Complex fuzzy sets with applications in decision-making

Document Type : Research Paper


1 Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Pakistan

2 Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan



In this paper, we discussed the conjunctive
normal form, disjunctive normal form, duality principle, equality of two sets
and a semi Boolean algebra of complex fuzzy sets (CFSs). We established some
basic results and particular examples with respect to standard complex fuzzy
intersection, standard complex fuzzy union and standard complex fuzzy
complement functions with the same function for determining the phase term. We
used CFSs in signals and systems because the behavior of CFSs is similar to
Fourier transforms in certain cases. Moreover, we developed a new algorithm
using a Cartesian product of complex fuzzy sets for applications in signals
and systems by which we identified a reference signal out of the large number
of signals detected by a digital receiver.