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ISBN 978-952-5726-09-1 (Print)
Proceedings of the Second International Symposium on Networking and Network Security (ISNNS ’10)
Jinggangshan, P. R. China, 2-4, April. 2010, pp. 069-072
Research on Weights Assigning Based on
Element Consistency Level in Judgment Matrice
Xixiang Zhang 1 , Jianxun Liu 2 , Liping Chen 2 , and GuangxueYue 1,3
1
Mathematics and Information Engineering School of Jiaxing University , Jiaxing, China
3 Guangdong University of Business Studies ,GuangZhou, China
Email: Zhangmiddle@126.com
2
Library of Jiaxing University , Jiaxing, China
Abstract—It is easy for an expert to express his/her
preferences using fuzzy linguistic term such as ‘good’, ‘very
good’ in group decision making because of uncertainty
existing. The linguistic 2-tuple representation model was
selected to represent fuzzy linguistic term. To obtain the
objective decision power in a linguistic 2-tuple judgment
matrix given by an expert, the paper put forward a new
approach to calculate weight based on element consistency
level. The proposed method thought of calculating the
different weight to aggregate different element according to
the element consistency level. And an illustrated example
was used to demonstrate the proposed method.
Index Terms—weight, linguistic 2-tuple, group decision
making, element consistency level
I. INTRODUCTION
With the development of science and technology, and
with the explosion of knowledge and information, the
decision-making problem becomes more and more
complicated, a decision-maker can not resolve it because
of his/her limited experience and wisdom[1,2]. Thus,
decision power assigning became a hot topic. Lots of
scholars were attracted to do research in this field.
Bidily put forward a method that experts were asked to
evaluate other experts and got the weight of each expert.
Yang analyzed the method proposed by Bodily and put
forward a new method to designate the experts’ weight
[4]. Ye and Hong studied the method to classify the
experts and assigning the weight to experts by building
interval-valued attribute value and clustering them[5]. Yu
and Fan proposed a new maximal tree clustering analysis
method based on the traditional ideas of maximal tree
clustering method and the dynamic semantic
representation[6]. Fedrizzi (1992) developed a GDSS
based on clustering to classify experts and gave the
experts different weights according its clustering result[7].
Zhou and Wei (2006) judge the consistency level and
consensus based on the distance of matrices given by
experts and proposed a new method for deriving posterior
weight based on reliability of expert's fuzzy judgment
matrix[8]. Chen and Fan(2005) made statistical analysis
Herrera-Viedma, Chiclana, Herrera and Alonso (2007)
studied the method to designate experts’ weights based
on additive consistency in incomplete group decision
making environment[11].
The preceding decision power assigning methods were
objective method, which obtained from the information
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given by the decision makers. These methods to assign
experts’ weight gave an expert a fixed weigh to aggregate
all the element into group decision making. There exists
different element consistency level in a judgment matrix
given by an expert, it will be more reasonable to
calculating the different decision power for aggregating
different element. Thus, the paper proposed a new weight
assingning method based on linguistic 2-tuple judgment
matrix.
II. SOME PRELIMINARIES
The 2-tuple linguistic presentation model can avoid
information loss in processing and computing linguistic
information, and maintain accuracy and consistency of
linguistic information [11]. Gong and Liu proposed fuzzy
information fusion method based on linguistic 2-tuple
representation model, which can transfer other fuzzy
information expressed by fuzzy interval-value or fuzzy
triangular number into linguistic 2-tuple representation
model [12]. Through the transfer model, fuzzy
information expressed by other representation model and
linguistic 2-tuple can be fused together. Therefore, study
on weight designating method based on linguistic 2-tuple
representation model is practical and meaningful.
Suppose there are n alternatives denoted as
A={A 1 ,A 2 , … ,A n } in group decision making and m
experts to make decision which is denoted as
E={E 1 ,E 2 ,…,E m }. The experts use fuzzy linguistic term to
express their preferences on alternatives. And the fuzzy
linguistic term set is composed of nine terms, which is
denoted as S={s 0 =absolutely worse , s 1 =extremely
worse , s 2 =much worse , s 3 =worse , s 4 =no
difference,s 5 =better, s 6 =much better, s 7 =extremely
better,s 8 =absolutely better}. And the linguistic terms
were expressed by linguistic 2-tuple representation model.
The literature about linguistic 2-tuple representation
model was demonstrated as follows.
Suppose S={s 0 , s 1 , …,s g } be a set of labels assessed
in a linguistic term set with odd elements, which has the
following properties: 1ordered: when the index i≥j,
there must exist s i ≥s j ; 2a negation operator: Neg(s i )=
s g-i ; 3 there exists a min and max operator: si ≥ s j means
max(s i , sj )=si and min(s i , s j )=s j [13].
Let β be the result of an aggregation of the indexes of
a set S={s0, s1, …,sg}, for example, the result of a