41] is used to obtain weights. The computing procedures are introduced to obtain the weight information under PULTS [47].

(1) Build the PUL correlation coefficient matrix $\textit{PULCCM}=(\textit{PULCC}_{jt})_{n\times n}$ by Eq. (3).

$\displaystyle\textit{PULCC}_{jt}=\frac{\mathop{\sum}\limits_{i=1}^{m}\left(% \begin{array}[]{l}\left(\mathop{\sum}\limits_{\phi=1}^{\#\textit{NPULDM}_{ij}(% p)}\frac{(g(L_{ij}^{\phi})p_{ij}^{\phi}-g(\bar{L}_{j}^{\phi})\bar{p}_{j}^{\phi% })+(g(U_{ij}^{\phi})p_{ij}^{\phi}-g(\bar{U}_{j}^{\phi})\bar{p}_{j}^{\phi})}{2}% \right)\cdot\\ \left(\mathop{\sum}\limits_{\phi=1}^{\#\textit{NPULDM}_{ij}(p)}\frac{(g(L_{it}% ^{\phi})p_{it}^{\phi}-g(\bar{L}_{t}^{\phi})\bar{p}_{t}^{\phi})+(g(U_{it}^{\phi% })p_{it}^{\phi}-g(\bar{U}_{t}^{\phi})\bar{p}_{t}^{\phi})}{2}\right)\end{array}% \right)}{\begin{array}[]{l}\sqrt{\mathop{\sum}\limits_{i=1}^{m}\left(\mathop{% \sum}\limits_{\phi=1}^{\#\textit{NPULDM}_{ij}(p)}\frac{(g(L_{ij}^{\phi})p_{ij}% ^{\phi}-g(\bar{L}_{j}^{\phi})\bar{p}_{j}^{\phi})+(g(U_{ij}^{\phi})p_{ij}^{\phi% }-g(\bar{U}_{j}^{\phi})\bar{p}_{j}^{\phi})}{2}\right)^{2}}\cdot\\ \sqrt{\mathop{\sum}\limits_{i=1}^{m}\left(\mathop{\sum}\limits_{\phi=1}^{\#% \textit{NPULDM}_{ij}(p)}\frac{(g(L_{it}^{\phi})p_{it}^{\phi}-g(\bar{L}_{t}^{% \phi})\bar{p}_{t}^{\phi})+(g(U_{it}^{\phi})p_{it}^{\phi}-g(\bar{U}_{t}^{\phi})% \bar{p}_{t}^{\phi})}{2}\right)^{2}}\end{array}}$

(8) $\displaystyle j,t=1,2,\ldots,n$

where

$\displaystyle[\bar{L}_{j}^{\phi},\bar{U}_{j}^{\phi}](\bar{p}_{j}^{\phi})=\left% [\frac{\mathop{\sum}\limits_{i=1}^{m}L_{ij}^{\phi}}{m},\frac{\mathop{\sum}% \limits_{i=1}^{m}U_{ij}^{\phi}}{m}\right]\left(\frac{\mathop{\sum}\limits_{i=1% }^{m}p_{ij}^{\phi}}{m}\right)$

and

$\displaystyle[\bar{L}_{t}^{\phi},\bar{U}_{t}^{\phi}](\bar{p}_{t}^{\phi})=\left% [\frac{\mathop{\sum}\limits_{i=1}^{m}L_{it}^{\phi}}{m},\frac{\mathop{\sum}% \limits_{i=1}^{m}U_{it}^{\phi}}{m}\right]\left(\frac{\mathop{\sum}\limits_{i=1% }^{m}p_{it}^{\phi}}{m}\right).$

(2) Obtain the PUL standard deviation (PULSD) of attribute.

$\displaystyle\textit{PULSD}_{j}=\sqrt{\frac{1}{m-1}\mathop{\sum}\limits_{i=1}^% {m}\left(\mathop{\sum}\limits_{\phi=1}^{\#\textit{NPULDM}_{ij}(p)}\frac{(g(L_{% ij}^{\phi})p_{ij}^{\phi}-g(L_{j}^{\phi})p_{j}^{\phi})+(g(U_{ij}^{\phi})p_{ij}^% {\phi}-g(U_{j}^{\phi})p_{j}^{\phi})}{2}\right)^{2}},$ (9) $\displaystyle j=1,2,\ldots,n,$

(3) Compute the weights of attributes.

$\displaystyle w_{j}=\frac{\textit{PULSD}_{j}\mathop{\sum}\limits_{t=1}^{n}(1-% \textit{PULCC}_{jt})}{\mathop{\sum}\limits_{j=1}^{n}\left(\textit{PULSD}_{j}% \mathop{\sum}\limits_{t=1}^{n}(1-\textit{PULCC}_{jt})\right)},j=1,2\ldots,n,$ (10)

where $w_{j}\in[0,1]$ and $\mathop{\sum}\limits_{j=1}^{n}w_{j}=1$ .

Step 5. Sum up the weighted comparability sequence.

$\displaystyle\textit{WCS}_{i}=\mathop{\sum}\limits_{j=1}^{n}\left(w_{j}\cdot% \mathop{\sum}\limits_{\phi=1}^{\#\textit{PULDM}_{ij}(p)}\frac{g(L_{ij}^{\phi})% p_{ij}^{\phi}+g(U_{ij}^{\phi})p_{ij}^{\phi}}{2}\right),i=1,2,\ldots,m,j=1,2,% \ldots,n$ (11)

Step 6. Sum up the power weight of comparability sequences for each put forward altemative.

$\displaystyle\textit{PWCS}_{i}=\mathop{\sum}\limits_{j=1}^{n}\left(\mathop{% \sum}\limits_{\phi=1}^{\#\textit{PULDM}_{ij}(p)}\frac{g(L_{i}^{\phi})p_{ij}^{% \phi}+g(U_{ij}^{\phi})p_{ij}^{\phi}}{2}\right)^{w_{i}},i=1,2,\ldots,m,j=1,2,% \ldots,n$ (12)

Step 7. Calculate the altematives’ relative weights through following three aggregation strategies.

$\displaystyle RW_{ia}=\frac{\textit{WCS}_{i}+\textit{PWCS}}{\mathop{\sum}% \limits_{i=1}^{m}(\textit{WCS}_{i}+\textit{PWCS}_{i})}$ (13) $\displaystyle RW_{ib}=\frac{\textit{WCS}_{i}}{\min\textit{WCS}_{i}}+\frac{% \textit{PWCS}_{i}}{\min\textit{PWCS}_{i}}$ (14) $\displaystyle RW_{ia}=\frac{\zeta(\textit{WCS}_{i})+(1-\zeta)(\textit{PWCS}_{i% })}{\zeta\max_{i}\textit{WCS}_{i}+(1-\zeta)\max_{i}\textit{PWCS}_{i}},0% \leqslant\zeta\leqslant 1$ (15)

where $\zeta=0.5$ in this easay.

Step 8. Calculate the final value of each put forward alternative $FV_{i}$ by Eq. (16).

$\displaystyle FV_{i}=\sqrt[3]{RW_{ia}RW_{ib}RW_{ic}}+\frac{RW_{ia}+RW_{ib}+RW_% {ic}}{3}$ (16)

Step 9. Depending on the calculating results of $FV_{i}$ , all the altematives can be ranked. The higher value of $FV_{i}$ is, the optimal altemative will be.
4. The numerical example and comparative analysis

4.1 A numerical example

The 18th National Congress of the Communist Party of China clearly put forward that it is necessary to increase the support for the cultivation of innovative and entrepreneurial talents and make important arrangements for the cultivation of innovative and entrepreneurial talents. The cultivation of innovative and entrepreneurial talents has become an important mission of higher education. Cultivating college students’ innovative and entrepreneurial ability is a historical mission entrusted to colleges and universities by the development of the times, and it is also a complex systematic project [48, 49]. It needs not only the teaching and scientific research strength of colleges and universities, but also the strong support from all walks of life to jointly establish an excellent and perfect environment and inspire college students to be brave in innovation and entrepreneurship. Innovation and entrepreneurship education has become a brand-new model pursued by higher education all over the world. The entrepreneurial craze of American college students began in 1983, and the main characteristics of its innovation and entrepreneurship education are entrepreneurial culture-led, university-led and market-driven [50, 51, 52]. Since 1999, Germany has successively implemented the “survival” plan and the entrepreneurship education promotion plan in universities to support the entrepreneurship education of college students. The main characteristics of innovation and entrepreneurship education for German college students are university-led, government-supported and market-participated. In 1998, Tsinghua University held the first “Entrepreneurship Cup” college students’ entrepreneurial plan competition in China, which was the embryonic form of college students’ scientific and technological entrepreneurship in China. In 2014, in order to meet the needs of the development of college students’ innovation and entrepreneurship, the Central Committee of the Communist Youth League, the Ministry of Education and other ministries and commissions jointly organized the “Creating Youth” National College Students’ Entrepreneurship Competition on the basis of the “Challenge Cup” China College Students’ Entrepreneurship Plan Competition. In 2015, the Ministry of Education and relevant ministries and commissions co-sponsored the “internet plus” Innovation and Entrepreneurship Competition for College Students. The development and training of innovative and entrepreneurial talents is the basic support to enhance the core competitiveness of the country. Colleges and universities bear the historical mission entrusted by the times [53, 54, 55]. We should cultivate college students’ innovative and entrepreneurial ability from the aspects of integrating innovative and entrepreneurial education into the talent training system, establishing innovative and entrepreneurial education training system and building innovative and entrepreneurial practice support platform. The key point of innovation and entrepreneurship education for college students is to cultivate students’ awareness of innovation and entrepreneurship, have the spirit of innovation and entrepreneurship, practice their entrepreneurial dreams, and create an innovative and entrepreneurial cultural atmosphere on campus. Colleges and universities should carry out brand academic, scientific, technological and cultural activities based on the discipline characteristics of each college. Encourage and support college students to develop innovative and entrepreneurial associations, and promote the vigorous development of innovative and entrepreneurial associations in colleges and universities [53, 54, 55, 56, 57]. Colleges and universities should give strong support to innovative and entrepreneurial associations in terms of venue, funding guarantee and activity conditions, and at the same time, strengthen the training management of members of the associations to improve the professional service level of the whole associations. In order to strengthen the extensive contact between associations and society, colleges and universities need to actively guide and lead associations into various off-campus entrepreneurial bases to learn and exchange, promote the docking of resources between associations and off-campus enterprises, effectively enhance the comprehensive ability of associations, and promote the transformation of innovation and entrepreneurial achievements [58, 59, 60]. In addition, colleges and universities should also carry out publicity on innovation and entrepreneurship education through various forms and carriers, hold innovation and entrepreneurship salons and other activities regularly, expand students’ innovative and entrepreneurial ideas, stimulate students’ awareness of innovation and entrepreneurship, and improve students’ innovative and entrepreneurial performance, so as to enhance the campus innovative and entrepreneurial cultural environment. The college students’ innovation and entrepreneurship ability evaluation is the conventional MAGDM issue. Thus, in this part, a given numerical example related to college students’ innovation and entrepreneurship ability evaluation is provided to demonstrate the superiority of the developed method. There is a panel with five possible college students’ innovation and entrepreneurship colleges $\textit{IEC}({i=1,2,3,4,5})$ to select. There are four selected attributes for invited experts to assess these five potential college students’ innovation and entrepreneurship colleges: ⟀ S₁ is denoted the innovative and entrepreneurial environment; ⟁ S₂ is denoted as innovative and entrepreneurial cost; ⟂ S₃ is denoted as innovative and entrepreneurial achievements; ⟃ S₄ is denoted as innovative and entrepreneurial education. The S₂ is cost attribute, others attributes are beneficial attributes. These five potential college students’ innovation and entrepreneurship colleges are to be evaluated through the following LTSs

$\displaystyle L=\{l_{-3}=\textit{extremely poor}(EP),l_{-2}=\textit{very poor}% (VP),$ $\displaystyle l_{-1}=\textit{poor}(P),l_{0}=\textit{medium}(M),l_{1}=\textit{% good}(G),$ $\displaystyle l_{2}=\textit{very good}(VG),l_{3}=\textit{extremel good}(EG)\}$

by the five DMs through above given four attributes. These results are listed in the Tables 1–5.

Table 1
Linguistic decision matrix by the first DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[VP, M]	[P, M]	[P, M]	[G, VG]
IEC₂	[VG, EG]	[EP, VP]	[VG, EG]	[M, G]
IEC₃	[M, G]	[G, VG]	[G, EG]	[P, M]
IEC₄	[VP, P]	[P, G]	[P, M]	[VP, M]
IEC₅	[P, M]	[G, VG]	[P, M]	[EP, P]

Table 2

Linguistic decision matrix by the second DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[P, M]	[M, G]	[VP, P]	[VG, EG]
IEC₂	[P, M]	[VP, P]	[VP, M]	[G, EG]
IEC₃	[G, VG]	[M, G]	[M, G]	[M, VG]
IEC₄	[P, M]	[G, EG]	[M, G]	[G, VG]
IEC₅	[EP, P]	[M, G]	[M, G]	[P, M]

Table 3

Linguistic decision matrix by the third DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[VP, M]	[P, M]	[P, M]	[M, G]
IEC₂	[VG, EG]	[EP, VP]	[P, M]	[G, EG]
IEC₃	[M, G]	[VG, EG]	[G, EG]	[VG, EG]
IEC₄	[M, VG]	[M, G]	[P, M]	[G, VG]
IEC₅	[P, M]	[G, VG]	[VP, P]	[M, G]

Table 4

Linguistic decision matrix by the fourth DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[G, VG]	[VG, EG]	[P, M]	[G, VG]
IEC₂	[M, VG]	[P, M]	[VG, EG]	[M, G]
IEC₃	[M, G]	[G, VG]	[M, G]	[M, VG]
IEC₄	[VP, P]	[G, EG]	[P, M]	[VP, M]
IEC₅	[M, G]	[G, VG]	[P, M]	[P, M]

Table 5

Linguistic decision matrix by the fifth DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[G, VG]	[P, M]	[M, G]	[M, G]
IEC₂	[VG, EG]	[VP, P]	[VG, EG]	[G, EG]
IEC₃	[VG, EG]	[VG, EG]	[VG, EG]	[VG, EG]
IEC₄	[P, M]	[G, EG]	[G, VG]	[M, G]
IEC₅	[P, M]	[M, G]	[M, G]	[P, M]

Then, the PULCoCoSo method is put forward to tackle MAGDM issues for college students’ innovation and entrepreneurship ability evaluation.

Step 1. Transform the cost into the benefit indicator (Tables 6–10).

Table 6

Linguistic decision matrix by the first DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[VP, M]	[M, G]	[P, M]	[G, VG]
IEC₂	[VG, EG]	[VG, EG]	[VG, EG]	[M, G]
IEC₃	[M, G]	[VP, P]	[G, EG]	[P, M]
IEC₄	[VP, P]	[P, G]	[P, M]	[VP, M]
IEC₅	[P, M]	[VP, P]	[P, M]	[EP, P]

Table 7

Linguistic decision matrix by the second DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[P, M]	[P, M]	[VP, P]	[VG, EG]
IEC₂	[P, M]	[G, VG]	[VP, M]	[G, EG]
IEC₃	[G, VG]	[P, M]	[M, G]	[M, VG]
IEC₄	[P, M]	[EP, P]	[M, G]	[G, VG]
IEC₅	[EP, P]	[P, M]	[M, G]	[P, M]

Table 8

Linguistic decision matrix by the third DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[VP, M]	[M, G]	[P, M]	[M, G]
IEC₂	[VG, EG]	[VG, EG]	[P, M]	[G, EG]
IEC₃	[M, G]	[EP, VP]	[G, EG]	[VG, EG]
IEC₄	[M, VG]	[P, M]	[P, M]	[G, VG]
IEC₅	[P, M]	[VP, P]	[VP, P]	[M, G]

Table 9

Linguistic decision matrix by the fourth DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[G, VG]	[EP, VP]	[P, M]	[G, VG]
IEC₂	[M, VG]	[M, G]	[VG, EG]	[M, G]
IEC₃	[M, G]	[VP, P]	[M, G]	[M, VG]
IEC₄	[VP, P]	[EP, P]	[P, M]	[VP, M]
IEC₅	[M, G]	[VP, P]	[P, M]	[P, M]

Table 10

Linguistic decision matrix by the fifth DM

Alternatives	S₁	S₂	S₃	S₄
IEC₁	[G, VG]	[M, G]	[M, G]	[M, G]
IEC₂	[VG, EG]	[G, VG]	[VG, EG]	[G, EG]
IEC₃	[VG, EG]	[EP, VP]	[VG, EG]	[VG, EG]
IEC₄	[P, M]	[EP, P]	[G, VG]	[M, G]
IEC₅	[P, M]	[P, M]	[M, G]	[P, M]

Step 2. Transform the linguistic variables into PUL-matrix (Table 11).

Table 11

PUL-matrix

Alternatives	S₁	S₂
IEC₁	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{0}}],0.4}\rangle,\langle{[{l_{-1},l_{0% }}],0.2}\rangle,\\ \langle{[{l_{1},l_{2}}],0.4}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-1},l_{0}}],0.6}\rangle,\langle{[{l_{0},l_{1}% }],0.2}\rangle,\\ \langle{[{l_{2},l_{3}}],0.2}\rangle\}\\ \end{array}$
IEC₂	$\begin{array}[]{l}\{\langle{[{l_{-1},l_{0}}],0.2}\rangle,\langle{[{l_{0},l_{2}% }],0.2}\rangle,\\ \langle{[{l_{2},l_{3}}],0.6}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{{-3}},l_{-2}}],0.4}\rangle,\langle{[{l_{-2},l% _{-1}}],0.4}\rangle,\\ \langle{[{l_{-1},l_{0}}],0.2}\rangle\}\\ \end{array}$
IEC₃	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0.6}\rangle,\langle{[{l_{1},l_{2}}% ],0.2}\rangle,\\ \langle{[{l_{2},l_{3}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0.2}\rangle,\langle{[{l_{1},l_{2}}% ],0.4}\rangle,\\ \langle{[{l_{2},l_{3}}],0.4}\rangle\}\\ \end{array}$
IEC₄	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{-1}}],0.4}\rangle,\langle{[{l_{{-1}},l% _{0}}],0.4}\rangle,\\ \langle{[{l_{0},l_{2}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-1},l_{1}}],0.2}\rangle,\langle{[{l_{0},l_{1}% }],0.2}\rangle,\\ \langle{[{l_{1},l_{3}}],0.6}\rangle\}\\ \end{array}$
IEC₅	$\begin{array}[]{l}\{\langle{[{l_{-3},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.6}\rangle,\\ \langle{[{l_{0},l_{1}}],0.2}\rangle\}\\ \end{array}$	$\{{\langle{[{l_{0},l_{1}}],0.4}\rangle,\langle{[{l_{1},l_{2}}],0.6}\rangle}\}$
Alternatives	S₃	S₄
IEC₁	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.6}\rangle,\\ \langle{[{l_{0},l_{1}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0.4}\rangle,\langle{[{l_{1},l_{2}}% ],0.4}\rangle,\\ \langle{[{l_{2},l_{3}}],0.2}\rangle\}\\ \end{array}$
IEC₂	$\begin{array}[]{l}\{\langle{[{l_{{-2}},l_{0}}],0.2}\rangle,\langle{[{l_{-1},l_% {0}}],0.2}\rangle,\\ \langle{[{l_{2},l_{3}}],0.6}\rangle\}\\ \end{array}$	$\{{\langle{[{l_{0},l_{1}}],0.4}\rangle,\langle{[{l_{1},l_{3}}],0.6}\rangle}\}$
IEC₃	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0.4}\rangle,\langle{[{l_{1},l_{3}}% ],0.4}\rangle,\\ \langle{[{l_{2},l_{3}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-1},l_{0}}],0.2}\rangle,\langle{[{l_{0},l_{2}% }],0.4}\rangle,\\ \langle{[{l_{2},l_{3}}],0.4}\rangle\}\\ \end{array}$
IEC₄	$\begin{array}[]{l}\{\langle{[{l_{-1},l_{0}}],0.6}\rangle,\langle{[{l_{0},l_{1}% }],0.2}\rangle,\\ \langle{[{l_{1},l_{2}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{0}}],0.4}\rangle,\langle{[{l_{0},l_{1}% }],0.2}\rangle,\\ \langle{[{l_{1},l_{2}}],0.4}\rangle\}\\ \end{array}$
IEC₅	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.4}\rangle,\\ \langle{[{l_{0},l_{1}}],0.4}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-3},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.6}\rangle,\\ \langle{[{l_{0},l_{1}}],0.2}\rangle\}\\ \end{array}$

Step 3. Calculate the normalized PUL-matrix (Table 12).

Table 12

The normalized PUL-matrix

Alternatives	S₁	S₂
IEC₁	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.4}\rangle,\\ \langle{[{l_{1},l_{2}}],0.4}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-3},l_{-2}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.2}\rangle,\\ \langle{[{l_{0},l_{1}}],0.6}\rangle\}\\ \end{array}$
IEC₂	$\begin{array}[]{l}\{\langle{[{l_{-1},l_{0}}],0.2}\rangle,\langle{[{l_{0},l_{2}% }],0.2}\rangle,\\ \langle{[{l_{2},l_{3}}],0.6}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0.2}\rangle,\langle{[{l_{1},l_{2}}% ],0.4}\rangle,\\ \langle{[{l_{2},l_{3}}],0.4}\rangle\}\\ \end{array}$
IEC₃	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0.6}\rangle,\langle{[{l_{1},l_{2}}% ],0.2}\rangle,\\ \langle{[{l_{2},l_{3}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-3},l_{-2}}],0.4}\rangle,\langle{[{l_{-2},l_{% -1}}],0.4}\rangle,\\ \langle{[{l_{-1},l_{0}}],0.2}\rangle\}\\ \end{array}$
IEC₄	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{-1}}],0.4}\rangle,\langle{[{l_{{-1}},l% _{0}}],0.4}\rangle,\\ \langle{[{l_{0},l_{2}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-3},l_{-1}}],0.6}\rangle,\langle{[{l_{-1},l_{% 0}}],0.3}\rangle,\\ \langle{[{l_{0},l_{1}}],0.1}\rangle\}\\ \end{array}$
IEC₅	$\begin{array}[]{l}\{\langle{[{l_{-3},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.6}\rangle,\\ \langle{[{l_{0},l_{1}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{-1}}],0}\rangle,\langle{[{l_{-2},l_{-1% }}],0.6}\rangle,\\ \langle{[{l_{-1},l_{0}}],0.4}\rangle\}\\ \end{array}$
Alternatives	S₃	S₄
IEC₁	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.6}\rangle,\\ \langle{[{l_{0},l_{1}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0.4}\rangle,\langle{[{l_{1},l_{2}}% ],0.4}\rangle,\\ \langle{[{l_{2},l_{3}}],0.2}\rangle\}\\ \end{array}$
IEC₂	$\begin{array}[]{l}\{\langle{[{l_{{-2}},l_{-1}}],0.1}\rangle,\langle{[{l_{-1},l% _{0}}],0.3}\rangle,\\ \langle{[{l_{2},l_{3}}],0.6}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0}\rangle,\langle{[{l_{0},l_{1}}],% 0.4}\rangle,\\ \langle{[{l_{1},l_{3}}],0.6}\rangle\}\\ \end{array}$
IEC₃	$\begin{array}[]{l}\{\langle{[{l_{0},l_{1}}],0.4}\rangle,\langle{[{l_{1},l_{2}}% ],0.2}\rangle,\\ \langle{[{l_{2},l_{3}}],0.4}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{{-1}},l_{0}}],0.2}\rangle,\langle{[{l_{0},l_{% 2}}],0.4}\rangle,\\ \langle{[{l_{2},l_{3}}],0.4}\rangle\}\\ \end{array}$
IEC₄	$\begin{array}[]{l}\{\langle{[{l_{-1},l_{0}}],0.6}\rangle,\langle{[{l_{0},l_{1}% }],0.2}\rangle,\\ \langle{[{l_{1},l_{2}}],0.2}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{0}}],0.4}\rangle,\langle{[{l_{0},l_{1}% }],0.2}\rangle,\\ \langle{[{l_{1},l_{2}}],0.4}\rangle\}\\ \end{array}$
IEC₅	$\begin{array}[]{l}\{\langle{[{l_{-2},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.4}\rangle,\\ \langle{[{l_{0},l_{1}}],0.4}\rangle\}\\ \end{array}$	$\begin{array}[]{l}\{\langle{[{l_{-3},l_{-1}}],0.2}\rangle,\langle{[{l_{-1},l_{% 0}}],0.6}\rangle,\\ \langle{[{l_{0},l_{1}}],0.2}\rangle\}\\ \end{array}$

Step 3. Decide the attributes weights $w_{j}({j=1,2,\ldots,n})$ by Eqs (3)–(10) as listed in Table 13.

Table 13

The attributes weights $w_{j}$

	S₁	S₂	S₃	S₄
$w_{j}$	0.1441	0.4350	0.2329	0.1910

Step 4. Sum up the weighted comparability sequence by the Eq. (11).

$\displaystyle\textit{WCS}_{1}={0.5026},\textit{WCS}_{2}={0.7520},\textit{WCS}_% {3}={0.5022},\textit{WCS}_{4}={0.4051},\textit{WCS}_{5}={0.3754}$

Step 5. Sum up the power weight of comparability sequences by the Eq. (12).

$\displaystyle\textit{PWCS}_{1}={3.3715},\textit{PWCS}_{2}={3.7252},\textit{% PWCS}_{3}={3.3353},\textit{PWCS}_{4}={3.2060},\textit{PWCS}_{5}={3.1549}$

Step 6. Calculate the alternatives’ relative weights by utilizing three aggregation strategies.

$\displaystyle RW_{1a}={0.2004},RW_{2a}={0.2316},RW_{3a}={0.1985},RW_{4a}={0.18% 68},RW_{5a}={0.1826}$ $\displaystyle RW_{1b}={2.4075},RW_{2b}={3.1841},RW_{3b}={2.3950},RW_{4b}={2.09% 53},RW_{5b}={2.0000}$ $\displaystyle RW_{1c}={0.8653},RW_{2c}={1.0000},RW_{3c}={0.8571},RW_{4c}={0.80% 65},RW_{5c}={0.7885}$

Step 7. Calculate the final value of each alternative $FV_{i}$ by Eq. (16).

$\displaystyle FV_{1}=1.9051,FV_{2}=2.3754,FV_{3}=1.8916,FV_{4}=1.7104,FV_{5}=1% .6508$

Step 8. Relying on the results of $FV_{i}$ , the order is: $\textit{MIIS}_{2}>\textit{MIIS}_{1}>\textit{MIIS}_{3}>\textit{MIIS}_{4}>% \textit{MIIS}_{5}$ and $\textit{MIIS}_{2}$ is the optimal college students’ innovation and entrepreneurship college.

4.2 Comparative analysis

Then, the PULCoCoSo method is compared with PULWA operator [39], PUL-TOPSIS method [39], PUL-GRP method [61], PUL-CODAS [62] and PUL-QUALIFLEX method [63]. The comparative decision results are shown in Table 14.

Table 14
Order of the different methods

	Ordering
PULWA operator [39]	$VA_{4}\succ VA_{2}\succ VA_{1}\succ VA_{5}\succ VA_{3}$
PUL-TOPSIS method [39]	$VA_{4}\succ VA_{2}\succ VA_{1}\succ VA_{5}\succ VA_{3}$
PUL-GRP method [61]	$VA_{4}\succ VA_{2}\succ VA_{1}\succ VA_{5}\succ VA_{3}$
PUL-CODAS [62]	$VA_{4}\succ VA_{2}\succ VA_{1}\succ VA_{5}\succ VA_{3}$
PUL-QUALIFLEX method [63]	$VA_{4}\succ VA_{2}\succ VA_{1}\succ VA_{5}\succ VA_{3}$
PUL-CoCoSo method	$VA_{4}\succ VA_{2}\succ VA_{1}\succ VA_{5}\succ VA_{3}$

On the basis of the WS coefficients [64, 65], the WS coefficient between the PULWA operator [39], PUL-TOPSIS method [39], PUL-GRP method [61], PUL-CODAS [62], PUL-QUALIFLEX method [63] and the proposed PUL-CoCoSo method is 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, respectively. From the above detailed analysis, it could be seen that these decision models have the same optimal college students’ innovation and entrepreneurship college and same worst college students’ innovation and entrepreneurship college. Furthermore, the order of these decision methods is same. This verifies the PULCoCoSo method is effective.

5. Conclusion

With the continuous expansion of higher education in China, higher education has changed from elite education to mass education. According to statistics, in 2017, the number of college graduates reached 7.95 million, setting a new record in history. While hailing the rapid development and popularization of higher education in China, we can’t help but face some hidden dangers, that is, many college students are facing the dilemma of “adventure land”, and as a weak part of higher education-higher vocational education, the employment situation of students is even more severe, which is undoubtedly a challenge to education in China. However, the current demand for talents in China is not saturated, which shows that there is a structural imbalance in the existing talent supply and demand system, and it also shows that the training methods of talents in Chinese universities do not fully meet the needs of economic and social development, nor do they fully meet the requirements of talents’ own development. Under the background of “double innovation”, major universities need to get out of the misunderstanding and solve the problems in talent training. Therefore, innovation and entrepreneurship education and the cultivation of innovation and entrepreneurship ability are particularly necessary. The college students’ innovation and entrepreneurship ability evaluation could be regarded as the classical MAGDM issue In this paper, the PUL-CoCoSo method based on the PULTSs and CoCoSo method is proposed for MAGDM. The weights of attribute based on the CRITIC method are obtained under PULTSs. Finally, the college students’ innovation and entrepreneurship ability evaluation has been given to demonstrate the PUL-CoCoSo for MAGDM under PULTSs and some good comparative analysis is done to demonstrate the advantages of PUL-CoCoSo under PULTSs. For the future research, the designed models and methods in this paper can be extended and applied to other uncertain and vague decision making [66, 67, 68, 69, 70, 71] and other uncertain and vague environment [72, 73, 74, 75, 76, 77, 78, 79].

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Advanced CoCoSo method for uncertain MAGDM: Evaluating college students’ entrepreneurial skills

Abstract

Keywords

1. Introduction

2. Preliminaries

4.1 A numerical example

Table 1 Linguistic decision matrix by the first DM

Table 14 Order of the different methods

References

Table 1
Linguistic decision matrix by the first DM

Table 14
Order of the different methods