Information Technology Reference
In-Depth Information
Chapter 1
Intuitionistic Fuzzy Aggregation
Techniques
Intuitionistic fuzzy set (IFS), introduced by Atanassov (1983, 1986), is the gener-
alization of Zadeh's fuzzy set (Zadeh 1965). IFS is characterized by a membership
function and a non-membership function, and thus can depict the fuzzy character of
data more comprehensively than Zadeh's fuzzy set which is only characterized by a
membership function. For example, if a girl wants to find a boyfriend, and evaluates
the boy from five aspects, she may feel satisfied with three aspects, unsatisfied with
one aspect and uncertainwith one aspect of the boy. In such a case, fuzzy sets can only
reflect the satisfied aspect, which loses some uncertain information, while IFSs can
describe all the satisfied, unsatisfied and uncertain information. In a variety of voting
events, in addition to the support and the objection, there is usually the abstention
which indicates the hesitation or the indeterminacy of the voter to the object. IFSs are
more suitable to deal with these cases than fuzzy sets. The core of an IFS is intuition-
istic fuzzy values (IFVs) (Xu and Yager 2006; Xu 2007), each of which is composed
of a membership degree, a non-membership degree, and a hesitancy degree. IFVs
are a powerful tool to depict uncertain or fuzzy information. In many fields, such as
decision making, cluster analysis, and information retrieval, etc., information aggre-
gation is an essential process. Therefore, how to aggregate IFVs is an interesting and
important research topic, which has received great attention from researchers and a
lot of intuitionistic fuzzy aggregation techniques have been developed (Xu and Yager
2006, 2009, 2011; Xu 2007, 2010; Xu and Chen 2007b; Boran et al. 2009; Tan and
Chen 2010; Xu and Cai 2010a, b; Zhao et al. 2010; Beliakov et al. 2011; Xu and
Xia 2011). Xu and Cai (2010b, 2012) provided a survey of these intuitionistic fuzzy
aggregation techniques, and their applications in various fields. Recently, Xia and Xu
(2010) developed various generalized intuitionistic fuzzy point aggregation opera-
tors, which can control the certainty degrees of the aggregated arguments with some
parameters. Xu (2011) gave a series of intuitionistic fuzzy power aggregation opera-
tors, whose weighting vectors depend upon the input arguments and allow the values
being aggregated to support and reinforce each other. Xia et al. (2012a, b) proposed
a geometric Bonferroni mean, based on which they defined the intuitionistic fuzzy
geometric Bonferroni means and their generalized versions. Based on Archimedean
 
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