An Evaluation Method Based on Cloud Model for the Credit of High-tech SMEs Guo-qiang Zhou1, Xue-qing Wang1, Rui Liu2, Li-guo Sun3 2 1 College of Management and Economics, Tianjin University, Tianjin, P. R. China Nuclear and Radiation Safety Center, Ministry of Environmental Protection, Beijing, P. R. China 3 China Bohai Bank, Tianjin, P. R. China (steven661@tju.edu.cn) Abstract – In the process of resolving financing difficulties of high-tech small and medium enterprises (SMEs) in China, the evaluation of credit risk of high-tech SMEs becomes a very challenging problem for the bank. This paper proposes a novel evaluation method based on cloud model to measure the credit risk of Chinese listed high-tech SMEs. Finally, an example is provided for illustrative purpose, and the indexes system of credit evaluation is established of 25 key factors, embedded within five broad categories- credit quality, organizational level, operation level, R&D level and network position. This research shows that it is a better way to use this method to realize transforming qualitative terms described in a natural language to distribution patterns of quantitative values, especially for high-tech SMEs. Keywords – Cloud model, credit evaluation, credit risk, credit scoring, high-tech SMEs I. INTRODUCTION In recent years, the credit of high-tech small and medium enterprises (SMEs) has been gaining much more importance according to their high growth in financial world [1]. However, the credit guarantee risk is very high in SMEs due to their particular characteristics, which lead to a low credit scoring in general [2], [3]. The evaluation of credit risk of high-tech SMEs becomes a very challenging problem for the bank. Therefore, it is essential to develop an accurate credit scoring model for high-tech SMEs for the efficient management of bank. Most well-known evaluation models use probability or fuzzy set theory to hold randomness or fuzziness respectively, such as the decision trees [4], artificial neural networks [5], genetic algorithm [6], etc. Among all of these methods, only cloud model based models consider both aspects of uncertainty. Cloud model is the innovation and development of membership function in fuzzy theory [7], which transforms qualitative terms described in a natural language to distribution patterns of quantitative values [8]. It is successfully used in spatial analysis [9], target recognition [10], intelligent algorithm improvement [11] and so on. Therefore, in this paper, we propose an evaluation method based on cloud model for the credit of high-tech SMEs. As credit evaluation is a typical multi-attribute evaluation problem, it is more significant in applying this novel approach to credit evaluation so as to demonstrate its usefulness. II. METHODOLOGY A. Basic concepts of cloud model Suppose that r is the language value of domain U , and mapping Cr ( x) : U [0,1] , x X ( X U ) , x Cr ( x) , then the distribution of Cr ( x) in U is called the membership cloud of r , or cloud in short, and each projection is called a cloud drop in the distribution. If the distribution of Cr ( x) is normal, it is named normal cloud model. B. Numerical characteristics of the cloud model The normal cloud model is determined by the following three parameters: expectation Ex , entropy En , and hyper entropy He . Expectation Ex represents the values that mostly stand for this qualitative concept, generally it is the value x that corresponds to the gravity center of the cloud, it should belongs to this qualitative concept hundred percent. Entropy En is the measurement of the qualitative concept fuzzy degree, it determines the range of the cloud and about 99.74% cloud drops fall within the range between [ Ex 3 En, Ex 3 En ] , and it reflects the numerical value range acceptable by concept and represents the margin with double-sided property. Hyper entropy He is the entropy of entropy, it reflects the dispersion degree of the entropy of concept [12]. A cloud model can be denoted with vector C ( Ex, En, He) . The numerical characteristics of the cloud Model are shown in Fig. 1. Fig. 1. Numerical characteristics of the cloud model C. Normal cloud model Let U be a quantitative universal set and r be the x U , which is a random realization of the concept r , and x satisfies x N ( Ex, En ' 2 ) , where En ' N ( En, He 2 ) , and the certainty degree of x on r is qualitative concept related to U. If e ( x Ex )2 2( En' )2 (1) Then the distribution of x on U is a normal cloud [13], and every x is defined as a cloud drop. Given the three parameters Ex , En , He , the normal cloud model can be generated [14]. Input: Ex , En , He , and the number of the cloud drops n . Output: n of cloud drops x and their degree . Step 1. Generate a normally distributed random 2 ' number Eni with expectation En and variance He , i.e., ' Eni NORM ( En, He ) . 2 Step 2. Generate a normally distributed random number xi with expectation Ex and variance Eni' 2 , i.e., xi NORM ( Ex, Eni' 2 ) . Step 3. Calculate i e Step 4. ( xi Ex )2 En (2) xi with certainty degree of i becomes one n cloud drops are D. Cloud model-based credit evaluation algorithm In the evaluation method based on cloud model, gravity center of cloud can be denoted as: T ab (3) In the type, a means the position of gravity center of cloud, depicting with the expectation value Ex , then if the expectation value Ex changes, the position of gravity center of cloud also corresponds of change; b means the height of gravity center of cloud, depicting with the heavy value of power, which takes often value (0.371). Therefore, the variety that passes gravity center of cloud can reflect the variety of system information status, the concrete step of the evaluation method based on cloud model is as follows: Step1: Confirming index system and index power weight. Step2: Denoting the cloud model of each index. Denotation of accurate-number type and languagedescription type are different in cloud model. Withdraw a set of sample n to constitute to make policy matrix, so , Exn ) min( Ex1 , Ex2 , max( Ex1 , Ex2 , , Exn ) (5) 6 And the index of language-description type can be denoted as follow: Ex En Ex2 En2 Exn Enn Ex 1 1 (6) En1 En2 Enn En En1 En2 Enn (7) Step3: Denoting status of the system. n indexes can be depicted with n cloud models, therefore the evaluation system containing n indexes can be denoted with dimension comprehensive cloud, n T (T1 , T2 , , Tn ) , Ti ai bi (i 1, 2, n) , and when the status of evaluation system occurrences variety, the gravity center changes to T (T1 , T2 , ' ' ' ' , Tn ) . Step4: Measuring the variety of cloud gravity center based on power-added deviation degree. Suppose that each index of the ideal status of a system is given, then the vector of cloud gravity center can be depicted as T a b (T1 , T2 , , a ( Ex10 , Ex2 0 , , Exn 0 ) , b (b1 , b2 , , bn ) , bi wi 0.371 , and the normal status of vector of n dimension comprehensive cloud gravity 0 2 Eni'2 cloud drop in the domain. Step 5. Repeat Steps 1 to 4 until generated. the index of accurate-number type can be denoted as follow: Ex Ex2 Exn Ex 1 (4) n T 0 0 0 Tn ) center is denoted as T (T1 , T2 , , Tn ) . Generally power-added deviation degree can be used to measure the variety of cloud gravity center between ideal status and normal status. The vector of n dimension comprehensive cloud gravity under normal status is normalized to T (T1 , T2 , G G G G , Tn ) , among them, (Ti Ti 0 ) / Ti 0 , Ti Ti 0 Ti (i 1, 2, , n) (8) 0 0 (Ti Ti ) / Ti , Ti Ti G Therefore, power-added deviation degree (0 1) is denoted as: n ( wT ) i i G (9) i 1 Under the ideal status, 0 . Step5: Confirming the evaluation set based on cloud model. Generally, the more numbers of evaluation scales, the more accurate of the evaluation results. According to the feature of high-tech SMEs, five-scale evaluation set is adopted (see Fig. 2): V (v1 , v2 , v3 , v4 , v5 ) (bad (C ), general ( B), good ( A), verygood ( AA), best ( AAA)) Select 10 high-tech SMEs in the second-board Market in China as test sample set S Si i 1, 2, ,10 , including electronics information, medical apparatus, biological pharmacy, etc. Finance data comes from database in CSMAR Solution [15], and other qualitative indexes are descripted by the expert evaluation languish. Take company S1 (NO. 300002) in the test sample set as example, the status of each credit evaluation index are shown in Table Ⅰ, Table Ⅱ, Table Ⅲ, Table Ⅳ and Table Ⅴ. TABLE Ⅰ Fig. 2. Five-scale evaluation set based on cloud model Status of credit quality U 1 Status U 11 1 37920 33470815 general good 2 37920 33470815 general good 3 37920 33470815 good good 4 37920 252764848 good very good Ideal 100000 300000000 best best III. Application example A. Confirming index system and sample data The index system of credit evaluation of high-tech SMEs includes total 25 indexes, 5 major type as follows: U12 U13 U14 credit quality U1 -register capital U 11 , history credit condition U12 , equipment level U13 and guarantee U14 ; Organizational level U 2 -business strategy U 21 , TABLE Ⅱ organization system U 22 , stability of management team U 23 , stability of R&D team U 24 , business proposal U 25 ; Operation level U 3 - turnover ratio of accounts receivable U 31 , turnover ratio of total assets U 32 , return on total assets ratio U 33 , operating profit ratio U 34 , income growth ratio U 35 , profit growth ratio U 36 , liquidity ratio U 37 , debt asset ratio U 38 , after-sales service U 39 ; R&D level U 4 - R&D input U 41 , intellectual property rights U 42 , R&D character U 43 ; Network position U 5 -market share U 51 , public relations U 52 , industry trend U 53 , geography position U 54 . Status of organizational level U 2 Status U 21 U 22 U 23 U 24 U 25 1 1.701 good very good good good 2 1.789 good good good good 3 1.660 general good good good 4 1.912 good very good general very good Ideal 2.000 best best best best TABLE Ⅲ Status of operation level U 3 Status U 31 U 32 U 33 U 34 U 35 U 36 U 37 U 38 U 39 1 2.450 0.307 0.121 0.420 0.545 0.266 12.400 0.069 good 2 0.436 0.073 0.028 0.378 -0.267 -0.245 11.178 0.068 general 3 0.776 0.188 0.075 0.407 0.613 0.816 11.305 0.067 good 4 1.563 0.255 0.091 0.358 -0.277 -0.577 6.884 0.095 good Ideal 1.000 0.100 0.030 0.500 0.200 0.100 10.000 0.050 best TABLE Ⅳ Status of R&D level U 4 U 41 U 42 U 43 1 19435331 66500 general 2 29018320 76110 bad 3 38857798 1076920 bad Status 4 12724180 49268370 bad Ideal 50000000 50000000 best A2 2.450 0.436 0.776 1.563 A 3 TABLE Ⅴ Status of network position U 5 U 51 U 52 U 53 U 54 1 general very good very good best 2 general good best best 3 bad very good very good best 4 general good very good best best best best best Status Ideal 1.701 1.789 1.660 1.912 A4 0.50 0.75 0.50 0.50 0.50 0.50 0.25 0.50 0.50 0.50 0.75 0.25 0.50 0.50 0.75 0.50 0.50 0.50 0.307 0.121 0.420 0.545 0.266 12.400 0.069 0.50 0.073 0.028 0.378 0.267 0.245 11.178 0.068 0.25 0.188 0.075 0.407 0.613 0.816 11.305 0.067 0.255 0.091 0.358 0.277 0.577 6.884 0.095 0.25 0.25 0 0.25 19435331 29018320 38857798 12724180 66500 0.25 76110 0 1076920 0 49268370 0 A5 0.75 0.75 0.50 1 0.75 0.75 0.50 0.75 1 1 1 1 Expectation Ex and entropy En of each index cloud model are calculated by the above policy matrixes (see Table Ⅵ, Table Ⅶ, Table Ⅷ, Table Ⅸ and Table Ⅹ). TABLE Ⅵ Expectation Ex and entropy En of credit quality U 1 B. Denoting the cloud model of each index Parameter U 11 Ex 37920 En 0 Normalize the evaluation languish set (bad, general, good, very good, best) to (0, 0.25, 0.50, 0.75, 1), and thus the policy matrix A1 - A5 is constituted as follow: 37920 37920 37920 37920 A1 0.25 0.50 33470815 0.25 0.50 33470815 0.50 252764848 0.50 U13 U14 88294323.3 0.375 0.563 36549005.5 0.042 0.042 TABLE Ⅶ 0.50 0.75 33470815 U12 Expectation Ex and entropy En of organizational level U 2 Parameter U 21 U 22 U 23 U 24 U 25 Ex 1.766 0.438 0.625 0.438 0.563 En 0.042 0.042 0.042 0.042 0.042 TABLE Ⅷ Expectation Ex and entropy En of operation level U 3 Parameter U 31 U 32 U 33 U 34 U 35 U 36 U 37 U 38 U 39 Ex 1.306 0.206 0.079 0.391 0.154 0.065 10.442 0.075 0.438 En 0.336 0.039 0.016 0.010 0.148 0.232 0.919 0.005 0.042 TABLE Ⅸ TABLE Ⅹ Expectation Ex and entropy En of R&D level U 4 Expectation Ex and entropy En network position U 5 U 41 U 42 U 43 Parameter U 51 U 52 U 53 U 54 Ex 25008907.25 12621975 0.063 Ex 0.188 0.625 0.813 1 En 4355603 8200311.667 0.042 En 0.042 0.042 0.042 0 Parameter C. Confirming the power weight of indexes ACKNOWLEDGMENT The power weights of indexes are shown in Table Ⅺ. TABLE Ⅺ The power weights of indexes wi wi 1 wi 2 wi 3 wi 4 wi 5 wi 6 wi 7 wi 8 wi 9 0.36 0.58 0.14 0.07 0.21 - - - - - 0.16 0.11 0.19 0.19 0.19 0.33 - - - - 0.23 0.17 0.17 0.07 0.07 0.09 0.09 0.12 0.12 0.11 0.13 0.25 0.59 0.17 - - - - - - 0.12 0.56 0.11 0.26 0.07 - - - - - This work was partially supported by the National Natural Science Foundation of China (Grants No. 71172148) and Soft Science Research Projects of the Ministry of Housing and Urban-Rural Construction (Grants No. 2011-R3-18). The authors are also grateful to the referees for their helpful comments and valuable suggestions for improving the earlier version of the paper. REFERENCES D. Result and analysis Through cloud model computation, the credit evaluation value of high-tech SMEs: 5 PS ( wi PU ) 0.487 1 i 1 i Then the credit evaluation value is input into the fivescale evaluation set based on cloud model (see Fig. 3). It will activate two cloud objects: A and B, but the activation degree of A is far larger than B, so the credit evaluation of company S1 (NO. 300002) obtains A. Fig. 3. Result of credit evaluation of company S 1 IV. Conclusion In this paper, credit evaluation applications in hightech SMEs are discussed, and an evaluation method based on cloud model is formulated. The application of this model is also illustrated. After this research, we find that it is a better way to use this method to realize transforming qualitative terms described in a natural language to distribution patterns of quantitative values, especially for high-tech SMEs. 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