Some properties on possibility interval-valued intuitionistic fuzzy soft sets

This paper's main goal is to present and examine some fundamental characteristics of possibility interval-valued intuitionistic fuzzy soft sets (PIVIFSSs). Initially, the cardinality measure is concentrated on PIVIFSSs and its performance under the union and intersection are analyzed. Furthermore, the operators @, $, and * are formally defined and applied to PIVIFSSs. Their validity is established through rigorous mathematical proofs verifying the commutative, associative, and distributive properties. Additionally, the definitions and analyses of the necessary and sufficient operators are presented to justify their adequacy and relevance. Finally the cardinality measure is applied to a group decision making problem and obtained an optimal solution.