直觉模糊数-一种新的决策工具 (2013.10.17) 3

徐泽水. 区间直觉模糊信息的集成方法及其在决
策中的应用. 控制与决策, 2007, 22(2): 215219. Cited times: 354. (2007年以来该期刊发
表论文中引用率排名第一)
Z. S. Xu*, X. Q. Cai. Intuitionistic Fuzzy Information Aggregation: Theory and Applications. Springer-Verlag, Science Press, 2012.
n wi
g1 (1,2 ,...,n ) i
i 1
n
wi
wi wi ( i ) , 1 (1 vi ) i 1 i 1
n n
Z. 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: 63
f1 (1,2 ,...,n ) wi i , wi vi i 1 i 1
n n
G. Beliakov, H. Bustince, D. P. Goswami, U. K. Mukherjee, N. R. Pal (印度科学院院士、工程院院
士、IEEE Fellow、IFSA Fellow、IEEE Transactions on Fuzzy Systems前主编). On averaging operators for Atanassov’s intuitionistic fuzzy sets. Information
R(i ) 0.5 2 ( i vi ) d (1,0), i


Basic operational laws
Let ( , v ), 1 ( , v ) and 2 ( , v ) be three 2 2 1 1 intuitionistic fuzzy numbers, then (1) ( , );
(2) 1 2 (min{1 , 2 }, max{ 1 , 2 });
(3) 1 2 (max{1 , 2 }, min{ 1 ,2 }); (4) 1 2 ( 1 2 1 2 , v1 v2 );
(5) 1 2 (1 2 , v1 v2 v1 v2 );
直觉模糊数
一种新的决策工具
徐泽水
xuzeshui@
解放军理工大学理学院
Support
In a voting problem
Abstention
Objection
K. Atanassov. Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 1986, 20(1): 87-96.
A x, A ( x), A ( x) | x X
Intuitionistic fuzzy numbers
, v
The intuitionistic fuzzy number ( , ) has a physical interpretation, for example, if
Systems, 2007, 15(6): 1179-1187. Cited times:
401.
2008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; ESI高被引论文.
Z. S. Xu*, R.R. Yager (IEEE Life Fellow, IFSA Fellow). Some
1. Intuitionistic fuzzy weighted aggregation operators
f1 (1, 2 ,..., n ) wii 1 (1 i ) wi , i 1 i 1
n n
(vi ) i 1
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
引次数最多的20篇论文之一(摘自Scopus))
f ( x)
1 e 2
( x u )2 2 2
,
x
Z. S. Xu. Intuitionistic preference relations and their application in group decision making. Information Sciences, 2007, 177 (11): 2363-2379. Cited times: 255
(6) (1 (1 ) , v ), 0;
(7) ( ,1 (1 v ) ), 0.
All the results above are intuitionistic fuzzy numbers.
Basic properties
(2) 1 1 2 1 ;
(3) (1 2 ) 1 2 ;
(4) (1 2 ) 1 2 ;
(5) 1 2 (1 2 ) ;
(6) 1 2 1 2 .
Z. S. Xu. Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy
Theorem. Let ( , v ), 1 (1 , v1 ) and 2 (2 , v2 ) be
three intuitionistic fuzzy numbers, and , 1 , 2 0, then
(1) 1 1 2 1 ;
E. Szmidt, J. Kacprzyk (国际模糊系统协会(IFSA)前主 席、IEEE Fellow、IFSA Fellow、波兰科学院院士 ). Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives. in: E. Rakus-Andersson, R. R. Yager, N. Ichalkaranje, L. C. Jain, (Eds.), Recent Advances in Decision Making, Berlin: Springer-Verlag, 2009, pp. 7-19.
Cited times: 3738
Growth trend graph of papers about intuitionistic fuzzy sets indexed in SCI-Expanded, SSCI
Growth trend graph of papers about intuitionistic fuzzy sets indexed by EI Compendex
Sciences, 2011, 181: 1116-1124. Cited times: 66
n 1 n 1 f1 (1 , 2 ,..., n ) h1 wi h1 ( i ) , h2 wi h2 ( vi ) i 1 i 1
geometric aggregation operators based on intuitionistic fuzzy sets. International J6, 35(4): 417-433. Cited times: 393 (2006 年以来该期刊发表论文中引用 率排名第一；ESI高被引论文)
(2007 年以来该期刊发表论文中引用 率排名第七; ESI高被引论文)
x1
x2
...
xn
...
x1 ( 11 , v11 ) ( 12 , v12 ) x 2 ( 21 , v21 ) ( 22 , v22 ) x n ( n 1 , vn 1 ) ( n 2 , vn 2 )
( , ) (0.5,0.3)
which can be interpreted as “the vote for resolution is 5 in favor, 3 against, and 2 abstentions”.
An order relation between intuitionistic fuzzy numbers
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. SpringerVerlag , in Series:《Studies in Fuzziness and Soft Computing》, Heidelberg, New York, 2013.
Definition. Let i ( i , i )(i 1,2) be two intuitionistic fuzzy numbers, s(i ) i i and h(i ) i i (i 1,2) are the scores and the accuracy degree of 1 and 2 respectively, then (1) if s(1 ) s( 2 ), then 1 2 ; (2) if s(1 ) s( 2 ), then (i) if h(1 ) h( 2 ), then 1 2 ; (ii) if h(1 ) h( 2 ), then 1 2 .
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 一; ESI高被引论文)
( 1n , v1n ) ( 2 n , v2 n ) ( nn , vnn )
Z. S. Xu, H. C. Liao. Intuitionistic Fuzzy Analytic Hierarchy Process. IEEE Transactions on Fuzzy Systems, 2013, in press.