Algebraic and Graphical Interpretation of Complex Fuzzy Annulus (an Extension of Complex Fuzzy Sets)

  • Ganeshsree SelvachandranEmail author
  • Omar Awad Mashaan
  • Abdul Ghafur Ahmad
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 652)


Complex fuzzy sets, which include complex-valued grades of memberships, are extensions of standard fuzzy sets that better represent time-periodic problem parameters. However, the membership functions of complex fuzzy sets are difficult to enumerate, as they are subject to personal preferences and bias. To overcome this problem, we generalize complex fuzzy sets to the complex fuzzy annulus, whose image is a sub-disk lying in the unit circle in the complex plane. The set theoretic operations of this concept are introduced and their algebraic properties are verified. The proposed model is then applied to a real-life problem, namely, the influencers of the Malaysian economy and the time lag between the occurrences of these influencers and their first manifestations in the economy.


Complex fuzzy set Fuzzy annulus Interval-valued fuzzy set 



The author would like to gratefully acknowledge the financial assistance received from the Ministry of Education, Malaysia and UCSI University, Malaysia under Grant no. FRGS/1/2014/ST06/UCSI/03/1.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  • Ganeshsree Selvachandran
    • 1
    Email author
  • Omar Awad Mashaan
    • 2
  • Abdul Ghafur Ahmad
    • 2
  1. 1.Department of Actuarial Science and Applied Statistics, Faculty of Business and Information ScienceUCSI UniversityKuala LumpurMalaysia
  2. 2.School of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaUKM BangiMalaysia

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