Interval-valued intuitionistic quadri-partitioned neutrosophic sets in psychological research with examples and theoretical insights

Abstract

This manuscript presents a comprehensive study of interval-valued intuitionistic quadri-partitioned neutrosophic sets (IVIQPNSs) and their combination with soft sets (IVIQPNSSs), focusing on the relationships between the membership grades of truth, falsity, contradiction, and indeterminacy. Specifically, the sum of the truth and falsity membership grades is constrained such that it does not exceed unity, while the sum of all four membership grades (truth, indeterminacy, contradiction, and falsity) is bounded by three. The manuscript also explores operators such as necessity and possibility, establishing several key properties. Given that many psychiatric disorders exhibit ambivalent behavior, representing membership grades with IVIQPNSs is essential. This work give effective approach to diagnose psychiatric disorder with robust flexible framework in fuzzy environment.