1、1Application of Set Pair Analysis to Sport Event Risk Evaluation in Chinas Commercial Horse RacingAbstract. SPA is a new methodology to describe and process system uncertainty. It is different from stochastic or fuzzy methods in reasoning and operation, and it has been applied in many areas recently
2、. Taking the commercial horse race in Guangdong Province as an example, this paper states the necessity of constructing evaluation system of commercial horse race risk and the policies and laws, management systems, economic or event risks etc it may bring about. The application of SPA in risk evalua
3、tion is presented, which includes review of risk evaluation, introduction of CD that is a key role in SPA, arithmetic and tendency grade of CDs, and a risk evaluation approach proposed. Finally a case analysis is presented to illustrate the reasonability of this approach. It is found that this appro
4、ach is very convenient to operate, while the evaluation result is more comprehensible. Key words: Commercial horse racing, Sport event risk, Set Pair Analysis (SPA), Connecting Degree (CD). 21. Set Pair Analysis Method 1.1 Basic Concepts The set pair analysis theory is a kind of theory and method wh
5、ich uses the connection degree to treat the fuzzy, random and mediate uncertain system. The core thought is that the certainty and uncertainty are as a system, and the relationship between things is comprehensively characterized from identity, discrepancy and contrariety angles. Set pair is a pair o
6、f two related sets and SPA is a method to process many kinds of uncertainty according to the connecting degree = . The two sets have three relations: identical, different, and contrary and CD is an integrated description of these relations. Definition 1: Assuming = is a set pair of two sets and . Fo
7、r some application, has total attributes and of them are mutual of and , and of them are contrary, residual = attributes are neither mutual nor opposite, then the connecting degree of . where is identical degree, is different degree, and is contrary degree. Usually, we use , and denote them, respect
8、ively, and + + =1. For an example, we defined the full score is 10 when we evaluated a design project, the highest score is 9 and the 3lowest one is 8, then we can considered this design project would at least get 8 and lost 1 (10-9). However, score between 8 and 9 is uncertain. Then we can describe
9、 the final score of this design project with =0.8+0.1 +0.1 . Definition 2: If the CD is , where , and is arbitrary positive number, , and is a uncertain number. When consists of many uncertainties, can be divided into , , and , which donate stochastic uncertainty, fuzzy uncertainty, agency uncertain
10、ty and uncertainty derived from incomplete information, etc. then the CD is 1.2 Addition between CDs Sum of n CDs is equal to the product of n and the average CD of n CDs, namely 1.3 Subtraction between CDs While subtract a CD from the addition of n CDs, the arithmetic is 1.4 Multiplication between
11、CDs Multiplication between CDs adopts the method which simplifying firstly, then implementing operation, and recovering the result finally. For an example, =0.5+0.3 +0.2 , =0.3+0.5 +0.2 , we want the product of and . Firstly, we simplified , to (0.5+0.3 ) and (0.3+0.5 ) respectively, then 4the CD =(
12、0.5+0.3 )(0.3+0.5 )=0.15+0.34 +0.15 . For is uncertain, the square of is also uncertain. Then the product of and can be simplified to =0.15+0.49 . Finally, we recover the result above, c= 0.15 =0.36, so = 0.15+0.49 +0.36 . 1.5 Division between CDs While dividing the product of n CDs by a CD, we also
13、 adopt the method which simplifying firstly, then implementing operation, and recovering the result finally. The division of 2 CDs is Then, we can acquire the unknown coefficient according to the rule of coefficient equality. 1.5 Set pair tendency Set pair tendency analysis is a system analysis appr
14、oach to rank the CDs based on a, b and c of each CD. In the expression of CD, a and c are deterministic and b is uncertain, a, b and c are non-negative and satisfy the unitary condition, namely, a+b+c=1. By comparing a, b and c of each CD, we can get the set pair tendency, as shown Table 1. Table 1
15、Relations of set pair tendency and a, b, c 2. Sport event risk evaluation in Chinas commercial horse racing 5Table 2 shows evaluation information for risk management in a project of commercial horse racing in Guangdong Province, there are total 7 kinds of risks to be evaluated. Table 2 Comprehensive
16、 evaluation table of sport event risk of commercial horse racing References 1T. Richard and M.A. Mukhtar, Intertrack wagering and the demand for parimutuel horse racing, Journal of Economics and Business, vol.47, pp.369-383, 1995. 2M.R. Su, Z.F. Yang, B. Chen and S. Ulgiati, Urban ecosystem health a
17、ssessment based on emergy and set pair analysisA comparative study of typical Chinese cities, Ecological Modelling, vol.220, pp.2341-2348, 2009. 3M.R. Su, Z.F. Yang and B. Chen, Set pair analysis for urban ecosystem health assessment, Communications in Nonlinear Science and Numerical Simulation, vol
18、.14, pp.1773-1780, 2009. 4Y. Liu, Study on Environment Evaluation and Protection Based on Set Pair AnalysisA Case Study of Chongqing, Energy Procedia, vol.14, pp.14-19, 2012. 5F. Xu, X.P. Zheng, J. Zhang, Z.T. Fu and X.S. Zhang, A hybrid reasoning mechanism integrated evidence theory and set pair analysis in Swine-Vet, Expert Systems with Applications, 6vol.37, pp.7086-7093, 2010.
