Possibility neutrosophic hypersoft set is the generalisation of possibility neutrosophic soft set, and it is the blend of possibility neutrosophic set and hypersoft set. It tackles the insufficiencies of possibility intuitionistic fuzzy set and soft set for the entitlement of degree of indeterminacy and multi-argument approximate function, respectively. This kind of function maps the sub-parametric tuples to the power set of universe. It emphasises the partitioning of each attribute into its attribute-valued set that is missing in the existing fuzzy soft set-like structures. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. This makes the decision-making process more flexible and reliable. This research aims to initiate a novel structure that hybridises the possibility neutrosophic set with the hypersoft set for dealing with uncertainties efficiently. Therefore, the possibility neutrosophic hypersoft set is developed by employing theoretic, axiomatic, graphical and algorithmic approaches. After conceptual characterisation of its essential elementary notions, decision-support systems are presented based on AND and OR operations with the proposal of algorithms to assist the decision-making process. Similarity measures between possibility neutrosophic hypersoft sets are elaborated with the support of daily life applications. The comparison of the proposed work is discussed with the existing relevant models under certain evaluating features.

In this research work, an approach to determine the critical path of activity network with normalized heptagonal fuzzy data is proposed. In the proposed model, we attempt to develop a method for solving litigation problems by experts when they share the same information but differ in their opinions. The concepts for a critical path method (CPM) optimization with two kinds of data are as follows: those are to be optimistic and those considered being pessimistic. A numerical example is given for the illustration of the proposed approach and gain more insights. Based on the findings of the proposed work, we observe that the floating times with optimistic data are always smaller than or equal to the corresponding floating times for the pessimistic data.