International Journal of Fuzzy Systems

, Volume 19, Issue 5, pp 1279–1289 | Cite as

Analyzing the Ranking Method for Fuzzy Numbers in Fuzzy Decision Making Based on the Magnitude Concepts

  • Vincent F. Yu
  • Luu Huu Van
  • Luu Quoc Dat
  • Ha Thi Xuan Chi
  • Shuo-Yan Chou
  • Truong Thi Thuy Duong
Article

Abstract

Ranking fuzzy numbers is an important component in the decision-making process with the last few decades having seen a large number of ranking methods. Ezzati et al. (Expert Syst Appl 39:690–695, 2012) proposed a revised approach for ranking symmetric fuzzy numbers based on the magnitude concepts to overcome the shortcoming of Abbasbandy and Hajjari’s method. Despite its merits, some shortcomings associated with Ezzati et al.’s approach include: (1) it cannot consistently rank the fuzzy numbers and their images; (2) it cannot effectively rank symmetric fuzzy numbers; and (3) it cannot rank non-normal fuzzy numbers. This paper thus proposes a revised method to rank generalized and/or symmetric fuzzy numbers in parametric forms that can surmount these issues. In the proposed ranking method, a novel magnitude of fuzzy numbers is proposed. To differentiate the symmetric fuzzy numbers, the proposed ranking method takes into account the decision maker’s optimistic attitude of fuzzy numbers. We employ several comparative examples and an application to demonstrate the usages and advantages of the proposed ranking method. The results conclude that the proposed ranking method effectively resolves the issues with Ezzati et al.’s ranking method. Moreover, the proposed ranking method can differentiate different types of fuzzy numbers.

Keywords

Generalized fuzzy numbers Magnitude concept Fuzzy ranking method Fuzzy decision making 

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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Vincent F. Yu
    • 1
  • Luu Huu Van
    • 1
  • Luu Quoc Dat
    • 2
  • Ha Thi Xuan Chi
    • 3
  • Shuo-Yan Chou
    • 1
  • Truong Thi Thuy Duong
    • 4
  1. 1.Department of Industrial ManagementNational Taiwan University of Science and TechnologyTaipeiTaiwan
  2. 2.University of Economics and BusinessVietnam National UniversityHanoiVietnam
  3. 3.International UniversityVietnam National UniversityHo Chi MinhVietnam
  4. 4.Banking AcademyHanoiVietnam

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