Abstract
This paper introduces the theory of possibility \(q\) -rung interval-valued fuzzy soft (P \(q\) -rung IVFS) sets and demonstrates their application to real-life decision-making problems. P \(q\) -rung IVFS sets generalize Pythagorean fuzzy soft sets and offer a novel approach to handling uncertainty. We propose a new similarity measure between two P \(q\) -rung IVFS sets, supported by examples. As a practical application, we explore the process of purchasing a computer, highlighting the decision-making stages involved. Using the soft set method, we present an algorithm for solving decision-making problems under uncertainty. Finally, we demonstrate the effectiveness of these methods with an illustrative example.
