译文西 安 邮 电 学 院毕 业 设 计（论 文）题 目： 基于三角模糊数的软件项目风险评估 院 （系）： 通信与信息工程学院 专 业： 电子信息科学与技术 班 级： 电科0703班 学生姓名： 范文超 导师姓名： 兰蓉 职称： 讲师 起止时间： 2011年1月3日至2011年6月10日 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 11, NO. 1, FEBRUARY 200345Fuzzy Risk Analysis Based on Similarity Measuresof Generalized Fuzzy NumbersShi-Jay Chen and Shyi-Ming Chen, Senior Member, IEEEAbstractIn this paper, we present a new method for fuzzyrisk analysis based on similarity measures of generalized fuzzy numbers. Firstly, we present a method called the simple center of gravity method (SCGM) to calculate the center-of-gravity (COG) points of generalized fuzzy numbers. Then, we use the SCGM to propose a new method to measure the degree of similarity between generalized fuzzy numbers. The proposed similarity measure uses the SCGM to calculate the COG points of trapezoidal or triangular generalized fuzzy numbers and then to calculate the degree of similarity between generalized fuzzy numbers. We also prove some properties of the proposed similarity measure and use an example to compare the proposed method with the existing similarity measures. The proposed similarity measure can overcome the drawbacks of the existing methods. We also apply the proposed similarity measure to develop a new method to deal with fuzzy risk analysis problems. The proposed fuzzy risk analysis method is more flexible and more intelligent than the existing methods due to the fact that it considers the degrees of confidence of decisionmakers opinions.Index TermsCenter-of-gravity (COG) points, fuzzy risk anal-ysis, generalized fuzzy numbers, similarity measures.I. INTRODUCTIONHE traditional center-of-gravity (COG) method 25 isIn this paper, we also present a new method to calculate thedegree of similarity between fuzzy numbers based on COG points of fuzzy numbers. The proposed similarity measure can overcome the drawbacks of the existing methods. Based on the proposed similarity measure, we present a new method for fuzzy risk analysis based on the similarity measure of general-ized fuzzy numbers. The proposed fuzzy risk analysis method is more flexible and more intelligent than the existing methods due to the fact that it considers the degrees of confidence of decisionmakers opinions.The rest of this paper is organized as follows. In Section II, we briefly review the definitions of generalized fuzzy numbers and their arithmetic operations 3, 4, the traditional COG) method 2, 14, 21 and the existing similarity measures of fuzzy numbers 7, 17, 26. In Section III, we present an SCGM to calculate the COG points of generalized fuzzy num-bers. In Section IV, we present a new method to calculate the degrees of similarity between generalized fuzzy numbers based on the COG points of generalized fuzzy numbers. Furthermore, we also prove some properties of the proposed similarity mea-sure. We also use an example to compare the proposed similarity measure with the existing methods. In Section V, we use the pro-Tvery useful to deal with the defuzzification problems 2,posed similarity measure of generalized fuzzy numbers to deal21, 31-33 and the fuzzy ranking problems 10, 11 byusing the COG points. However, there are some drawbacks in the traditional COG method, i.e., it cannot directly calculate the COG point of a crisp interval or a real number, and it is very time-consuming to calculate the COG point. In 8, we have presented a new method, called the simple center-of-gravity method (SCGM), to calculate the COG points of fuzzy numbers based on the concepts of plane vectors and linear equations. The proposed SCGM method can overcome the drawbacks of the traditional COG method.To measure the similarity of fuzzy numbers is very important in the research topic of fuzzy decision-making 6, 16, 26 and fuzzy risk analysis 7, 19, 29. Some methods have been presented to calculate the degree of similarity between fuzzy numbers 7, 17, 26. However, there are some drawbacks in the existing similarity measures, i.e., they cannot correctly calculate the degree of similarity between two generalized fuzzy numbers in some situations.Manuscript received February 10, 2002; revised May 28, 2002 and June 27, 2002. This work was supported in part by the National Science Council, Re-public of China, under Grant NSC 90-2213-E-011-054.The authors are with the Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, Republic of China (e-mail: smchenet.ntust.edu.tw).with the fuzzy risk analysis problems. The conclusions are dis-cussed in Section VI.II. PRELIMINARIESIn this sectio