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

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.