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

Abstract

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. 

DOI:10.5281/zenodo.11123590