Approach to Multi-Criteria Decision-Making in a Neutrosophic Picture Hyper-Soft Set Environment using Generalized Neutrosophic TOPSIS.

Given the complexity of today's world, we might need to work with numbers requiring multi-attribute functions, such as those having positive, neutral, and negative membership and those having truth, indeterminacy, and falsity membership. Adding these numbers together to get a single real number is the most important factor. In situations like this, decision-makers have more difficult choices and are unable to apply the single attribute function of the soft set theory. To address this constraint, the hyper-soft set theory with multi-attribute functions is introduced. We combine the notion of neutrosophic hypersoft set with picture fuzzy hypersoft set to form a single theory of neutrosophic picture hypersoft set in this study. We introduce the notions of correlation coefficient and weighted correlation coefficient and demonstrate its fundamental properties for neutrosophic picture hypersoft set. Then, we introduce the notions of a weighted average operator and a weighted geometric operator for neutrosophic picture hypersoft set by using the various aggregation operators with a suitable example. Making decisions based on several factors and choosing the best option is multi-criteria decision-making or MCDM. When ranking and choosing options based on a distance metric, one essential and useful strategy is the Technique of order preference by similarity to an ideal solution (TOPSIS). We demonstrate the accuracy of the fuzzy TOPSIS methodology by extending it to neutrosophic fuzzy TOPSIS and using neutrosophic picture hypersoft set theory to describe the MCDM problem in this study. We provide a generalized neutrosophic TOPSIS approach to demonstrate correlation coefficients and the effectiveness of this approach with an appropriate example. Finally, we offer a comparison to prior studies to demonstrate the viability of the proposed approach. [ABSTRACT FROM AUTHOR]