The Study on Venture Investment Evaluation Based on Linguistic Variables for Chinese Case

The venture investment evaluation plays a very important role in the venture investment operation process. The goal of the paper is development of evaluation index systems and evaluation methods for venture investment. Firstly, the evaluation index systems of venture investment project are constructed in accordance with China's practical situation. Then evaluation models have been presented. In the models, operational laws of linguistic variables and distance of two linguistic variables are defined; and a single objective optimization model is constructed by maximizing deviation method to get the objective weights of indexes, and alternatives are ranked by TOPSIS and grey relation methods respectively. Finally, a numerical example is given to illustrate the evaluation procedures of two approaches. The case shows that two different approaches get the same result, but TOPSIS is simpler apparently.


Introduction
The venture investment evaluation plays a very important role in the venture investment operation process which can have direct infl uence on the venture investment's success or failure. At present, a large number of studies have been carried on the choice of venture investment projects. All of the studies can be divided into two aspects: the research of evaluation index system and the research of evaluation approaches.
Venture capital (VC) researchers frequently address questions of venture capitalists' investment behavior, along with due diligence and its related issues, by focusing on venture capitalists' investment criteria. Tyebjee and Bruno (1984) got 23 factors which should be considered by the venture investment company during their track interview with 90 venture investment organizations, and they divided them into four parts: the market, the product differences, the management capacity and the resisting strength to environmental threat. The seminal study by MacMillan et al. (1985) proposes that fi ve of the 10 most important decision criteria are related to the personality or experience of the entrepreneurs. Muzyka et al. (1996) provide some evidence that European venture capitalists, especially, attach importance to management team criteria rather than the characteristics of the lone entrepreneur. According to these authors, product and market criteria are only of average importance, while criteria of the fund and the respective terms of a deal's structure are of minor importance. Zustshi et al. (1999) investigated 31 of Singapore's 58 risk entities; the results however reveal that criteria adopted by Singapore VCs are not very different from those adopted by VCs in other countries including U.S. The results also confi rm that the entrepreneur's characteristics or the top management's capabilities are seen as being primary indicators of the venture's potential. Further examination of VCs investment process revealed that the investment criteria adopted by successful VCs were no different from those adopted by less successful VCs. This confi rms that investment selection is a multi-stage process wherein venture assessment is only one of the steps in this process. Tang (2002) proposed an evaluation index system which can be used by all investment companies. This evaluation index system could be summarized as the following three aspects: the characteristics of risk entrepreneurs, venture enterprises' own characteristics and the market environment, for a total of 28 indicators. Zhao (2007) constructed the index systems for venture investment evaluation, included one-level indicators of Management, Market, Product and technology and Financial characteristics, and 20 two-level indicators. Shi (2005) embarks the form evaluating anticipated income and risk, constructs the appraisal target system that contains seven core targets, which are entrepreneur, management, product and technology, marketing, fi nance, society effects and withdrawal of venture capital, and forty-seven concrete targets. Kollmann and Kuckertz (2010) analyzed the decision process of venture capitalists and focused on aligning the evaluation uncertainty in the decision criteria of venture capitalists with the progress of the process, and concentrated on 15 important investment criteria (Table 1) based on the relevant literature. Despite the reduced number of criteria, this is a catalogue that a venture capitalist would most likely perceive as largely complete. However, these evaluation criteria did not consider the situation in China. Jiang and Ruan (2010) constructed the risk assessment index for high-tech projects which considered each side of project risks and at the same time classify the risks in accordance with a certain standard. Combined with China's national conditions and domestic high-tech industries, the investment risks of high-tech projects can be divided into six aspects: R&D risks, technology risks, production risks, management risks, market risks and environmental risks. Hu (2009) established the venture investment project evaluation indexes system, including risk assessment (it had the indicators of technology risk, market risk, management risk, exit risk and environmental risk) and effectiveness evaluation (it had the indicators of product effi ciency, market effi ciency, and corporate capacity, economic and social benefi t).
As for the evaluation methods, Hu (2009) proposed the approach based on coeffi cient of variation to get the weight of indicators and to assess the risk and effectiveness of venture capital investment projects synthetically in detail in China. Li and Wei (2009) proposed the intuitionistic fuzzy weighted average (IFWA) operator and the intuitionistic fuzzy hybrid average (IFHA) operator based on intuitionistic fuzzy set to assess the venture investment. Jiang and Ruan (2010) combined Analytic Hierarchy Process (AHP) with BP Neural Network to establish a new and suitable risk assessment model of hightech projects. Firstly, they applied AHP to construct a comprehensive risk assessment index system and screened the assessment indexes according to their weights. Then, using MATLAB software with BP Neural Network model to simulate and analyze the example. The results showed that the combination model of Analytic Hierarchy Process with BP Neural Network model (AHP-BPNN) is effective. Guo (2010) made an analysis on the fi nancial yield of risk investment in engineering projects from the perspectives of sameness, difference and reverse based on Set Pair Theory. Combining the Set Pair Theory with the penalty-incentive mechanism of target weight, it forms a model profi t varying weight of the risk investing project and takes maximum connection as a principle to judge the profi ts of the project. Jia and Zhao (2009) proposed a comprehensive evaluation method for determining the evaluation indexes weight based on entropy coeffi cient and established a comprehensive evaluation model of multi-objective decisionmaking, and then they carried on a reasonable and effective evaluation for the venture capital management. Ke et al. (2010) proposed an improved model to evaluate the risk in real estate investment. This model fi rst avoided the information overlap caused by the  et al. (1985), Robinson (1987) Commitment Dixon (1991), Muzyka et al. (1996) Experience of the entrepreneur Track record Flynn (1991) Technical qualifi cation Shepherd (1999), Franke et al. (2006) Business qualifi cation Shepherd (1999), Franke et al. (2006) Product or service Innovativeness MacMillan et al. (1985), Mason and Stark (2004) Patentability Tyebjee and Bruno (1984), MacMillan et al. (1985) Unique selling proposition Mason and Stark (2004) Market characteristics Market volume Tyebjee and Bruno (1984), Mason and Stark (2004) Market growth Tyebjee and Bruno (1984), Mason and Stark (2004) Market acceptance Tyebjee and Bruno (1984), Mason and Stark (2004) Financial characteristics Fit to investment strategy Muzyka et al. (1996), Mason and Stark (2004) Return on investment Tyebjee and Bruno (1984), MacMillan et al. (1985) Exit possibilities Muzyka et al. (1996), Mason and Stark (2004) fuzziness and complexity of the indices and by the orthogonal transformation. It also adopted entropy method to reduce the subjectivity during the evaluating process. Fang and  proposed a risk control method which combined the Fuzzy evaluation model and the AHP model with respect to the investment evaluation indicators' characteristics of fuzzy and diffi cult to control; Su (2005) used the principal component analysis method to evaluate the risk investment projects; Zhang and Yang (2006) proposed a venture investment project risk evaluation index system from the aspects of production risk, market risk, technical risk, management risk, fi nancial risks and natural risk, and on this basis they gave a multi-level gray evaluation method which used the theory of gray system and combined with examples for risk investment projects. Wang (2006) proposed a venture investment comprehensive evaluation mathematical mode by use of pair analysis theory. Kuang and Chen (2006) studied the investment risks in real estate by use of improved genetic algorithm. Fu and Huang (2002) proposed integrated evaluation methods for risk investment projects on the base of KENDALL -W test and multi-attribute utility function (MAUF) theory. Ginevicius and Zubrecovas (2009) developed the model of real estate projects' effi ciency evaluation. The proposed model is designed for alternative projects, variants selection, investment resources allocation as well as real estate value maintenance and enhancement problems solution. The model of real estate projects' effi ciency evaluation covers all the investment decision-making cycle, the hierarchically-structured projects' evaluation criteria system, risk evaluation basing on stochastic dimensions as well as the mathematical methods adaptation for multiple criteria evaluation problems solution, risk assessment and adjusted mathematical methods. Hui, Lau and Lo (2009) proposed two fuzzy mathematical programming models to incorporate expert knowledge into the classical quadratic programming approach, i.e. Modern Portfolio Theory (MPT), through fuzzy set theory, in obtaining portfolio return optimization involving direct real estate investment. Kahraman and Kaya (2010) proposed two types of investment analyses. First, fuzzy parameters are used in the stochastic investment analysis. Then, another investment analysis is examined by using the concept of probability of a fuzzy event. Rutkauskas et al. (2008) proposed the conception of sustainable return investment decisions strategy in capital and money markets and modeling of investment decisions along sustainable development concept in capital and money markets.
In summary, there is not a widespread consensus on selection of the venture investment's evaluation index now, and the evaluation indexes constructed are also different. So this paper will establish a relatively scientifi c and sound risk evaluation index system from the perspective of selected investment projects for venture capital fi rms. In the evaluation method, considered that the risk evaluation indexes are mostly the qualitative indexes, this paper will mainly use the linguistic evaluation method to overcome the disadvantage of the evaluation methods mentioned above, which mainly depend on qualitative data. Moreover, considered that the indicators' weight is also very diffi cult to determine beforehand, the principle of deviation maximization will be used to determine the objective weight by establishing a single-objective optimization model, and the TOPSIS method and the grey relational method will be used to rank the alternatives. In order to achieve these tasks, the remainder of this paper is structured as follows. In Section 2, the index system of venture investment evaluation is established by investigation of the venture capital fi rms. In Section 3, the evaluation methods for venture investment evaluation based on linguistic variables are proposed, including a single-objective optimization model for getting the objective weights of indexes, which will be constructed by maximizing deviation method, and TOPSIS and grey relation method which are used to rank the alternatives respectively. In Section 4, an application example of venture investment evaluation is given by the proposed methods, and some conclusions are pointed out in Section 5.

Index System Establishment
Establishing an index system for venture investment evaluation directly affects the investment projects and success or failure of investment projects. So the prerequisite of venture investment evaluation is determining the scientifi c and sound venture evaluation indexes. On the foundation of the following principles as systematization, hierarchy, comprehensiveness, economy, comparability, operability, practicability and precedence, this paper establishes the index system as follows according to the proposals of 12 venture investment enterprises (shown in Table 2).

Evaluation index explanation
(1) The index of affecting investment venture Management venture: This venture means that the possibility is causing investment success or failure because of ill management.The management usually concerns about scientifi c research and development management, production management, marketing management, personnel management. It mainly includes enterprise management deci-sion level, the scientifi c applicability of organization institution and structure, personnel management and performance evaluation, production management venture, the capacity of enterprise marketing and so on. Technology venture: This venture means that the uncertainty of causing investment success or failure is because of the uncertainty of product and technology. It mainly includes intellectual property rights, technological advance, technological reliability, technological substitution, the degree of preventing technological imitation, the compatibility between technology and policy and industry standard and so on. Market venture: This venture means that the uncertainty of causing investment success or failure is because of the uncertainty of promoting product and technology in the markets. It mainly includes market stability, the diffi culty of market development, market acceptance capacity, market service capacity, competitor status, and the tendency of policy change and so on. Finance venture: This venture means that the uncertainty of causing investment success or failure is because of the uncertainty of enterprise fi nancing operation. It mainly includes the standardization of fi nance institution and the authenticity of fi nance information, the smooth of fi nancing channels, the rationality of investment plan and so on. Exit venture: This venture means that the uncertainty of causing investment success or failure is because of the uncertainty of venture investment exiting. It mainly includes the status of exit channel, possible exit time, and possible exit ways (as public offering, merger and purchase, venture enterprise repurchase, bankrupt liquidation) and so on.
(2) The index of affecting investment revenue Entrepreneur quality: At present, most positive analysis proves that venture investors pay the most attention to the qualities and abilities of venture entrepreneurs when they choose projects. Before venture investors invest in venture enterprises, they focus on the evaluation of venture entrepreneurs' character, on the qualities and abilities of venture entrepreneurs in order to make an investment decision through researching the infl uences these abilities exert on the future development of venture enterprises. Entrepreneur qualities mainly include entrepreneurs' personal qualities, entrepreneurs' knowledge qualities, entrepreneurs' abilities of integrating resources, entrepreneurs' abilities of meeting an emergency and forecasting ventures, entrepreneurs' prior achievement and so on. Enterprise management level: Effective management can reduce, even defuse the invest venture. So venture invest enterprises almost regard management as an important evaluation index of venture invest projects without exception. Concretely, they mainly evaluate these projects from several aspects as follows: enterprises' strategic planning, the qualities and abilities of management teams, enterprises' business culture and ideas, enterprises' organization structure, enterprises' job responsibilities and C&B, enterprises' personnel reserve, enterprises' information level and inner communication status and so on. Product and technology specifi city: Venture investors' interest on advanced and adaptive product and technology. Their most basic goal is to make use of the technology to satisfy present and potential requirement and acquire rich invest return fi nally. So there is certain request for the product and technology of venture enterprises when evaluating projects and the product and technology should have comparative advantage. It mainly includes technology patent level, product practicability, product adaptability, unique characteristic of product and so on. Enterprise profi t capacity: Enterprise profi t capacity affects directly the return ability of enterprise. It is indispensable indexes when the venture investors invest and it has a decisive infl uence on invest decision. The aspects of examining the enterprise profi t capacity mainly include enterprise revenue level and growth potential of revenue. When the enterprise revenue level is higher, venture investors are more likely to invest. The index of evaluating revenue level mainly include sale net profi t, asset payment rate, rights and interest of shareholder payment rate and so on; Growth potential of revenue refl ects the development prospect of enterprises. It is the core guarantee that venture invest can acquire high return. So when growth potential of revenue is higher, venture investors are more likely to invest. The index of evaluating growth potential of revenue mainly includes sale growth rate, profi t growth rate and so on. Market environment: Due to venture enterprises facing the future market, market evaluation of venture invest projects focuses on the development trend of market (that is, market current). It mainly includes the industry of venture enterprise, market scale, market growth, technical barrier and lead time, market competition status and so on. Policy environment: The operation of venture enterprises needs certain policy support. The evaluation of policy environment is also an important index when venture investors consider investing. It mainly includes the relative degree with the development direction of government industry, the relation with government correlation institution, tax incentive method and so on.

Description of the Decision Problems
Suppose that there are m evaluation objects A = (a 1 , a 2 , ..., a m ); n evaluation index C = (c 1 , c 2 , ..., c n ); the evaluation index value of each object composes a matrix T = [t ij ] m×n , t ij is the j-th index evaluation value of the i-th evaluation object, t ij is an element of an linguistic (or linguistic symbol) evaluation set S which is predefi ned. Here, linguistic evaluation set S is an ordered set which is composed of odd elements. For example, linguistic evaluation set S = (very poor, poor, slightly poor, middle, slightly good, good, very good) which is composed of 5 elements. This decision problem is: Aiming at linguistic decision matrix T = [t ij ] m×n given by each decision maker to solve index weight W and get the rank result of the project fi nally through certain decision analysis method.

Linguistic Evaluation Set and its Extension
Linguistic evaluation set S = (s 0 , s 1 , ..., s l-1 ) should be composed of odd elements (that is, l should be an odd number). In actual application, the value of l is as of 3,5,7,9. This paper uses l = 7, so S can be represented as follows: S = (s 0 , s 1 , s 2 , s 3 , s 4 , s 5 , s 6 ) = (very poor, poor, slightly poor, middle, slightly good, good, very good).
For linguistic set S, it should satisfy the following conditions: (1) if i > j, then s i  s j (that is, s i superior to s j ); (2) negative operator neg(s i ) = s j to make j = l -i; (3) if s i ≥ s j (that is, s i is not inferior to s j ) then max(s i , s j ) = s i ; (4) if s i ≤ s j (that is, s i is not superior to s j ) then min(s i , s j ) = s i .
For linguistic scale S = (s 0 , s 1 , ..., s l-1 ), there exists strict monotonic increasing relation between element s i and its subscript i (Herrera et al. 1996). So it can defi ne function f : s i = f (i), obviously, f (i) is the monotonic increasing function to subscript i. In order to prevent loss of linguistic decision information, original discrete linguistic scale S = (s 0 , s 1 , ..., s l-1 ) should be expanded to continuous linguistic scale s = {s  |  R} and the continuous linguistic scale still satisfi es the upper strict monotonic increasing relation.
The operational rules about linguistic variables refer to Wei et al.(2006).
Defi nition 1 (Wei et al. 2006): suppose s  , s β are two linguistic variables, then the distance between s α and s β can be defi ned as follows:

Using maximum deviation method to determine the index weight W
The uncertainty of attribute weight can cause the uncertainty of decision project ranking, so maximum deviation method is used to make the weight more accurate. Generally, the smaller the difference between the value t ij ( j = 1, 2, ..., n) of attribute c j in all decision project, the less important the function which the attribute weight exerts on project decision; conversely, the bigger the difference among the value t ij ( j = 1, 2, ..., n) of attribute c j in all decision project, the more important the function which the attribute weight exerts on project decision. So, from the aspect of ranking the decision projects or choosing the best one, the bigger the deviation between attribute values of all projects, the bigger the weight which should be assigned; the smaller the deviation between attribute values of all projects, the smaller the weight which should be assigned.
represents total deviation between a project and all the other projects, represents the total deviation of all indices in all projects.
Constructing the following Maximum Deviation model: Solving the model, the following expression is obtained: .
After being normalized, the w j can be obtained: (4)

Using TOPSIS to Determine Project Ranking
(1) Determining PIS and NIS PIS (Positive Ideal Solution) is the best project of a project set A i (i = 1, 2, ..., m), each attribute value is the corresponding best value of decision matrix; NIS(Negative Ideal Solution) is the worst project of a project set A i (i = 1, 2, ..., m), each attribute value is the corresponding worst value of decision matrix.
( 1, 2, , ) According to the size of relative closeness degree, evaluation projects can be ranked. The bigger the relative closeness degree is, the better the project is. So the most suitable project can be obtained.

Gray Correlation TOPSIS Evaluation Method
(1) Calculating the gray correlation coeffi cient between the i-th project and the ideal project for the j-th index: Here,   ij is the distance between  j v and t ij , distinguishing coeffi cient (Generally assigned the value 0.5). Thus gray correlation coeffi cient matrix between each project and positive ideal project is as follows: Gray correlation degree between the i-th project and positive ideal project is as follows: (3) Calculating the gray correlation relative closeness degree of each project: According to the size of relative closeness degree, evaluation projects can be ranked. The bigger the gray correlation relative closeness degree is, the better the project is. So, the most suitable project can be obtained.

Application Examples
A venture capitalist has 4 invest projects; experts evaluate each project according to 11 indices which are shown in Table 2. Evaluation linguistic set S = (s 0 , s 1 , s 2 , s 3 , s 4 , s 5 , s 6 ) = (very poor, poor, slightly poor, middle, slightly good, good, very good). The attribute values of each index in each project are shown in Table 3.The weight of each index is unknown. Then rank the projects to choose the best project. (3) Determining relative closeness degree   ûûû=ûûû=ûûû=ûûû  C So, the ranking of the 4 projects is: a a a a    .

Making use of gray correlation TOPSIS to rank the projects
(1) Solving the correlation coeffi cient and weighting correlation degree with the positive ideal solution According to formula (10), we fi rstly calculate (3) Calculating gray correlation relative closeness degree as follows: So, the ranking of the 4 projects is: a a a a    .

Conclusions
The magnitude of venture in venture investment is the important considered factor of venture investment decision, and it directly affects the success or failure of venture invest. Investment evaluation indices are mainly qualitative indices, so this paper adopts linguistic variables to evaluate each index and construct single object optimization model based on maximum deviation principle to solve the objective weight of index; then this paper adopts TOPSIS method and gray correlation method to rank the projects. From the aspect of ranking result, the two methods are consistent. The application of the case indicates that the two methods have same ranking infl uence. But TOPSIS method is easier to calculate obviously.