Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas

Vincent F. Yu, Ha Thi Xuan Chi, Luu Quoc Dat, Phan Nguyen Ky Phuc, Chien wen Shen

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


Although a number of recent studies have proposed ranking fuzzy numbers based on the deviation degree, most of them have exhibited several shortcomings associated with non-discriminative and counter-intuitive problems. In fact, none of the existing deviation degree methods has guaranteed consistencies between the ranking of fuzzy numbers and that of their images under all situations. They have also ignored decision maker's attitude toward risk, which significantly influences final ranking result. To overcome the above-mentioned drawbacks, this study proposes a new approach for ranking fuzzy numbers that ensures full consideration for all information of fuzzy numbers. Accordingly, an overall ranking index is obtained by the integration of the information from the left and the right (LR) areas between fuzzy numbers, the centroid points of fuzzy numbers and the decision maker's attitude toward risk. This new method is efficient for evaluating generalized fuzzy numbers and distinguishing symmetric fuzzy numbers. It also overcomes the shortcomings of the existing approaches based on deviation degree. Several numerical examples are provided to illustrate the superiority of the proposed approach. Lastly, a new fuzzy MCDM approach for generalized fuzzy numbers is proposed based on the proposed ranking approach and the concept of generalized fuzzy numbers. The proposed fuzzy MCDM approach does not require the normalization process and thus avoids the loss of information results from transforming generalized fuzzy numbers to normal form.

Original languageEnglish
Pages (from-to)8106-8117
Number of pages12
JournalApplied Mathematical Modelling
Issue number16-17
StatePublished - 1 Sep 2013


  • Generalized fuzzy numbers
  • MCDM
  • Ranking


Dive into the research topics of 'Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas'. Together they form a unique fingerprint.

Cite this