New operations on cubic intuitionistic fuzzy sets under P–order

Cubic intuitionistic fuzzy sets have the efficiency to handle hybrid information, which combines interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets. The aim is to define operators on cubic intuitionistic fuzzy sets that are capable of more effectively handling uncertain or imprecise information contained in image data. In this piece of work, few operators on the cubic intuitionistic fuzzy sets under P – order, such as arithmetic mean (@), geometric mean ($), multiplication operator (*), ‘#’ and necessity (□) and possibility (◇) operations on the cubic intuitionistic fuzzy sets under P – order, are defined. The concept of some more modal operators like Dα ́(A), F(α ́,β ́)(A), G(α ́,β ́)(A), H(α ́,β ́)(A), H^*(α ́,β ́)(A), J(α ́,β ́)(A) and J^*(α ́,β ́)(A) over cubic intuitionistic fuzzy sets under P – order are introduced. Additionally, the behaviour of cubic intuitionistic fuzzy modal operators is also carefully examined. Moreover, various properties related to operations on cubic intuitionistic fuzzy sets under P-order have been thoroughly studied and demonstrated.