A New Method for Ranking Intuitionistic Fuzzy Numbers

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 satisfiability and non-satisfiability of each alternative 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 technique 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, & Xu, 2005; Xu & Da, 2003) to IFNs, we propose a possibility degree method for ranking IFNs. And the ranking result by the proposed method may reflect the uncertainty of IFSs, and then provide more information to decision makers.