Complex fuzzy sets with applications in decision-making

In this paper, we discussed the conjunctivenormal form, disjunctive normal form, duality principle, equality of two setsand a semi Boolean algebra of complex fuzzy sets (CFSs). We established somebasic results and particular examples with respect to standard complex fuzzyintersection, standard complex fuzzy union and standard complex fuzzycomplement functions with the same function for determining the phase term. Weused CFSs in signals and systems because the behavior of CFSs is similar toFourier transforms in certain cases. Moreover, we developed a new algorithmusing a Cartesian product of complex fuzzy sets for applications in signalsand systems by which we identified a reference signal out of the large numberof signals detected by a digital receiver.

Keywords:

Complex fuzzy sets , duality principle , semi-Boolean algebra , signals and systems