直觉模糊数-一种新的决策工具 (2013.10.17) 3

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) ( , );
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 .
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
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
(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 )
(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 );
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
geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 2006, 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)
( , ) (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.
(6) (1 (1 ) , v ), 0;
(7) ( ,1 (1 v ) ), 0.
All the results above are intuitionistic fuzzy numbers.
Basic properties
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.
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
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
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
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.
A x, A ( x), A ( x) | x X
Intuitionistic fuzzy numbers
, v
Fra Baidu bibliotek
The intuitionistic fuzzy number ( , ) has a physical interpretation, for example, if
( 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.
直觉模糊数
一种新的决策工具
徐泽水
xuzeshui@263.net
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.
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, 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)
(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 ;
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