Cardinality and relative cardinality on cubic intuitionistic fuzzy sets

The cardinality of a set is a measurement of its size or power in classical set theory. One must distinguish between fuzziness and power measurements while dealing with fuzzy situations. Numerous attempts have been made to determine the cardinality of an intuitionistic fuzzy sets and an interval-valued intuitionistic fuzzy sets. For cubic intuitionistic fuzzy sets, sigma count \(\left(\sum count\right)\) $\left(\sum ,c,o,u,n,t\right)$ and relative sigma count \(\left(Rel\sum count\right)\) $\left(R,e,l,\sum ,c,o,u,n,t\right)$ are defined and additionally, certain significant findings are supported by the suggested definition. Finally, we have created a decision-making and multi-criteria decision-making process inspired by the \(Rel\sum count\) $Rel\sum count$ in the cubic intuitionistic fuzzy environment, and the suggested methodology is exemplified with a statistical analysis.