A study on bilateral matching of dual objectives of new R&D institution-talent team based on cloud model-regret theory

Abstract

To study the bilateral matching problem of new R&D institution-talent teams based on uncertain linguistic assessment information and multiple indicators-multiple talents, a cloud model regret theory-based information gathering method is proposed, and a bi-objective bilateral matching model based on single-indicator utility maximization and overall indicator utility maximization is constructed.. The method firstly constructs the demand indicators of new R&D institutions for talent teams, uses cloud data to characterize uncertain group linguistic assessment information, and converts cloud data into cloud perceived utility based on power function; secondly, calculates the indicator weights of each expert based on entropy power method, and secondly uses entropy power method to calculate comprehensive indicator weights, optimally solves objective expert weights based on the minimum variance of assessment information among experts, and integrates with subjective expert Again, based on regret theory, the cloud perceived utility of each talent under each index is converted into regret cloud perceived utility, and set with the index weights and expert weights into comprehensive cloud perceived utility; finally, a local-whole dual-objective bilateral matching model is constructed to obtain the matched talent team, and example analysis and method comparison are used to show that the method has feasibility and effectiveness.

Keywords

New R&D institution talent team cloud model regret theory bilateral matching

1 Introduction

New R&D institutions rely on scientific and technological R&D capabilities to accelerate the promotion and application of advanced technologies in enterprises and regional industries; use platform science and education resources as support to introduce, train, and gather scientific research leaders and innovative and entrepreneurial talents; and use scientific research instruments and equipment as the basis to promote independent innovation of enterprises and high-quality development of regional industries [1]. New R&D institutions are products of scientific and technological revolution and industrial change, based on industry and application goals to carry out source science and technology research and development, compared with traditional research institutions, diversified investment subjects, modernized management systems, market-oriented operation mechanisms, flexible employment mechanisms, and more clearly industry-oriented R&D and innovation goals.

In 2010, the Regulations of Zhongguancun National Funding Innovation Demonstration Zone was promulgated, taking the lead in supporting strategic scientists to take the lead in forming new R&D institutions. In 2019, the Ministry of Science and Technology issued the Guidance on Promoting the Development of New R&D Institutions, vigorously advocating and supporting the construction and development of new R&D institutions. At present, most new R&D institutions are in the start-up and growth stages of their life cycle, and there is an urgent need to introduce a large number of high-level scientific and technological talent to form talent teams. Combined with the development characteristics and stages of new R&D institutions, the institutions have many demand indicators for talent, and they hope to match the best talents under each indicator, but the overall quality of the talents must also be high; therefore, the bilateral matching between new R&D institutions and talent teams is many-to-many matching, and the two goals of maximum utility of a single indicator and maximum utility of the overall indicator should be considered. Therefore, the bilateral matching of new R&D institutions and talent teams based on the assessment information of uncertain language groups under demand indicators needs to solve the following six problems: first, the design problem of demand indicators; second, the characterization problem of assessment information; third, the weight problem of assessment indicators; fourth, the weight problem of assessment experts; fifth, the psychological behavior problem of decision-makers; and sixth, the bilateral matching model.

The demand indicators of new R&D institutions for talent teams can be derived from R&D institution and talent assessments. Meng & Song suggested that new R&D institutions have distinctive characteristics in terms of technology development, transformation, innovation, and business incubation [1]. Caviggioli et al. used data on projects, universities, patents, and the economy to study the development of technological specialization in European regions [2]. Han & Ma suggested that new R&D institutions have four properties: public good, economic, social, and innovative [3]. Jiang & Zhu constructed a dynamic grey target assessment model for the performance of new R&D institutions from four evaluation indicators: innovation source-innovation process-innovation level-innovation outcome, three reference points of peer-development-expectation, and four stages [4]. Jun & Kim proposed that the performance evaluation of new R&D institutions should consider five indicators: papers, patents, technology transfer, commercialization, and new employment [5]. Lu & Zhuang explored four drivers of new R&D institutions to enhance innovation capacity: government, university, technology, and market [6].

Bilateral matching was first proposed by Professor Gale of Brown University and Professor Sharply, a famous economist, in 1962, and they were based on preference order given by both parties for stable matching, and many scholars carried out bilateral matching studies based on preference order [7 –10] and later researchers carried out bilateral matching studies based on fuzzy numbers [11, 12], based on linguistic information [13, 14], they considered the uncertainty and diversity of information, but most of the studies are still based on preference order, while in reality many evaluation data are uncertain and specific values, and the characterization methods are fuzzy numbers [15, 16], cloud models [17, 18], interval gray numbers [19, 20], etc. Among them, the cloud model was proposed by Professor Deyi Li in 1995 to deal with the uncertainty conversion of qualitative concepts and quantitative descriptions; it has strong adaptability in that it can convert any form of information into cloud data, and the three numerical characteristics of cloud data, Expectation Ex, Entropy En, and Hyperentropy He, fully express the uncertainty of the data. The pervasiveness of the cloud model is particularly strong; therefore, bilateral matching based on the cloud model will also have strong pervasiveness, yet almost no one has studied it. In this study, we considered cloud-model-based bilateral matching.

In the process of studying bilateral matching, some researchers have added theories of decision makers’ psychological behavior, such as prospect theory proposed by Tversky and Kahneman [21] and regret theory proposed by Bell, Loomes, and Sugden [22]. Prospect theory suggests that whether decision makers are satisfied with the assessment results depends not only on the assessment data itself but also on the utility value of comparing with the reference point. Regret theory suggests that whether decision makers are satisfied with the assessment results depends not only on the assessment data itself but also on the utility value of comparing that data with other data, both of which show the psychological characteristics of decision makers’ comparison and consider the realistic risk factors of decision making. However, prospect theory needs to find reference point da, and regret theory generally compares with the optimal sequence or with the max-min sequence [23, 24], so this paper adopts regret theory to gather information in the absence of reference point data, and unlike other studies, this paper will adopt global regret theory, i.e., the utility value of talent under a certain indicator is compared with all other In contrast to other studies, this paper will adopt a global regret theory, in which the utility value of a talent under a certain indicator is compared with the utility values of all other talents under that indicator, and the sum of the regret values obtained is weighted with the utility values under that indicator to obtain the regret utility value, instead of comparing only with the best talent. This is one of the innovations of the present study. To match a new R&D organization with the best talent, this study expands the scope of regret so that every kind of regret may be included in the decision to improve the resolution of talent.

The author had full communication with the Director of the Human Resource Department of Institution Y. He suggested that Institution Y had four problems in the process of introducing talent. First, the development characteristics of new R&D institutions are market-oriented, flexible, high-end, and high conversion rates, and the assessment indexes for introducing scientific and technological talent should be more in line with the development needs of new R&D institutions. For example, they should have a keen market sense and a higher connection with the market; they should have higher requirements for technology and master more high-end and core technologies; they should have the ability to promote projects; and they should be able to apply for patents as well as convert them. He believes that market-technology-project-patent is the core ability of new R&D institutions to introduce scientific and technological talent, which is more in line with the development characteristics of new R&D institutions than the current assessment content. Second, experts prefer language evaluation when introducing scientific and technological talent, which has great uncertainty, and this uncertainty should be fully considered in the process of conversion into data. Third, new R&D institutions, due to their high end, especially need talent teams, and it is difficult to form high-end scientific and technological achievements by one person alone in many jobs. When introducing scientific and technological talents, often only the overall quality of the talent is considered and ranked based on the overall quality, it is difficult to form a complementary talent ability, and it is difficult to form a talent team. Therefore, we should consider not only the overall ability of talent but also the ability of individual indicators of talent, which is conducive to the formation of talent teams. Fourth, after the introduction of scientific and technological talents, comparing the introduced talents and unintroduced talents, later development data found that there will be a better development of unintroduced talents, resulting in regret. Therefore, the regret theory construct should be fully considered in the introduction process to avoid future regret.

This study is a many-to-many bilateral matching of multiple demand indicators and multiple talents for new R&D organizations, which should consider not only the maximum utility value of the talent under a single indicator, but also the maximum utility value of the talent under the overall indicator, so that the matching constitutes a talent team that can meet the requirements of individual indicators and ensure a high overall quality. Therefore, this study considers dual-objective bilateral matching of new R&D institutions and talent teams based on cloud model-regret theory. First, the demand index of new R&D institutions for talent is constructed, and multiple experts are invited to provide uncertain group language assessment information, which is converted into cloud data based on the cloud model and then into cloud perceived utility based on the power function. Second, the comprehensive index weights are solved based on the quadratic entropy weight method, objective expert weights are solved based on the variance minimum optimization method, and subjective expert weights are assembled to form comprehensive expert weights. Again, the global regret formula of regret theory is applied to convert the cloud perception utility into regret perception utility, and the integrated cloud perception utility is obtained with the integrated indicator weights and integrated expert weight set. Finally, a multi-indicator-multi-talent bilateral matching model is constructed based on the dual objectives of single-indicator utility maximization and overall indicator utility maximization of talents to obtain matched talent teams. The operational steps and practicality of the method are illustrated in detail with case and method comparisons.

2 Building a bilateral matching model for new R&D institutions and talent teams

2.1 Constructing a new R&D institution-talent team demand index system

I searched for “New R&D institutions” and “Capabilities” in “Web of Science” and entered the abstracts of the 50 most relevant papers into Gooseeker software. The abstracts of the 50 most relevant papers were entered into Gooseeker software for word separation, word selection, and co-linear matching. The co-linear matching matrix generated by the system was entered into Gephi software for clustering analysis, and the results are shown in Fig. 1.

Fig. 1

Keyword clustering diagram of the capability of new R&D institutions.

As can be seen from Fig. 1, new R&D institutions need the following types of capabilities: first, the ability to expand regional networks and scale, and the ability to record and publish R&D results; second, cooperation with universities and regions to learn knowledge, apply methods, and form entrepreneurial and systematic engineering and technology capabilities; third, advancing learning knowledge and management development to internationalization and industrialization, forming scientific and technical papers, applying for invention patents, and forming industrial intelligent manufacturing capability; and fourth, insight into the development trend of science and technology innovation, closely matching the market demand, and forming new market-based and high-level science and technology innovation capability. New R&D institutions focus on combining R&D results with the market, breaking through core technologies, solving “neck” problems, and continuously transforming results. Considering the convenience of expert evaluation, the number of indicators in this study should not be too large and the content of indicators should be the most necessary and core of new R&D institutions, which are closely related to their performance. After studying the literature, consulting experts, and analyzing the development reports of new R&D institutions, this study summarizes four dimensions and eight indicators of market-technology-project-patent, as shown in Fig. 2.

Fig. 2

Demand indicators of new R&D institutions for talent teams.

New R&D institutions are faced with a system project that requires talent teamwork, and each talent is good at different indicators, from m. The existing scientific and technological talents are selected based on the demand indicators of the talents needed by the talent team (m > n). If there are n indicators, choose n talents to form a team of talents with the greatest total utility, and also to ensure that the overall utility of the selected talents is also the greatest. There are multiple indicators and talents in the new R&D organization and talent team matching, which belong to many-to-many matching, as shown inFig. 3.

Fig. 3

Bilateral matching chart between new R&D institutions and talent teams.

In Fig. 3, there is only one new R&D organization: the red love heart indicates n demand indicators, the smiley face indicates m talents, the green smiley face indicates no matched successful talents, the red smiley face indicates matched successful talents, and the red smiley face constitutes the matched talent team. There are m talent to be matched through the preliminary examination, new R&D institutions have n demand indicators, invite s the talents evaluated by experts based on demand indicators, and provide uncertain group language information. Therefore, we need a method to gather uncertain language assessment information to achieve bilateral matching between the new R&D institution and the talent team.

2.2 Cloud-based model for aggregating uncertain language assessment data into cloud data

s experts evaluate m talents based on n demand indicators to get s decision matrix $A^{p} = [a_{ij}^{p}], i = 1, 2, \dots m, j = 1, 2, \dots n, p = 1, 2, \dots s$ , i means there are m scientific and technical talents, j means there are n talent team demand indicators, and p means there are s experts. $A^{p} = [\begin{matrix} a_{11}^{p} & a_{11}^{p} & \dots & a_{1 n}^{p} \\ a_{21}^{p} & a_{22}^{p} & \dots & a_{2 n}^{p} \\ \dots & \dots & \dots & \dots \\ a_{m 1}^{p} & a_{m 2}^{p} & \dots & a_{mn}^{p} \end{matrix}] .$

Definition 1: Let U be a quantitative domain represented by exact values and C be a qualitative concept of U. If the quantitative value x is a random realization of the qualitative concept C, x is a random number with a stable tendency for C with determinacy μ_x ∈ [0, 1]. $μ : U \to [0, 1] \forall x \in Ux \to [0, 1] .$

The distribution of x over the theoretical domain U is called a cloud, and x is a cloud drop.

E_x is the mathematical expectation in the theoretical domain; E_n is the entropy, which indicates the uncertainty of the qualitative concept, the larger the entropy E_n, the higher the uncertainty of the expectation; H_e is the entropy of the entropy, which indicates the uncertainty of the entropy, usually reflected in the thickness of the cloud, the larger the super-entropy H_e, the thicker the cloud. The three numerical characteristics of the cloud model are shown in Fig. 4.

Fig. 4

Numerical characteristics of the cloud model.

Because the language assessment itself also has some uncertainty, the standard cloud of the cloud model is applied to convert the language assessment values into cloud data. Based on the golden partition method, the theoretical domain [0,1] is divided into five assessment levels, and 0.618 is set as the multiplier between the parameters of the cloud model of adjacent levels. The closer to the central region of the theoretical domain [0,1], the smaller the entropy and super entropy of the assessment levels. The midpoint 0.500 of the theoretical domain [0,1] was taken as the middle evaluation level, and its cloud model parameters E_x = 0.500 and H_e = 0.005 were used to establish the cloud model transformation scale for language evaluation, as shown in Table 1.

Table 1

Cloud model transformation scales for uncertain language assessment

Grade	Evaluation Language	Satisfaction	Conversion scale
Level 1	Very poor	0–0.2	(0.000, 0.103,0.013)
Level 2	Poor	0.2–0.4	(0.309, 0.064,0.008)
Level 3	Fair	0.4–0.6	(0.500, 0.039,0.005)
Level 4	Good	0.6–0.8	(0.691, 0.064,0.008)
Level 5	Very good	0.8–1.0	(1.000, 0.103,0.013)

According to the conversion scale, we get s cloud data decision matrix $B^{p} = [b_{ij}^{p}], i = 1, 2, \dots m, j = 1, 2, \dots n, p = 1, 2, \dots s$ , $b_{ij}^{p}$ is the expected vue E_x of the converted cloud data, i means there are m talents, j means there are n indicators, p means s experts. In the assessment process, if there is [good or very good] indicates an assessment value between good and very good, which increases the uncertainty of the assessment, the average value of the converted scale of two assessment values is used to indicate the expected value in this study.

2.3 Converting cloud data to cloud-aware utility based on power functions

The literature [21] argues that people are always risk averse and risk averse is decreasing, and the power function can express this decreasing curve well, and according to the power function transformation, the s cloud-perceived utility decision matrix is obtained $C^{p} = [c_{ij}^{p}], i = 1, 2, \dots m, j = 1, 2, \dots n, p = 1, 2, \dots s$ . $c_{ij}^{p} = (b_{ij}^{p})^{α}$ (1)

α is the risk-aversion coefficient of the decision-makers, 0 < α < 1. A larger α indicates greater risk aversion of decision-makers, and a smaller α indicates less risk aversion of decision-makers. The conversion from cloud data to cloud perceived utility considers the decision-maker’s risk aversion factor.

2.4 Calculation of index weights based on quadratic entropy weighting method

The entropy weighting method was used to determine the weight of an index using objective assessment data [25]. The entropy weight method considers information as a measure of the degree of order in the system, and entropy as a measure of the degree of disorder in t system. The entropy value is used to reflect the amount of information provided by the indicator and to judge the discrete degree of an indicator: the smaller the entropy value of its information, the more information is provided, and the greater the discrete degree of the indicator, the greater the weight of the indicator on the assessment. In this study, we used the entropy weighting method, as shown in Equation formula (2.2)–(2.4).

$P_{ij}^{p} = \frac{c_{ij}^{p}}{\sum_{i = 1}^{m} c_{ij}^{p}}$ (2)

$H_{j}^{p} = - \frac{1}{\ln (m)} \sum_{i = 1}^{n} P_{ij}^{p} \ln (P_{ij}^{p})$ (3)

$ω_{j}^{p} = \frac{1 - H_{j}^{p}}{\sum (1 - H_{j}^{p})}$ (4)

$P_{ij}^{p}$ denotes the affiliation of the cloud data, and $\ln (P_{ij}^{p})$ denotes the logarithm of the affiliation of the cloud data, and $ω_{j}^{p}$ denotes the indicator weights under the evaluation of the pth expert. The indicator weights thus derived may vary little or a lot, and we put the indicator weights of the s experts together to form the indicator weight matrix D = [d_pj] , p = 1, 2, ⋯ s, j = 1, 2, ⋯ n, and again use the entropy weight method to obtain the unified comprehensive index weights of the s experts, as shown in t formula (2.5)–(2.7).

$P_{pj}^{d} = \frac{d_{pj}}{\sum_{p = 1}^{s} d_{pj}}$ (5)

$H_{j} = - \frac{1}{\ln (s)} \sum_{p = 1}^{s} P_{pj}^{d} \ln (P_{pj}^{d})$ (6)

$φ_{j} = \frac{1 - H_{j}}{\sum (1 - H_{j})}$ (7)

2.5 The objective expert weights are solved based on the minimum variance optimization of inter-expert evaluation information, and the subjective expert weights are aggregated to obtain the combined expert weights

In this paper s experts assessed m talents based on n demand indicators and obtained s assessment matrices. Owing to the different backgrounds of the experts, different levels of knowledge about talent, and different understandings of the demand indicators of the new R&D organizations, the resulting assessment values are different. The assessment information given by each expert is very important, but to minimize the gap between the ratings of experts, we set the objective expert weight as π_1p, the subjective expert weight as π_2p, and the comprehensive expert weight as π_p, and establish an optimization model M - 1 to solve the objective expert weight π_1p based on the minimum variance of assessment information among experts. ${MinZ}_{1} = \sum_{j = 1}^{n} \frac{1}{s} {[\bar{c_{j}^{p}} * π_{1 p} - \frac{1}{s} \sum_{p = 1}^{s} (\bar{c_{j}^{p}} * π_{1 p})]}^{2}$ (8)

$s . t . {\begin{matrix} π_{1 p} \in [0, 1] (2.9) \\ \sum_{p = 1}^{s} π_{1 p} = 1 (2.10) \end{matrix}$

In the M - 1 model, the MinZ₁ denotes the minimum variance of the utility value after multiplying the mean value of the assessed cloud-perceived utility among different experts by the expeeights, and $\bar{c_{j}^{p}}$ is the mean of the cloud-perceived utility of the p -th expert under the j -th indicator, and π_1p is the objective weight of the p -th expert. π_1p ∈ [0, 1] so that π_1p conforms to the normative requirements. $\sum_{p = 1}^{s} π_{1 p} = 1$ denotes the sum of the weights of the s experts1.

In the M - 1 model, Min Z₁ denotes the minimum variance of the utility value after multiplying the mean value of the assessed cloud-perceived utility among different experts by the expert weights, $\bar{c_{j}^{p}}$ is the mean value of the cloud-perceived utility of the p- expert under the j -th metric, π_1p is the objective weight of the p -th expert, π_1p ∈ [0, 1] so that π_1p conform to the normative requirements. $\sum_{p = 1}^{s} π_{1 p} = 1$ denotes the sum of the weights of the s expertsas one.

Theorem 1. M - 1 The model must have an optimal solution.

According to the existence theorem of optimality, any single-objectivplan with a bounded feasible domain must be optimal in its feasible domain. The M - 1 model is a single-objective planning problem, and the feasible domain of the model exists and is bounded. Thus, the M - 1 model must have an optimal solution. The objective expert weights π_1p are solved using Lingo software.

By introducing parameter δ, objective expert weight coefficient is δ and subjective expert weight coefficient is 1 - δ, the combined expert weight is $π_{p} = δ * π_{1 p} + (1 - δ) π_{2 p}$ (9)

2.6 Calculating the perceived utility of regret clouds based on regret theory

In this study, we consider global regret instead of local regret; that is, the cloud perceived utility $c_{ij}^{p}$ of the p -th expert for the i -th talent at the j -th metric is compared with the cloud perceived utility $c_{kj}^{p} (k \neq i)$ of the expert for all other talents at the j - metric one by one, and the sum of regret values is obtained collectively. If $c_{ij}^{p} > c_{kj}^{p} (k \neq i)$ , the decision maker thinks that choosing the i -th talent obtains better results than choosing the k -th talent, and the decision maker feels happy; if $c_{ij}^{p} < c_{kj}^{p} (k \neq i)$ , the decision maker thinks that choosing the i -th talent gets worse results than choosing the k -th talent, and the decision maker feels regret; if $c_{ij}^{p} = c_{kj}^{p} (k \neq i)$ , the decision maker believes that choosing the i -th talent obtains the same result achoosing the k -th talent, and the decision maker is neither happy nor regretful. Regret theory divides the perceived utility into two parts: one part is the cloud perceived utility of the expert, and the other part is the sum of regret values formed by comparing the cloud perceived utility of the matching talent with the cloud perceived utility of all other participating matching talents one by one. The two parts add up to form the cloud perceived utility of regret in this paper (see Equation (2.12).

$\begin{matrix} r_{ij}^{p} = {ɛ * c}_{ij}^{p} + (1 - ɛ) * \sum_{k \neq i} \\ [1 - \exp (- θ) (c_{ij}^{p} - c_{kj}^{p})] \end{matrix}$ (10)

$r_{ij}^{p}$ is the cloud perceived utility of regret under the j -th metric of the i -th talent of the p -th expert, ɛ is the adjustment coefficient of cloud perceived utility and regret value, ɛ ∈ [0, 1], ɛ > 0.5 means the cloud perceived utility has more influence on matching than the sum of regret value, ɛ < 0.5 means the sum of regret value has a greater influence on matching than the cloud perceived utility, ɛ = 0.5 means that the cloud perceived utility and the sum of regret value have the same influence on matching. θ is the regret avoidance coefficient of the decision maker; the larger θ means the greater the regret avoidance of the decision maker; a smaller θ means a smaller regret avoidance by the decision maker. $c_{ij}^{p} - c_{kj}^{p}$ denotes the difference between the i -th talent and the k -th talent cloud perceived utility under the p -th expert assessment. In the formula, the utility value of regret formation is the sum of the regret value of the selected talent and all talents not selected, which is global regret, while regret theory also converts the difference in regret into the form of a power function, indicating that the decision-maker’s regret risk aversion is also decreasing utility.

2.7 Construct a bilateral matching model based on the dual objective of maximizing the utility of a single indicator of talent and maximizing the utility of the overall indicator

Let μ : P ∪ Q → Q ∪ P be a one-to-one mapping, if ∀P_i ∈ P, ∀ Q_j ∈ Q, satisfies μP_i = Q_j ∈ Q and μ (Q_j) = P_i ∈ P, then we call μ is a two-way mching. μ (P_i) = Q_j denotes P_i with Q_j in μ in the match and μ (Q_j) = Q_j indicates tt Q_j in μ does not match. To study the bilateral matching problem of new R&D institutions and talent teams, we should consider not only the performance of talents under single indicators but also the overall performance of talents under all indicators; therefore, we set up the dual objectives of maximizing the utility of talents under single indicators and maximizing the overall utility.ce both are linear programming,he dual objectives can be converted into single objectives by connecting them with weighted β coefficients, so as to construct the bilateral matching integer programming model, which makes the matching the tt team timal combination under the single-indicator and overall-indicator dualobjectives.

We need to set the regret cloud perception utility $r_{ij}^{p}$ with the indicator weight φ_j and expert weight π_p to obtain the integrated cloud perception utility, which considers both the influence role of indicators and experts, as shown in Equation (2.13) $t_{ij} = \sum_{p = 1}^{s} [(r_{ij}^{p} * φ_{j}) * π_{p}]$ (11)

t_ij is the comprehensive cloud-perceived utility under the j -th index of the i -th talent, and the new R&D institution-talent bilateral matching model M - 2 is constructed based on the dual objectives of maximizing the single-index utility and maximizing the overall utility of thetalent.

\begin{matrix} {Max Z}_{2} = β * \sum_{j = 1}^{n} \sum_{i = 1}^{m} (t_{ij} * σ_{ij}) \\ + (1 - β) (\sum_{j = 1}^{n} t_{ij}) * (\sum_{j = 1}^{n} σ_{ij}) \end{matrix}

(12)

s . t . {\begin{matrix} σ_{ij} \in [0 or 1] (2.15) \\ \sum_{j = 1}^{n} σ_{i} ⩽ 1 (2.16) \\ \sum_{i = 1}^{m} σ_{j} = 1 (2.17) \end{matrix}

In the M - 2 model, MaxZ₂ indicates that the sum of the single-indicator utility and overall utility of the matched talent under each indicator is maximized bi-objectively. There are three constraints. σ_ij ∈ [0 or 1] indicates that σ_ij can only be 0 or 1, respectively. Therefore, the M - 1 model is a typical integer programming model: when σ_ij = 0, talent is not matched under the indicator; when σ_ij = 1, talent is successfully matched under the indicator; $\sum_{j = 1}^{n} σ_{i} ⩽ 1$ indicates that talent may be successfully matched or not; $\sum_{i = 1}^{m} σ_{j} = 1$ means that there must be one talent matched successfully under each indicator. In other words, the M - 2 model will matches n talents to form a talent team.

Theorem 2. The M - 2 model must have an optimal solution.

According to the optimal existence theorem, any singlobjective plan with a bounded feasible domain must be optimal in its feasible domain. M - 2 model is a single-objective planning problem, and the feasible domain of the model exists and is bounded. Therefore, the M - 2 model must have an optimal solution. Lingo software is used to solve σ_ij, and the solved σ_ij = 1 means that the j -th index of the i -th talent is successfully matched with the new R&D organization to obtain the matching result of the new R&D organization and the talent team.

2.8 The methodological steps in this article

The steps of the new R&D organization-talent team bilateral matching method based on the cloud model-regret theory are as follows:

Step 1 Constructing demand indicators for talent teams in new R&D institutions and inviting experts to evaluate m talents based on n demand indicators tobtain the decision matrix of uncertain language assessment information.

Step 2 Converting uncertain language assessment information into cloud data based on cloud model.

Step 3 Converting cloud data into cloud-perceived utility based on power functions.

Step 4 Calculating comprehensive index weights based oqdratic entropy weighting method.

Step 5 Construct an optimization model based on varian mimization to solve objective expert weights and calculate comprehensive expert weights by combining subjective expert weights.

Step 6 Converting cloud perceived utility into regret perceived utility based on regret theory.

Step 7 Aggregate regret perception utility, indicator weights, and expert weights into a comprehensive cloud perception utility.

Step 8 Construct a bilateral matching model of new R&D institution-talent teams based on the dual objectives of maximizing the single indicator utility, maximizing the overall utility of talent, and solving the bilateral matching results.

3 Case study

3.1 Background analysis

The new R&D institution Y was established in September 2016, which is jointly formed by the talent team, X Industrial Research Institute and local government, and belongs to the mixed ownership enterprise, providing intelligent robot machine solutions, highly competitive in innovative product development, key technology breakthroughs, and core component development, and has been awarded the new R&D institution performance excellence award by Z Province for many years, hoping to strive to become the Z Province intelligent equipment innovation The main business areas are The main business areas are whole field planning for intelligent manufacturing, intelligent services and special robots R&D, sales, production and industrialization, which have successfully developed 4 collaborative robots and 9 indoor unmanned vehicles to achieve navigation and positioning with friendly human-machine interaction interface and voice interaction function, which are applied to many scenarios. Institution Y has passed seven qualification system certifications, such as GJB9001, CCRC, and ITSS. It has gathered 173 high-level R&D, management, and professional technical talents, of which 45% are graduate students and senior engineers. It has established postgraduate workstations in cooperation with several universities ranked within 50 nationwide and jointly trained 77 postgraduates in total. Institution Y innovated the project management system. The project manager is responsible for gathering first-class talents and top technologies, organizing major original innovation projects for the industry, and giving full play to the autonomy in managing the team, conducting strategic research, project establishment, and fund allocation. Institution Y allows science and technology talents to enjoy more income from technology appreciation, and fully mobilizes the innovation and entrepreneurship of science and technology talents by means of equity income and option determination, so that science and technology talents can “earn both fame and profit”. Agency Y provides career planning, five insurance, one fund, talent apartments, paid annual leave, meal allowances, transportation allowances, communication allowances, regular physical examinations, professional training, platform training, project bonuses, talent housing, and other welfare benefits. The workplace is located in the Yangtze River Delta.

Agency Y has always attached importance to the introduction and cultivation of talent teams, recruiting IT talent year-round. 32 people were recruited, and the personnel department finally passed six people in the preliminary examination and entered the final interview after screening, preliminary examination, and practice. Among the six talents, choose four to form a talent team, not only the quality of the single indicator of the talent, but also the quality of the comprehensive indicator of the talent, which forms the bilateral matching problem of the new R&D institution Y and the talent team.

3.2 Data and process analysis

In the first step, assessment indicators are identified and initial assessment values are collected.

The new R & D institutions invited 4 experts, respectively, representatives of competent department leaders, industry experts, science and technology experts and management experts, based on the four demand indicators of “market - technology - project - patent” In the process of scoring, each scientific and technological talent was given a rating. During the scoring process, each tech talent provided a detailed self-identified competency report based on the four demand indicators, followed by a 30-minute interview and defense, which was divided into three parts: self-introduction, answering according to the questions raised by the experts, and explaining why they chose Agency Y and described their future direction of effort. The experts rated the technical talent based on their competency report and the effectiveness of the interview and defense, using a five-level linguistic scale of “very poor, poor, fair, good, very good”. When the experts cannot accurately express the assessment of the scientific and technical talents with five levels of language, two levels of language assessment values can appear simultaneously under a certain index, such as [fair, good], which means that the scientific and technical talents’ rating under this index is between fair and good, expanding the uncertainty of the language information. The specific assessment information comes from the human resources department of institution Y, as shown in Table 2.

Table 2
Information on the uncertain language assessment of talents in new R&D institutions

S1-T Markets Technology Projects Patents S2-T Markets Technology Projects Patents

T1 Good Very good Very good Poor T1 Fair Very good Fair Very good

T2 Very good Fair Poor Good T2 Fair Fair Poor Poor, average

T3 Fair Poor, average Very good Fair T3 Fair Fair, good Good Very poor, poor

T4 Good Fair, good Fair Fair T4 Fair Good Very poor Fair

T5 Poor Good Very good Fair T5 Good Fair Fair Good

T6 Very poor Fair Poor Good T6 Very good Poor, average Good Fair, good

S3-T Markets Technology Projects Patents S4-T Markets Technology Projects Patents

T1 Fair Good Good Fair T1 Fair Fair Good Good, very good

T2 Good Fair Poor Fair T2 Fair Fair Fair Fair

T3 Good Poor Fair Very good T3 Good Fair, good Very good Fair

T4 Poor, average Very good Good Fair, good T4 Very good Good Good Poor

T5 Good Poor Good Poor, average T5 Good Poor Good Fair

T6 Poor Very good Fair Good T6 Very good Very poor, poor Fair Good

S1-T	Markets	Technology	Projects	Patents	S2-T	Markets	Technology	Projects	Patents
T1	Good	Very good	Very good	Poor	T1	Fair	Very good	Fair	Very good
T2	Very good	Fair	Poor	Good	T2	Fair	Fair	Poor	Poor, average
T3	Fair	Poor, average	Very good	Fair	T3	Fair	Fair, good	Good	Very poor, poor
T4	Good	Fair, good	Fair	Fair	T4	Fair	Good	Very poor	Fair
T5	Poor	Good	Very good	Fair	T5	Good	Fair	Fair	Good
T6	Very poor	Fair	Poor	Good	T6	Very good	Poor, average	Good	Fair, good
S3-T	Markets	Technology	Projects	Patents	S4-T	Markets	Technology	Projects	Patents
T1	Fair	Good	Good	Fair	T1	Fair	Fair	Good	Good, very good
T2	Good	Fair	Poor	Fair	T2	Fair	Fair	Fair	Fair
T3	Good	Poor	Fair	Very good	T3	Good	Fair, good	Very good	Fair
T4	Poor, average	Very good	Good	Fair, good	T4	Very good	Good	Good	Poor
T5	Good	Poor	Good	Poor, average	T5	Good	Poor	Good	Fair
T6	Poor	Very good	Fair	Good	T6	Very good	Very poor, poor	Fair	Good

As can be seen from Table 2, the assessment information given by the four experts was uncertain linguistic information, and some of them expanded the interval of linguistic information, such as [poor, fair] indicating between poor and fair. The assessment information provided by the four experts varied greatly and did not visualize the strengths and weaknesses of their talents.

In the second step, the uncertain language assessment information is converted to feature values of cloud data according to the conversion scale in Table 1, see Table 3.

Table 3

Characteristic values of cloud data for the assessment of talents in new R&D institutions

S1-T	Markets	Technology	Projects	Patents	S2-T	Markets	Technology	Projects	Patents
T1	0.6910	1.0000	1.0000	0.3090	T1	0.5000	1.0000	0.5000	1.0000
T2	1.0000	0.5000	0.3090	0.6910	T2	0.5000	0.5000	0.3090	0.4045
T3	0.5000	0.4045	1.0000	0.5000	T3	0.5000	0.5955	0.6910	0.1545
T4	0.6910	0.5955	0.5000	0.5000	T4	0.5000	0.6910	0.0000	0.5000
T5	0.3090	0.6910	1.0000	0.5000	T5	0.6910	0.5000	0.5000	0.6910
T6	0.0000	0.5000	0.3090	0.6910	T6	1.0000	0.4045	0.6910	0.5955
S3-T	Markets	Technology	Projects	Patents	S4-T	Markets	Technology	Projects	Patents
T1	0.5000	0.6910	0.6910	0.5000	T1	0.5000	0.5000	0.6910	0.8455
T2	0.6910	0.5000	0.3090	0.5000	T2	0.5000	0.5000	0.5000	0.5000
T3	0.6910	0.3090	0.5000	1.0000	T3	0.6910	0.5955	1.0000	0.5000
T4	0.4045	1.0000	0.6910	0.5955	T4	1.0000	0.6910	0.6910	0.3090
T5	0.6910	0.3090	0.6910	0.4045	T5	0.6910	0.3090	0.6910	0.5000
T6	0.3090	1.0000	0.5000	0.6910	T6	1.0000	0.1545	0.5000	0.6910

In the third step, the eigenvalues of cloud data are converted to cloud-aware utility according to Equation (2 .1) by taking α = 0.88, see Table 4.

Table 4

Cloud perceived utility of new R&D organizations for talent assessment

S1-T	Markets	Technology	Projects	Patents	S2-T	Markets	Technology	Projects	Patents
T1	0.7223	1.0000	1.0000	0.3558	T1	0.5434	1.0000	0.5434	1.0000
T2	1.0000	0.5434	0.3558	0.7223	T2	0.5434	0.5434	0.3558	0.4509
T3	0.5434	0.4509	1.0000	0.5434	T3	0.5434	0.6337	0.7223	0.1933
T4	0.7223	0.6337	0.5434	0.5434	T4	0.5434	0.7223	0.0000	0.5434
T5	0.3558	0.7223	1.0000	0.5434	T5	0.7223	0.5434	0.5434	0.7223
T6	0.0000	0.5434	0.3558	0.7223	T6	1.0000	0.4509	0.7223	0.6337
S3-T	Markets	Technology	Projects	Patents	S4-T	Markets	Technology	Projects	Patents
T1	0.5434	0.7223	0.7223	0.5434	T1	0.5434	0.5434	0.7223	0.8627
T2	0.7223	0.5434	0.3558	0.5434	T2	0.5434	0.5434	0.5434	0.5434
T3	0.7223	0.3558	0.5434	1.0000	T3	0.7223	0.6337	1.0000	0.5434
T4	0.4509	1.0000	0.7223	0.6337	T4	1.0000	0.7223	0.7223	0.3558
T5	0.7223	0.3558	0.7223	0.4509	T5	0.7223	0.3558	0.7223	0.5434
T6	0.3558	1.0000	0.5434	0.7223	T6	1.0000	0.1933	0.5434	0.7223

In the fourth step, the comprehensive index weights are calculated according to Equations (2.2 –(2.7), see Fig. 5.

Fig. 5

Indicator weights and combined indicator weights for experts S1-S4.

From Fig. 5, it can be seen that the indicator weights of experts S1-S4 are different: S1 considers market analysis ability as the most important and patent ability unimportant; S2 considers project incubation ability as the most important and market analysis ability unimportant; S3 and S4 almost overlap, both considering science and technology supply ability the most important and project incubation ability unimportant; the combined indicator weights consider market and methods to be relatively important.

In the fifth step, the objective expert weights and comprehensive expert weights are calculated according to Equations (2 .8)–(2.11), and the subjective expert weights are (0.2,0.3,0.3,0.2), and the parameter δ = 0.5 is taken, see Fig. 6.

Fig. 6

Objective expert weights, subjective expert weights a combined expert weights.

From Fig. 6, it can be seen that the decision power oexperts S1-S4 in the objective expert weight does not differ much, and the decision power of experts S1 and S2 is slightly larger; the decision power of experts S2 and S3 in the subjective expert weight is larger, and the difference with experts S2 and S4 is more obvious; the comprehensive expert weight is between the objective expert weight and the subjective expert weight, and the decision power of experts S2 and S3 is slightly larger.

In the sixth step, the perceived utility of the regret cloud is calculated according to Equation (2.12), taking ɛ = 0.5 and θ = 0.3, as shown in Table 5.

Table 5

Cloud perceived utility of new R&D organizations’ assessment of talent regret

S1-T	Markets	Technology	Projects	Patents	S2-T	Markets	Technology	Projects	Patents
T1	0.9867	1.5919	1.4795	–0.0504	T1	0.3414	1.5919	0.6382	1.6788
T2	1.7228	0.3413	–0.3418	0.9833	T2	0.3414	0.3413	0.1087	0.1769
T3	0.4914	0.0744	1.4795	0.4878	T3	0.3414	0.5975	1.1259	–0.5848
T4	0.8931	0.6230	0.3334	0.4878	T4	0.4013	0.7936	–0.7639	0.4947
T5	–0.0466	0.8445	1.4795	0.4878	T5	0.8446	0.3413	0.6382	0.9389
T6	–1.1235	0.3413	–0.3418	0.9833	T6	1.5920	0.0744	1.1259	0.6945
S3-T	Markets	Technology	Projects	Patents	S4-T	Markets	Technology	Projects	Patents
T1	0.4600	0.8092	0.9310	0.3413	T1	0.1394	6151	0.7400	1.3191
T2	0.9570	0.3040	–0.1088	0.3413	T2	0394	6151	0.2311	0.4424
T3	0.9570	–0.2448	0.4326	1.5919	T3	0.6532	0.8640	1.4958	0.4424
T4	0.2724	1.3462	0.9310	0.5396	T4	1.3290	1.0048	0.7400	–0.0373
T5	0.9570	–0.2448	0.9310	0.0744	T5	0.6532	0.0843	0.7400	0.4424
T6	–0.0798	1.5594	0.4326	0.8445	T6	1.4159	–0.3913	0.2311	0.9403

As can be seen from Table 5, regret cloud perceived utility does not meet the normative requirements; some values exceed 1, indicating that the decision maker is very satisfied with the talent in comparison with all other talents under this indicator; some values are negative, indicating that the decision maker is very dissatisfied with the talent in comparison with all other talents under this indicator.

In the seventh step, the integrated cloud-aware utility is calculated according to Equation (2.13), see Fig. 7.

Fig. 7

Integrated cloud-aware utility of talent under each metri.

From Fig. 7, it can be seen that.

The comprehensive cloud perceived utility of different talents under each indicator was different. The comprehensive cloud perceived utility curves under market and patent indicators are relatively flat, indicating that the gap between talents’ assessments under these two indicators is not large; the comprehensive cloud perceived utility curves under technology and project indicators are more volatile, indicating that the gap between talents’ assessments under these two indicators is large.

The comprehensive cloud perceived utility of patents is generally lower than that of other indicators, indicating that the overall patent incubation capacity must be strengthened.

Based on market indicators, T2 is the best and T6 is the worst; based on technical indicators, T1 is the best and T5 is the worst; based on project indicators, T3 is the best and T2 is the worst; based on patent indicators, T6 is the best and T4 is the worst.

Different talents are suitable indicators. T1 had the best technical ability but the worst patent ability; T2 had the best market ability but the worst project ability; T3 had the best project ability but the worst patent ability; T4 had the best technical ability but the worst patent ability; T5 had the best project ability but the worst patent ability; and T5 had the best market ability but the worst patent ability.

In the eighth step, the matching results are solved according to Equations (2 .14)–(2.17) and the methods are compared.

Method A: The method of this paper with β = 0.6.

Method B: Based on the methods in this study, without considering regret theory, β = 0.6.

Method C: Based on the method described in this paper, considering only regret theory with optimal comparison, β = 0.6.

Method D: Based on the method presented in this paper, only the optimal matching of the talent single index is considered: β = 1.

Method E: Based on the method presented in this paper, only the optimal matching of the talent overall index is considered: β = 0.

Based on the above methods, the matching results are shown in Table 6.

Table 6

Bilateral matching results of new R&D institutions and talent teams under different methods

Method	Bilateral matching results
A	T1-J2 T3-J3 T4-J1 T6-J4
B	T1-J2 T3-J3 T4-J1 T5-J4
C	T1-J2 T3-J3 T4-J1 T5-J4
D	T1-J2 T2-J1 T3-J3 T6-J4
E	T1-J4 T3-J3 T4-J1 T5-J2

In Table 6, T denotes talent and J denotes indicators, and the bilateral matching results show the following:

Different methods match slightly different results, and some methods match talents between them, although they are the same, but the matching indicators are different, that is, the division of labor is different. The first market indicator matches talent T4 or T2; the second technical indicator matches talent T1 or T5; the third project indicator matches talent T3; and the fourth patent indicator matches talent T5, T6, or T1.

Combined with the above five methods, the probability of success of talent matching is different: the probability of success of talent T1 matching is 100% the probability of success of talent T2 matching is 20% the probability of success of talent T3 matching is 100% the probability of success of talent T4 matching is 80% the probability of success of talent T5 matching is 60% and the probability of success of talent T6 matching is 40%. In other words, talents T1 and T3 can be matched regardless of the method used, indicating that T1’s ability under a certain index is outstanding and the overall quality is relatively high.

4 Conclusion

4.1 The innovation of this paper

First, the method of cloud model and power function provides a good basis for the decision to match talent teams in new R&D institutions, solves the method of matching assessment values characterized by uncertain linguistic values, and converts cloud data into cloud perceived utility, which not only considers the uncertainty of assessment values and the maximum possibility of assessment value conversion but also increases the riskiness of decision making, is closer to reality, and is simple to calculate.

Second, this study designs an evaluation index system for new R&D institutions for talent teams based on the characteristics and development needs of new R&D institutions, considering both the macro aspects of talent (market ability and technical ability) and micro aspects of talent (project ability and patent ability), and considering both the external ability of talent (market ability and project ability) and the internal ability of talent (technical ability and patent ability), so that the design can comprehensively grasp the development of talent that new R&D institutions need to match.

Third, there are weights among indicators, and this paper applies entropy weighting method twice to determine indicator weights, the first time using entropy weighting method to determine different indicator weights of each expert, and the second time using entropy weighting method to determine comprehensive indicator weights, which can avoid extreme distribution of indicator weights of each expert while improving the resolution of assessment information, which is more in line with the actual situation and ensures the effective transmission of assessment information.

Fourth, in group decision-making, most decisions consider the 100 points rated by expert A and the 100 points rated by expert B as having the same utility while ignoring the decision dominance in expert evaluation. In this paper, expert weights are considered, and both objective and subjective weights are considered when calculating the index weights, and the comprehensive expert weights are determined through the objective-subjective connection coefficient, which fully considers the expert’s decision rights and makes the comprehensive cloud perceived utility of the assemblage more reasonable.

Fifth, this study uses the global regret theory to convert cloud perceived utility into regret cloud perceived utility, considering not only the cloud perceived utility of experts to talents, but also the sum of regret values obtained by comparing the matched talents with the cloud perceived utility of all other participating matched talents one by one, and weighting the sum of cloud perceived utility and regret values together; thus, the calculation is more in line with the psychological characteristics of decision makers when making decisions, adding a new exploration of the integration of decision-makers’ psychological behaviors into decision theory.

Sixth, the new R&D institutions and talent teams examined in this study are matched bilaterally with multiple indicators and multiple talents, which is a many-to-many matching. Many times when organizations select talent, they often also select multiple talents without forming a team, and only consider the comprehensive assessment value of each talent to make a ranking selection. Due to the strong marketability, high level of science and technology, and high transformation requirements of new R&D institutions, there is a greater need for talent teams to form talent synergy. Therefore, this study considers not only the performance of talents under single indicators, but also the overall performance of talents under all indicators, and constructs a bilateral matching model of new R&D institutions and talent teams based on the dual objectives of maximizing the utility of single indicators of talent and maximizing the utility of overall indicators, so that the matched talents can not only form a team and have the ability to excel but also have high comprehensive quality.

4.2 Research findings

The method in this study uses cloud model data transformation, confirms indicator and expert weights, assembles information based on global regret theory, and finally constructs a bi-objective many-to-many bilateral matching model. The method in this paper considers the uncertainty of information, decision risk, psychological behavior of decision makers, subjective and objective factors, and local and overall optimal dual objectives. The calculation is very simple and can be automated, which greatly improves the efficiency and effectiveness of matching, with strong universality and practicality.

First, the calculation of indicator weights, expert weights, and regret cloud perceived utility in this study is based on the evaluation information of the same batch of talents involved in matching, so that it can ensure that each matching is the best single indicator ability and overall indicator ability among the batch of talents. There will not be a situation in which no talent is matched, and the same applies if a different batch of talents is involved in matching or a different batch of experts is evaluated, and the matching result will change with the talents involved in matching and the experts involved in evaluation.

Second, in the process of bilateral matching between new R&D institutions and talent teams, this study sets the weights of the single indicator utility and overall indicator utility. Different decision makers have different understandings of these two goals, and in the method comparison, we can see that the weights are different, and the matching results are not consistent.

Third, the bilateral matching of new R&D institutions and talent teams can also realize the precise training of talents, fully understand the advantages and disadvantages of talent, and carry out relevant training for the disadvantages of talent; for example, the patent incubation ability of all six talents in this study is relatively poor, so guidance and training in patent incubation should be carried out.

Due to the small amount of data collection, the author selected only one new R&D institution for the method calculation, and the sample size was still relatively small, so there are some limitations. The current study only considers institutions and talent and does not consider other factors such as the government. The current study considered only a static situation. In the future, the author will also conduct research on the bilateral matching of new R&D institutions and talents based on government supervision, and research on the dynamic matching of new R&D institutions and scientific and technological talents.

Footnotes

Acknowledgments

1. The National Natural Science Foundation of China (NSFC) project: A method and application of dynamic emergency group decision-making driven by ternary group intelligence information interaction for public emergencies, Project No. 72071106.

2. Jiangsu Province Education Reform and Development Strategic and Policy Research Major Project: Jiangsu high-level teacher team construction research, Project No. 202000206.

3. Jiangsu Higher Education Basic Science (Natural Science) Program, Project No. 21KJB510009.

4. Project of Jiangsu Provincial Education Department: Research on talent management innovation of universities based on big data in the context of “double first-class,” Project No. 2019SJA1734.

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