Similarity measure and sine exponential measure of possibility interval-valued neutrosophic hypersoft sets and their applications

The Hypersoft set (HSS) has been created as an extension of a soft set (SS) in order to address limitations for the thought of disjoint attribute-valued sets corresponding to distinct attributes. The HSSs melted with several fuzziness structures present in literature to handle real-world scenarios with complexity and uncertainty. One such extension is the interval-valued neutrosophic hypersoft set (iv-NHSS), which focuses on the partitioning of each attribute into its attribute-valued set with these attribute-valued sets, three iv-NHSmemberships degree line closed interval [0,1]. However, the iv-NHSS model is short of assessing the vague nature of parameters and sub-parameters that cause some doubt in DM opinions. This work focuses primarily on show the impact the degree of fuzzy possibility on efficient work of iv-NHSS when we introduce novel concepts of possibility interval valued neutrosophic hyper soft set (in short piv-NHSS) by giving all iv-NHSs-values, the fuzzy possibility degree increases the efficiency for the multi-argument approximately. Therefore, the axioms of set theory such as piv-NHS-subset, piv-NHS-null set, piv-NHS-absolute set and piv-NHSS-complement defined on this concept, as well as we investigated the union, intersection, AND, OR of two piv-NHSSs, and relevant laws, with the help of several numerical examples and piv-NHS-matrix representations. Moreover, we discovered both similarities measure and sine exponential measure between two piv-NHSSs and these measures are successfully applied in decision-making to judge choose the best tourist place. In the end, a conclusion of this work is presented with some suggestions for future studies of this work.