直觉模糊数-一种新的决策工具 (20131017) 3

1、徐泽水徐泽水 解放军理工大学理学院解放军理工大学理学院 Support In a voting problemObjectionAbstentionK. Atanassov. Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 1986, 20(1): 87-96.Cited times: 3738 ,( ),( ) |AAAxxxx X ,v(,)(0.5,0.3) The intuitionistic fuzzy number has a physical interpretation, for example, ifwhich can b

2、e interpreted as “the vote for resolution is 5 in favor, 3 against, and 2 abstentions”.(,) be two intuitionistic fuzzy numbers, and are the scores and the accuracy degree of and respectively, then (1) if then (2) if then (i) if then (ii) if then (,)(1,2)iiii( )iiis( )(1,2)iiihi12( )(),ss12;12( )(),s

3、s12()(),hh12;12( )(),hh12.12E. Szmidt, J. Kacprzyk (国际模糊系统协会国际模糊系统协会(IFSA)前主前主席、席、IEEE Fellow、IFSA Fellow、波兰科学院院士、波兰科学院院士). Amount of information and its reliability in the ranking of Atanassovs intuitionistic fuzzy alternatives. in: E. Rakus-Andersson, R. R. Yager, N. Ichalkaranje, L. C. Jain, (Eds

4、.), Recent Advances in Decision Making, Berlin: Springer-Verlag, 2009, pp. 7-19.( )0.5 2 ()(1,0),iiiiRvd Let and be three intuitionistic fuzzy numbers, then All the results above are intuitionistic fuzzy numbers.(, ),v222(,)v12121212(4)(,); v v12121212(5)(,); vvv v(6)(1 (1) ,),0;v111(,)v(7)(,1 (1) )

5、,0. v(1)(,);121212(2)(min, max,);121212(3)(max, min,);Theorem. Let and be three intuitionistic fuzzy numbers, and then 222(,)v12,0, 111(,)v(,),v1121(1);1121(2);1212(3) (); 1212(4)();1212(5)() ; 1212(6).Z. S. Xu. Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 2007, 15

6、(6): 1179-1187. Cited times: . 2008年中国百篇最具影响国际学术论文奖年中国百篇最具影响国际学术论文奖; ; 2007年以来该期刊发表论文中引用率排名第一年以来该期刊发表论文中引用率排名第一; ; ESI高被引论文高被引论文. .Z. S. Xu*, R.R. Yager (IEEE Life Fellow, IFSA Fellow). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems,

7、 2006, 35(4): 417-433. Cited times: ()Z. S. Xu*, X. Q. Cai. Intuitionistic Fuzzy Information Aggregation: Theory and Applications. Springer-Verlag, Science Press, 2012. Cited times: . ( (2007年以来该期刊发年以来该期刊发表论文中引用率排名第一表论文中引用率排名第一) ) 112111(,.,)1(1) ,() iiiinnnwwniiiiifwv 112111( ,.,)() , 1(1) iiiiinnn

8、wwwniiiigvZ. S. Xu, R.R. Yager. Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optimization and Decision Making, 2009, 8(2): 123-139. Cited times: 6311211( ,.,),iinnniiiifwwv G. Beliak

9、ov, H. Bustince, D. P. Goswami, U. K. Mukherjee, N. R. Pal (印度科学院院士、工程院院印度科学院院士、工程院院士士、IEEE Fellow、IFSA Fellow、IEEE Transactions on Fuzzy Systems前主编前主编). On averaging operators for Atanassovs intuitionistic fuzzy sets. Information Sciences, 2011, 181: 1116-1124. Cited times: 6611112112211(,.,)() ,()

10、iinnniiiifhwhhwh v Z. S. Xu. An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 2005, 20(8): 843-865. Cited times: 318 (2005年以来大陆地区计算机学科领域被年以来大陆地区计算机学科领域被引次数最多的引次数最多的20篇论文之一篇论文之一( (摘自摘自Scopus)22()21( ),2x uf xex Z. S. Xu. Intuitionistic preference relat

11、ions and their application in group decision making. Information Sciences, 2007, 177 (11): 2363-2379. Cited times: 255 ( (2007年以来该期刊发表论文中引用年以来该期刊发表论文中引用率排名第七率排名第七; ; ESI高被引论文高被引论文) )111112121121212222221122(,)(,)(,)(,) (,)(,)(,) (,)(,)nnnnnnnnnnnnvvvvvvvvv1x2xnx1x2xnx. . . .Z. S. Xu, H. C. Liao. Int

12、uitionistic Fuzzy Analytic Hierarchy Process. IEEE Transactions on Fuzzy Systems, 2013, in press. Z. S. Xu, R. R. Yager. Dynamic intuitionistic fuzzy multi-attribute decision making. International Journal of Approximate Reasoning, 2008, 48(1): 246-262. Cited times: 193 ( (2008年以来该期刊发表论文中引用率排名第年以来该期刊

13、发表论文中引用率排名第一一; ; ESI高被引论文高被引论文) )Z. S. Xu. Intuitionistic fuzzy multi-attribute decision making: An interactive method. IEEE Transactions on Fuzzy Systems, 2012, 20(2): 514-525. Z. S. Xu. Intuitionistic Preference Modeling and Interactive Decision Making. Springer- Verlag, in Series:Studies in Fuzziness and Soft Computing, Heidelberg, New York, 2013. Z. S. Xu, J. Chen, J. J. Wu. Clustering algorithms for intuitionistic fuzzy sets. Information Sciences, 2008, 17