A picture fuzzy set is one of the generalizations of Atanassove's (IFSs) fuzzy set. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called cubic root fuzzy sets (briefly, $\sqrt[3]{\cdot}$-Fuzzy sets) ...
A picture fuzzy set is one of the generalizations of Atanassove's (IFSs) fuzzy set. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called cubic root fuzzy sets (briefly, $\sqrt[3]{\cdot}$-Fuzzy sets) and Fermatean fuzzy sets to contrast $(3,3,\sqrt[3]{\cdot})$-picture sets. We introduce the notion of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals of $BCC$-algebras. After then, we study the homomorphic image and inverse image of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals under homomorphism of $BCC$-algebras. Moreover, the Cartesian product of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals of $BCC$-algebras is given. Finally, we introduce the concept of correlation for $(3,3,\sqrt[3]{\cdot})$-picture fuzzy sets, which is a new extension of the correlation of Atanassove's IFSs and investigated several properties.