Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem

Molodtsov introduced a soft set (SS) to model uncertainty parametrically, and Chaterjee et al. proposed the notion of quadripartitioned neutrosophic set (QNS) by dividing indeterminacy into two independent components, namely contradiction (C) and unknown (U). Afterwards, by combining the SS and QNS, a new concept known as quadripartitioned neutrosophic soft set (QNSS) is introduced. In relation to the concept of QNSS, another concept called interval-valued intuitionistic quadripartitioned neutrosophic soft set (in short IVIQNSS) is established to handle more complex indeterminate information parametrically with the restricted conditions. This paper aims to further generalize the existing soft models by introducing an IVIQNSS to explore another kind of imprecise knowledge. The IVIQNSS model can be viewed as a more flexible and powerful framework to encounter indeterminacy parametrically with T,F,C, and U as dependent interval quadripartitioned neutrosophic components where T,F,C,U⊆[0,1] such that sup⁡T+sup⁡F≤1, and sup⁡C+sup⁡U≤1. So, by using the IVIQNSS framework we are capable to address the indeterminate, inconsistent, and incomplete information more accurately. Different operations such as complement, AND, OR, union, intersection, etc. are defined on IVIQNSSs. Furthermore, an algorithm is constructed to solve decision-making (DM) problems based on IVIQNSS. Finally, an illustrative example is executed to validate the proposed study.