International Journal of Knowledge and Systems Science, 2(1), 43-49, January-March 2011 43
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Keywords: Intuitionistic Fuzzy Number, Multi-Criteria Decision Making, Possibility Degree Method,
Ranking, Score Function
1. INTRODUCTION
Since Zadeh (1965) introduced fuzzy sets theory,
some generalized forms have been proposed
to deal with imprecision and uncertainty.
Atanassov (1986) introduced the concept of an
intuitionistic fuzzy set (IFS) characterized by
a membership function and a non-membership
function. Gau and Buehrer (1993) introduced
the concept of vague sets. Bustince and Burillo
(1996) showed that vague sets are IFSs. IFSs
have been found to be more useful to deal with
vagueness and uncertainty problems than fuzzy
sets, and have been applied to many different
fields.
For the fuzzy multiple criteria decision
making (MCDM) problems, the degree of
A New Method for Ranking
Intuitionistic Fuzzy Numbers
Cui-Ping Wei, Qufu Normal University, China
Xijin Tang, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China
ABSTRACT
In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors frst defne a possibil-
ity degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score
function, the possibility degree formula provides additional information for the comparison of two intuitionistic
fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank
n intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making
problems.
satisfiability and non-satisfiability of each al-
ternative with respect to a set of criteria is often
represented by an intuitionistic fuzzy number
(IFN), which is an element of an IFS (Liu, 2003;
Xu, 2007). The comparison between alternatives
is equivalent to the comparison of IFNs. Chen
and Tan (1994) provided a score function to
compare IFNs. Hong and Choi (2000) pointed
out the defects and proposed an improved tech-
nique based on the score function and accuracy
function. Later, Li (2001) and Liu (2003) gave
a series of improved score functions. The above
functions are called evaluation functions. By
using these evaluation functions, we can obtain
certain rank of the IFNs. Since IFNs are of
fuzziness, the comparison between them may
also be expected to reflect the uncertainty of
ranking objectively.
In this paper, by extending the possibility
degree formula of interval values (Wang, Yang, DOI: 10.4018/jkss.2011010104