Research on the efficiency evaluation of venture capital of high-science and technology companies with dual hesitant fuzzy information

Abstract

High technology enterprise venture capital is one kind of important means that market economy system supports to put research findings into industrial production time, with whose proper function, have driven host country science and technology and development of the economy in the field of every. In venture capital reality affair activity, the rightness to the project appraises the key link being that venture capital is in motion and does business successfully. The task of this paper is to study on the multiple attribute decision making problems for evaluating the efficiency of venture capital of high-science and technology companies with dual hesitant fuzzy information and incomplete weight information. Then, exploiting the existing GRA methods, computation steps for tackling dual hesitant fuzzy multiple attribute decision-making problems with incomplete weight information are proposed. In the end, an example of evaluating the efficiency of venture capital of high-science and technology companies using the grey relational analysis based on the dual hesitant fuzzy information is proposed.

Keywords

Multiple attribute decision making dual hesitant fuzzy values grey relational analysis method high-science and technology companies venture capital efficiency evaluation

1 Introduction

Along with the acceleration of economic globalization, international competition becomes fiercer, the essential part of which is science and technology, especially the competition of autonomous innovation. A stratagem about technology development has been proposed explicitly that a transfer must be achieved to focus on the leapfrog development of technology and autonomous innovation, oriented from tracking and imitating. As a significant part of the national innovation system, private high-tech enterprises are the most active micro-innovation subjects, who will certainly speak louder on the future innovation stage. Therefore, it makes great sense on both practice and theory studying of high-tech enterprises and analyzing their innovation dynamic system.

Venture capital investment is the investment behavior that obtains high returns from the value-added capital withdraws of share rights brought by rapid growth of the enterprises invested, through investing in the small & medium-sized growing enterprises which are unlisted, especially the share rights of high-tech enterprises, and through implanting appropriate management. Since 1985, venture capital investment has been introduced into China, particularly since 1989’s First Proposal, it gradually got started and developed; as yet, it has achieved remarkable progress. Currently, many negotiation and investment cases of venture capital are carried out every year; however, each investment process, from the cooperative negotiation between a venture capital firm and a start-up enterprise to the final investment implementation, inevitably goes through a process of mutual communication, negotiation, and decision making. During this process, venture capital firms must face and resolve one realistic problem: whether the start-up enterprises have investment values and how costly to obtain their share rights, that is, how to confirm the values of those enterprises.

High technology enterprise venture capital is one kind of important means that market economy system supports to put research findings into industrial production time, with whose proper function, have driven host country science and technology and development of the economy in the field of every. In venture capital reality affair activity, the rightness to the project appraises the key link being that venture capital is in motion and does business successfully. The main task of this paper is to study on the multiple attribute decision making problems [1 –12] for evaluating the efficiency of venture capital of high-science and technology companies with dual hesitant fuzzy information and incomplete weight information. Afterwards, applying the former GRA methods, computing steps for tackling dual hesitant fuzzy multiple attribute decision-making problems with incomplete weight information are proposed. Based on the above definition, an example of evaluating the efficiency of venture capital of high-science and technology companies based on the grey relational analysis with dual hesitant fuzzy information is proposed.

2 Preliminaries

Definition 1. [13, 14] Let X be a dual hesitant fuzzy set (named as DHFS) on X is given as: $D = (〈 x, h (x), g (x) 〉 | x \in X)$ (1) where h (x) and g (x) means two sets of values in the range [0, 1], representing the possible membership degrees and non-membership degrees of the element x ∈ X to the set D respectively, and the following equations should be satisfied. $0 \leq γ, η \leq 1, 0 \leq γ^{+}, η^{+} \leq 1$

where γ∈ h (x), η ∈ g (x), γ⁺∈ h⁺(x) = ∪ _γ∈h(x) max { γ }, η⁺∈ g⁺(x) = ∪ _η∈g(x) max { η } for all x ∈ X.

Definition 2. [13, 14] Let d_i = (h_{d
_i}, g_{d
_i}) (i = 1, 2) be any two DHFEs, $s (d) = \frac{1}{# h} \sum_{γ \in h} γ - \frac{1}{# g} \sum_{η \in g} η$ the score function of d, and $p (d) = \frac{1}{# h} \sum_{γ \in h} γ + \frac{1}{# g} \sum_{η \in g} η$ the function of d, where # h and # g refer to the numbers of the units in h and g.

Definition 3. Let d_i = (h_{d
_i}, g_{d
_i}) (i = 1, 2) refer to any two DHFEs, $s (d_{i}) = \frac{1}{# h_{i}} \sum_{γ_{i} \in h_{i}} γ_{i} - \frac{1}{# g_{i}}$ ∑_{η_i∈g_i}η_i the score function of d_i, and the distance measure between d_i is defined as $∥ d_{1} - d_{2} ∥ = | s (d_{1}) - s (d_{2}) |$ (2)

3 Research on the efficiency evaluationof venture capital of high-scienceand technology companies with dual hesitant fuzzy information

Deng [15] developed the Grey relational analysis (GRA) approach and successfully utilized in tackling more and more MADM problems [16 –19]. In this section, we will use the grey relational analysis method to solve the multiple attribute decision making problems for quantitative prediction of mineral resources with dual hesitant fuzzy information and incomplete weight information. Let A ={ A₁, A₂, ⋯, A_m } be a discrete set of alternatives, and G ={ G₁, G₂, ⋯, G_n } be the state of nature. If the decision makers give several values for the alternative A_i via the state of nature G_j with anonymity, the above values is able to be regarded as a dual hesitant fuzzy numbers ${\tilde{d}}_{ij} = (h_{ij}, g_{ij})$ . Assume that the decision matrix $\tilde{D} = {({\tilde{d}}_{ij})}_{m \times n}$ is the dual hesitant fuzzy decision matrix, where ${\tilde{d}}_{ij} (i = 1, 2, \dots, m, j = 1, 2, \dots, n)$ are represented as DHFEs. Let w = (w₁, w₂, ⋯, w_n) is theweighting vector of the attribute G_j (j = 1, 2, ⋯, n), where w_j ∈ [0, 1], $\sum_{j = 1}^{n} w_{j} = 1$ . H is a set of the known weight information [20].

In the following, we develop an algorithm for evaluating the efficiency of venture capital of high-science and technology companies using the grey relational analysis with dual hesitant fuzzyinformation.

Step 1. Obtain the dual hesitant fuzzy positive ideal and dual hesitant fuzzy negative ideal answer. ${\tilde{r}}^{+} = (s (d_{1}^{+}), s (d_{2}^{+}), \dots, s (d_{n}^{+}))$ (3) ${\tilde{r}}^{-} = (s (d_{1}^{-}), s (d_{2}^{-}), \dots, s (d_{n}^{-}))$ (4) where $\begin{matrix} {\tilde{r}}_{j}^{+} = s (d_{j}^{+}) = max_{i} s (d_{ij}), \\ {\tilde{r}}_{j}^{-} = s (d_{j}^{-}) = min_{i} s (d_{ij}), j \in 1, 2, \dots, n . \end{matrix}$ (5)

Step 2. Compute the grey relational coefficient of each alternative from DHFPIS and DHFNIS:

The grey relational coefficient of each alternative from DHFPIS can be calculated as follows: $\begin{matrix} x_{ij}^{+} = \frac{min_{1 \leq i \leq m} min_{1 \leq j \leq n} ∥ {\tilde{r}}_{ij} - {\tilde{r}}_{j}^{+} ∥ + ρ max_{1 \leq i \leq m} max_{1 \leq j \leq n} ∥ {\tilde{r}}_{ij} - {\tilde{r}}_{j}^{+} ∥}{∥ {\tilde{r}}_{ij} - {\tilde{r}}_{j}^{+} ∥ + ρ max_{1 \leq i \leq m} max_{1 \leq j \leq n} ∥ {\tilde{r}}_{ij} - {\tilde{r}}_{j}^{+} ∥}, \\ i = 1, 2, \dots, m, j \in 1, 2, \dots, n . \end{matrix}$ (6) Meanwhile, the grey relational coefficient of each alternative from DHFPIS can be computed by the following equation: $\begin{matrix} y_{ij}^{-} = \frac{min_{1 \leq i \leq m} min_{1 \leq j \leq n} ∥ {\tilde{r}}_{ij} - {\tilde{r}}_{j}^{-} ∥ + ρ max_{1 \leq i \leq m} max_{1 \leq j \leq n} ∥ {\tilde{r}}_{ij} - {\tilde{r}}_{j}^{-} ∥}{∥ {\tilde{r}}_{ij} - {\tilde{r}}_{j}^{-} ∥ + ρ max_{1 \leq i \leq m} max_{1 \leq j \leq n} ∥ {\tilde{r}}_{ij} - {\tilde{r}}_{j}^{-} ∥}, \\ i = 1, 2, \dots, m, j \in 1, 2, \dots, n . \end{matrix}$ (7) in which the identification coefficient ρ = 0.5.

Step 3. Computing the degree of grey relational coefficient of each alternative from DHFPIS and DHFNIS as follows. $x_{i}^{+} = \sum_{j = 1}^{n} w_{j} x_{ij}^{+}, x_{i}^{-} = \sum_{j = 1}^{n} w_{j} x_{ij}^{-}, i = 1, 2, \dots, m .$ (8)

Therefore, to compute the $x_{i}^{-}$ and $x_{i}^{+}$ , we should compute the weight information in advance. Hence, we should construct a multiple objective optimization model to obtain the weight information. ${\begin{matrix} min x_{i}^{-} = \sum_{j = 1}^{n} w_{j} x_{ij}^{-}, i = 1, \dots, m \\ max x_{i}^{+} = \sum_{j = 1}^{n} w_{j} x_{ij}^{+}, i = 1, \dots, m \\ subject to : w \in H \end{matrix}$

Because each alternative is non-inferior, there are no any preference relation on the all the alternatives. Afterwards, we should simply the multiple objective optimization models by setting the same weight to the objective optimization model. ${\begin{matrix} max x = \sum_{i = 1}^{m} \sum_{j = 1}^{n} (x_{ij}^{+} - x_{ij}^{-}) w_{j} \\ subject to : w \in H \end{matrix}$

By calculating the above model, we are able to derive the optimal solution w = (w₁,w₂, ... ,w_n). Then, we can calculate the $x_{i}^{+} (i = 1, \dots, m)$ and $x_{i}^{-} (i = 1, \dots, m)$ by (Equations 6–7).

Step 4. Computing the relative relational degree of each alternative from DHFPIS, $x_{i} = x_{i}^{+} / - (x_{i}^{-} + x_{i}^{+}), i = 1, 2, \dots, m .$ (9)

Step 5. Rank all the alternatives A_i (i = 1, 2, ⋯, m) and then choose the optimal one(s) using x_i (i = 1, 2, ⋯, m).

Step 6. End.

4 Numerical example

Facing the challenges from knowledge-based economy and global integration, to develop hi-tech industries and to enhance the comprehensive national strength are very urgent. The practices of the developed country show that venture capital at the field of supporting innovation activities and hi-tech industries has a unique and irreplaceable role. It is a “roll booster” of hi-tech industries and a “motor” of economic growth. The business venture of hi-tech industries is a dynamic technical economic process. The high risk characteristics of venture capital are induced by the economic characteristics, future development’s uncertainty and many other factors of hi-tech business venture. The exertion of venture capital financial value needs a set of effective risk management mechanism. This mechanism fetches up the shortage between the hi-tech investment operation mechanism and traditional investment operation mechanism, which are inherent in technology innovation and technical transformation. The venture capital process is a dynamic on-limits and nonlinear complicated system, with higher risk and is more complicated. Increasing the study on the risk management during the venture capital process systematically will, on the one hand, enhance the risk management level of venture capital, and help to optimize the collocation of the resources; on the other hand, help to develop and enrich risk management theory of venture capital. Based on the studies made by other people before, the venture capital process is divided to three sub processes, which are financing, investing and exiting. Therefore, in this part, we illustrate a numerical example for evaluating the efficiency of venture capital of high-science and technology companies with dual hesitant fuzzy information to describe our approach. Particularly, we give a panel using 5 high-science and technology companies A_i (i = 1, 2, ⋯, 5) to evaluate. The expert group should be given using the given 4 attributes, that is, ding172G₁ is the economic benefits; ding173G₂ is the cost efficiency; ding174G₃ is the social benefits; ding175G₄ is the ecological benefit. To alleviate the effect between each other, the decision makers should be used to estimate the five high-science and technology companies A_i (i = 1, 2, 3, 4, 5) with the given attributes in anonymity and the decision matrix $\tilde{D} = {({\tilde{d}}_{ij})}_{5 \times 4}$ is given in Table 1, where ${\tilde{d}}_{ij} (i = 1, 2, 3, 4, 5, j = 1, 2, 3, 4)$ conform to the definition of DHFEs.

Step 1. Computing the fuzzy grey relational coefficient of each alternative from TFPIS and TFNIS $ξ^{+} = {(ξ_{ij}^{+})}_{5 \times 4} = [\begin{matrix} 0 . 60580 . 43840 . 75340 . 3449 \\ 0 . 70850 . 43120 . 33330 . 3993 \\ 1 . 0000 0 . 75350 . 47140 . 8157 \\ 0 . 60941 . 00001 . 00001 . 0000 \\ 0 . 51180 . 44860 . 57780 . 8307 \end{matrix}]$ $ξ^{-} = {(ξ_{ij}^{-})}_{5 \times 4} = [\begin{matrix} 0 . 73600 . 80920 . 37301 . 0000 \\ 0 . 63700 . 78141 . 00000 . 7167 \\ 0 . 51180 . 46420 . 53000 . 3740 \\ 0 . 75560 . 40310 . 33330 . 3449 \\ 1 . 0000 0 . 73280 . 43580 . 3686 \end{matrix}]$

Step 2. Through tackling the single objective optimization model, we are able to obtain the attribute weights: ω = (0.27, 0.13, 0.38, 0.22).

Step 3. Computing the degree of fuzzy grey relational coefficient of each alternative from TFPIS and TFNIS $\begin{matrix} ξ_{1}^{+} = 0.5132, ξ_{2}^{+} = 0.4494, ξ_{3}^{+} = 0.7572 \\ ξ_{4}^{+} = 0.9219, ξ_{5}^{+} = 0.6464 \\ ξ_{1}^{-} = 0.7618, ξ_{2}^{-} = 0.7813, ξ_{3}^{-} = 0.4541 \\ ξ_{4}^{-} = 0.4329, ξ_{5}^{-} = 0.5663 \end{matrix}$

Step 4. Calculating the fuzzy relative relational degree of each alternative from TFPIS $\begin{matrix} ξ_{1} = 0.4025, ξ_{2} = 0.3652, ξ_{3} = 0.6251 \\ ξ_{4} = 0.6805, C_{5} = 0.5330 . \end{matrix}$

Step 5. Utilizing to the fuzzy relative relational degree, the ranking list of the five marine service industries is: A₄ ≻ A₃ ≻ A₅ ≻ A₁ ≻ A₂. Thus, the most desirable high-science and technology company is A₄.

5 Conclusion

As is well known that the venture capital investment is full of risks, quick development, and high returns, and it is of great importance for the development of new technology. However, to promote the venture capital investment, it is crucial to identify and estimate the risk in advance, and then do something to prevent risk. Hence, it is very interesting to inquire systematically into the risk in venture capital project. Particularly, this paper demonstrate on how to investigate the multiple attribute decision making problems for estimating the efficiency of venture capital of high-science and technology companies with dual hesitant fuzzy information and incomplete weight information. Afterwards, using the GRA approach, computing steps for tackling dual hesitant fuzzy multiple attribute decision-making problems with incomplete weight information are proposed. At last, an example of evaluating the efficiency of venture capital of high-science and technology companies using the grey relational analysis with dual hesitant fuzzy information is proposed.

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